Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#72228092 |
| Fitting | C2×#3573 ⋊ C3⋊D3 |
3297 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 3297 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 98 points:
(3,16,5,36,10,4,21,11)(6,39,89,68,24,81,50,70,63,40,52,73,25,42,55,32,27,45,17,67,30,12,49,97)(7,15,19,69,9,14,51,71,8,41,53,72,26,43,54,33,28,44,18,35,29,13,20,34)(22,75,84,94,57,76,86,95,58,78,87,96,60,79,88,65,61,80,47,91,62,37,83,92)(23,46,48,74,31,38,56,66)(59,82,85,98,64,77,90,93);(1,2)(3,6,22)(4,12,37)(5,17,47)(7,27,59)(8,30,61)(9,31,58)(10,25,60)(11,32,65)(13,42,77)(14,45,79)(15,46,76)(16,40,78)(18,52,85)(19,55,87)(20,56,84)(21,50,86)(23,62,28)(24,64,26)(29,63,57)(33,70,93)(34,73,95)(35,74,92)(36,68,94)(38,80,43)(39,82,41)(44,81,75)(48,88,53)(49,90,51)(54,89,83)(66,96,71)(67,98,69)(72,97,91);(6,22)(7,26)(8,28)(9,29)(12,37)(13,41)(14,43)(15,44)(17,47)(18,51)(19,53)(20,54)(23,61)(24,59)(25,60)(27,64)(30,62)(31,57)(32,65)(33,69)(34,71)(35,72)(38,79)(39,77)(40,78)(42,82)(45,80)(46,75)(48,87)(49,85)(50,86)(52,90)(55,88)(56,83)(58,63)(66,95)(67,93)(68,94)(70,98)(73,96)(74,91)(76,81)(84,89)(92,97)160 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,16,5,36,10,4,21,11)(6,39,89,68,24,81,50,70,63,40,52,73,25,42,55,32,27,45,17,67,30,12,49,97)(7,15,19,69,9,14,51,71,8,41,53,72,26,43,54,33,28,44,18,35,29,13,20,34)(22,75,84,94,57,76,86,95,58,78,87,96,60,79,88,65,61,80,47,91,62,37,83,92)(23,46,48,74,31,38,56,66)(59,82,85,98,64,77,90,93), (1,2)(3,6,22)(4,12,37)(5,17,47)(7,27,59)(8,30,61)(9,31,58)(10,25,60)(11,32,65)(13,42,77)(14,45,79)(15,46,76)(16,40,78)(18,52,85)(19,55,87)(20,56,84)(21,50,86)(23,62,28)(24,64,26)(29,63,57)(33,70,93)(34,73,95)(35,74,92)(36,68,94)(38,80,43)(39,82,41)(44,81,75)(48,88,53)(49,90,51)(54,89,83)(66,96,71)(67,98,69)(72,97,91), (6,22)(7,26)(8,28)(9,29)(12,37)(13,41)(14,43)(15,44)(17,47)(18,51)(19,53)(20,54)(23,61)(24,59)(25,60)(27,64)(30,62)(31,57)(32,65)(33,69)(34,71)(35,72)(38,79)(39,77)(40,78)(42,82)(45,80)(46,75)(48,87)(49,85)(50,86)(52,90)(55,88)(56,83)(58,63)(66,95)(67,93)(68,94)(70,98)(73,96)(74,91)(76,81)(84,89)(92,97));