There seems to be a different opinion in the shafi'i madhab (and maliki madhab) that allows for obligatory hajj trip (that is, the first hajj) without mahram as long as you go with a group of trustworthy women. However, Hanbali and Hanafi madhab is very strict in not allowing traveling without mahram for more than 3 days even for hajj.
Imam Nawawi, the great Shafi’i jurist (may Allah have mercy on him) states in his monumental commentary of Sahih Muslim:
“There is a consensus (ijma’) of the Ummah that it is obligatory upon a woman to perform Hajj if she is able to do so, due to the general nature of the verse: “Pilgrimage to the house of Allah is a duty men owe to Allah for those who can afford the journey” (Ali Imran, 97), and because of the Hadith “Islam is based on five things”. However, scholars differ as to whether a Mahram is a pre-requisite for a woman to perform the Hajj. Abu Hanifa (Allah have mercy on him) considers it a condition for the Hajj to be obligatory unless the distance between her and Makkah is less than three Marahil. His opinion is also endorsed by a group of Hadith scholars, people of ra’i, Hasan al-Basri and Nakha’i (Allah have mercy on them all). However, Ata, Sa’id ibn Jubayr, Ibn Sirin, Malik, al-Awzai’i, Shafi’i (Allah have mercy on them all) say that a Mahram is not a pre-requisite in order for her travelling to Hajj; rather the condition is safety in the journey. Some of our (Shafi’i) scholars have said: “Safety will be acquired with the husband, Mahram or a group of trustworthy women, and Hajj is not obligatory if one of these three is not found. Therefore, if there was only one trustworthy woman, Hajj would not be obligatory, but to perform Hajj will be permissible. This is the correct opinion……
Our (Shafi’i) scholars differed as to the ruling of her travelling for optional Hajj, visiting family and friends, for business or other such journeys that are not obligatory. Some said: “It will be permissible for her travel for these causes with a group of trustworthy women just as this is permissible for the obligatory Hajj. However, the majority of the scholars (jumhur) state that it is impermissible for her to travel unless accompanied by her husband or Mahram, and this is the correct opinion due to the authentic and established narrations. Qadhi Iyad (a major Maliki scholar, m) said: “All the scholars have agreed on the fact that a woman can not travel besides Hajj and Umrah except in the company of her Mahram, with the exception of migrating from Dar al-Harb, for the reason that it is unlawful (haram) for her to remain in the lands of the Kuffar”. (Nawawi, al-Minhaj sharh Muslim ibn al-Hajjaj, P. 1015, Dar ibn Hazm, Beirut).
The above excerpt of Imam Nawawi (may Allah have mercy on him) indicates that the dispensation given for a woman to travel in a group of upright and trustworthy women or with one upright woman is only in the journey of Hajj. The great Maliki scholar, Qadhi Iyad (from whom Imam Nawawi quoted) relates the consensus of all the scholars.
Imam Nawawi (may Allah have mercy on him) confirms this in his al-Majmu’ where he states:
“The second opinion (in the Shafi’i school) is that a woman must not travel for other than Hajj without a Mahram, and this is the correct opinion and clearly related from Imam Shafi’i himself in his al-Umm. The reason is that to travel for other than Hajj is not obligatory”. Thereafter he quotes all the narrations that have been narrated from the Messenger of Allah (Allah bless him & give him peace) in this regard. (See: Kitab al-Majmu’ Sharh al-Muhazzab, 7/460).
The Maliki Madhab is also quite clear on this. We have already cited the opinion of Qadhi Iyad in Imam Nawawi’s commentary. Also, one of the major authorities in the Maliki school, Imam Dasouqi (may Allah have mercy on him) sates:
“If the journey is obligatory (like Hajj, m), it will be permissible for her to travel in the company of a Mahram, husband or a group of trustworthy and upright people. If the journey is recommended (mandub, and not obligatory), then it will be permitted for her to travel with only her husband or a Mahram and not in a group”. (Hashiya al-Dasouqi ala Sharh al-Kabir, 2/14).
Example: here in Indonesia majority follow shafi'i, and so do me and my family.
My father died at quite young age before he was able to go hajj, so for her first hajj, my mother went to hajj with her sister and her sister-in-law.