Finite Group DatabasebetaFinite Group Databasebeta| order | 15360 |
| isoclinism | isoclinic class of #72209698 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22×C4 | #11757162 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C22×#585 | A5 |
| socle | C23 | #14515300 |
| LCS | G | |
| UCS | C1 ◁ C22×C4 | |
2612 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 2612 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,30)(28,29)(31,34)(38,40)(39,41)(44,65)(45,67)(46,57)(47,58)(48,53)(49,59)(50,60)(52,80)(54,61)(55,62)(56,63)(66,93)(68,89)(70,86)(71,88)(72,83)(73,79)(74,84)(75,92)(76,81)(77,82)(78,87)(90,91)(94,100)(95,98)(97,99);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,31,29)(30,32,33)(34,35,36)(38,44,45)(39,51,52)(40,57,41)(46,73,53)(47,76,70)(48,66,80)(49,61,71)(50,54,72)(55,69,78)(56,85,84)(58,89,75)(59,86,62)(60,92,63)(65,93,82)(67,94,95)(68,88,74)(77,99,90)(79,98,97)(81,83,87)(91,96,100);(1,5)(2,3)(4,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,23)(22,24);(25,28)(30,34)(32,35)(33,36)(37,38)(39,46)(40,58)(41,48)(42,49)(43,50)(44,45)(47,77)(51,83)(52,86)(53,87)(54,72)(55,70)(56,75)(57,84)(59,73)(60,79)(61,71)(62,81)(63,68)(64,82)(65,93)(66,85)(67,69)(74,98)(76,94)(78,99)(80,89)(88,96)(90,95)(91,97)(92,100);(26,29)(27,31)(30,34)(32,35)(37,39)(38,46)(40,53)(41,61)(42,55)(43,56)(44,63)(45,68)(47,74)(48,71)(49,70)(50,75)(51,84)(52,69)(54,90)(57,83)(58,87)(59,76)(60,89)(62,65)(64,91)(66,92)(67,86)(72,95)(73,94)(77,98)(78,96)(79,80)(81,93)(82,97)(85,100)(88,99);(26,29)(27,31)(32,35)(33,36)(37,40)(38,47)(39,53)(41,57)(42,59)(43,60)(44,66)(45,69)(46,74)(48,78)(49,79)(50,73)(51,72)(52,68)(54,88)(55,76)(56,89)(58,82)(61,83)(62,86)(63,92)(64,77)(65,67)(70,80)(71,96)(75,94)(81,100)(84,95)(85,93)(87,97)(90,99)(91,98);(25,28)(27,31)(30,34)(32,35)(37,41)(38,48)(39,54)(40,57)(42,62)(43,63)(44,55)(45,70)(46,72)(47,78)(49,81)(50,68)(51,74)(52,73)(53,88)(56,65)(58,84)(59,86)(60,92)(61,91)(64,90)(66,76)(67,89)(69,80)(71,97)(75,93)(77,99)(79,100)(82,95)(83,98)(85,94)(87,96);(37,42,64,43)(38,49,82,50)(39,55,91,56)(40,59,77,60)(41,62,90,63)(44,61,65,54)(45,71,93,72)(46,70,97,75)(47,79,58,73)(48,81,95,68)(51,69,96,85)(52,78,100,84)(53,76,98,89)(57,86,99,92)(66,83,67,88)(74,80,87,94);(25,28)(26,29)(27,31)(30,34)(32,35)(33,36)92 conjugacy classes — view the full character table.
| maximal quotient of | #72209980 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,30)(28,29)(31,34)(38,40)(39,41)(44,65)(45,67)(46,57)(47,58)(48,53)(49,59)(50,60)(52,80)(54,61)(55,62)(56,63)(66,93)(68,89)(70,86)(71,88)(72,83)(73,79)(74,84)(75,92)(76,81)(77,82)(78,87)(90,91)(94,100)(95,98)(97,99), (1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,31,29)(30,32,33)(34,35,36)(38,44,45)(39,51,52)(40,57,41)(46,73,53)(47,76,70)(48,66,80)(49,61,71)(50,54,72)(55,69,78)(56,85,84)(58,89,75)(59,86,62)(60,92,63)(65,93,82)(67,94,95)(68,88,74)(77,99,90)(79,98,97)(81,83,87)(91,96,100), (1,5)(2,3)(4,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,23)(22,24), (25,28)(30,34)(32,35)(33,36)(37,38)(39,46)(40,58)(41,48)(42,49)(43,50)(44,45)(47,77)(51,83)(52,86)(53,87)(54,72)(55,70)(56,75)(57,84)(59,73)(60,79)(61,71)(62,81)(63,68)(64,82)(65,93)(66,85)(67,69)(74,98)(76,94)(78,99)(80,89)(88,96)(90,95)(91,97)(92,100), (26,29)(27,31)(30,34)(32,35)(37,39)(38,46)(40,53)(41,61)(42,55)(43,56)(44,63)(45,68)(47,74)(48,71)(49,70)(50,75)(51,84)(52,69)(54,90)(57,83)(58,87)(59,76)(60,89)(62,65)(64,91)(66,92)(67,86)(72,95)(73,94)(77,98)(78,96)(79,80)(81,93)(82,97)(85,100)(88,99), (26,29)(27,31)(32,35)(33,36)(37,40)(38,47)(39,53)(41,57)(42,59)(43,60)(44,66)(45,69)(46,74)(48,78)(49,79)(50,73)(51,72)(52,68)(54,88)(55,76)(56,89)(58,82)(61,83)(62,86)(63,92)(64,77)(65,67)(70,80)(71,96)(75,94)(81,100)(84,95)(85,93)(87,97)(90,99)(91,98), (25,28)(27,31)(30,34)(32,35)(37,41)(38,48)(39,54)(40,57)(42,62)(43,63)(44,55)(45,70)(46,72)(47,78)(49,81)(50,68)(51,74)(52,73)(53,88)(56,65)(58,84)(59,86)(60,92)(61,91)(64,90)(66,76)(67,89)(69,80)(71,97)(75,93)(77,99)(79,100)(82,95)(83,98)(85,94)(87,96), (37,42,64,43)(38,49,82,50)(39,55,91,56)(40,59,77,60)(41,62,90,63)(44,61,65,54)(45,71,93,72)(46,70,97,75)(47,79,58,73)(48,81,95,68)(51,69,96,85)(52,78,100,84)(53,76,98,89)(57,86,99,92)(66,83,67,88)(74,80,87,94), (25,28)(26,29)(27,31)(30,34)(32,35)(33,36));