This library gives complete access to the following groups of order 19683:
The rank 1 group
All rank 2 groups
All rank 3 groups with p-class not equal to 3
All rank 4 groups with p-class at least 4
All rank 5 groups with p-class at least 4
All rank 6 groups with p-class at least 4
All rank 7 groups with p-class at least 4
All rank 8 groups with p-class at least 3
The rank 9 group
This library gives partial information on the remaining groups of order 19683:
Rank 3 groups with p-class 3
Rank 4 groups with p-class 2
Rank 4 groups with p-class 3
Rank 5 groups with p-class 2
Rank 5 groups with p-class 3
Rank 6 groups with p-class 2
Rank 6 groups with p-class 3
Rank 7 groups with p-class 2
Rank 7 groups with p-class 3
For the groups that are not explicity available the following information is available:
Parent Group ID
Parent Group Order
p-class
Rank
Age
The groups are sorted first by their rank, then by p-class, then by parent group ids and finally by age. The data contained in this library was used in the 2022 enumeration of the groups of order 19683 [Bur22]. The computational tools used were developed in the 2021 enumeration of the groups of order 1024 [Bur21]. The available groups were generated using the p-group generation algorithm [O'B90] as implemented in the ANUPQ package [GNOH19]. The information on the remaining groups was calculated using the cohomological methods for enumerating p-groups as introduced in [EO99].
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