Finite Group DatabasebetaFinite Group Databasebeta| order | 5760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
150 conjugacy classes of subgroups; only the 10 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 10 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 80 points:
(1,8,39,73,68,55,65,48,2,14,56,70,72,37,78,30)(3,21,49,11,7,34,75,61,9,43,31,5,13,52,76,62)(4,26,69,35,67,44,40,29,10,45,80,53,64,23,18,47)(6,24,20,32,74,57,28,63,12,22,42,50,71,59,46,77)(15,58,25,33,66,54,17,19,16,60,38,51,79,36,27,41);(1,14,57,64)(2,8,59,67)(3,32,23,49)(4,46,77,48)(5,80,7,25)(6,56,12,39)(9,50,44,31)(10,28,63,30)(11,69,13,38)(15,18,58,34)(16,40,60,52)(17,53,65,68)(19,54,37,26)(20,43,29,74)(21,47,71,42)(27,35,78,72)(33,76,51,75)(36,55,45,41)35 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(2,𝔽9) |
| maximal normal subgroup of | ΓL(2,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,8,39,73,68,55,65,48,2,14,56,70,72,37,78,30)(3,21,49,11,7,34,75,61,9,43,31,5,13,52,76,62)(4,26,69,35,67,44,40,29,10,45,80,53,64,23,18,47)(6,24,20,32,74,57,28,63,12,22,42,50,71,59,46,77)(15,58,25,33,66,54,17,19,16,60,38,51,79,36,27,41), (1,14,57,64)(2,8,59,67)(3,32,23,49)(4,46,77,48)(5,80,7,25)(6,56,12,39)(9,50,44,31)(10,28,63,30)(11,69,13,38)(15,18,58,34)(16,40,60,52)(17,53,65,68)(19,54,37,26)(20,43,29,74)(21,47,71,42)(27,35,78,72)(33,76,51,75)(36,55,45,41));