Finite Group DatabasebetaFinite Group Databasebeta| order | 11520 |
| isoclinism | isoclinic class of #72209668 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #72209614 |
| commutator, hypocenter | G | C1 |
| Fitting, socle, cosocle | C25 | A6 |
| LCS | G | |
| UCS | C1 ◁ C2 | |
191 conjugacy classes of subgroups; only the 5 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 5 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(2,4)(3,5)(7,16)(8,12)(9,14)(10,15)(17,18,22,19)(20,30,27,31)(21,32,36,33)(23,37,26,38)(24,41,28,42)(25,44,29,45)(34,65,69,66)(35,70,72,71)(39,74,48,75)(40,54,49,57)(43,77,50,78)(46,62,51,59)(47,80,52,79)(53,86,56,87)(55,73,58,67)(60,91,63,92)(61,68,64,93)(76,95,83,96)(81,94,84,90)(82,88,85,89);(2,6,7)(3,13,14)(4,15,5)(8,10,11)(9,12,16)(18,23,20)(19,26,27)(21,34,35)(24,43,44)(25,46,47)(28,50,45)(29,51,52)(30,53,54)(31,56,57)(32,42,59)(33,41,62)(36,69,72)(37,40,73)(38,49,67)(39,76,70)(48,83,71)(55,88,81)(58,89,84)(61,91,82)(64,92,85)(65,77,95)(66,78,96)(68,86,94)(87,90,93);(2,8,9)(4,11,10)(5,13,16)(6,14,15)(17,20,21)(18,24,25)(19,28,29)(22,27,36)(23,39,40)(26,48,49)(30,41,55)(31,42,58)(32,60,61)(33,63,64)(34,67,68)(35,57,50)(43,72,54)(46,56,79)(47,81,82)(51,53,80)(52,84,85)(59,90,77)(62,94,78)(65,76,92)(66,83,91)(69,73,93)(70,86,75)(71,87,74);(17,22)(18,19)(20,27)(21,36)(23,26)(24,28)(25,29)(30,31)(32,33)(34,69)(35,72)(37,38)(39,48)(40,49)(41,42)(43,50)(44,45)(46,51)(47,52)(53,56)(54,57)(55,58)(59,62)(60,63)(61,64)(65,66)(67,73)(68,93)(70,71)(74,75)(76,83)(77,78)(79,80)(81,84)(82,85)(86,87)(88,89)(90,94)(91,92)(95,96);(1,2)(3,10)(4,11)(5,12)(6,7)(8,9)(13,16)(14,15);(1,3)(2,10)(4,8)(5,6)(7,12)(9,11)(13,14)(15,16);(1,4)(2,11)(3,8)(5,15)(6,16)(7,13)(9,10)(12,14);(1,5)(2,12)(3,6)(4,15)(7,10)(8,16)(9,13)(11,14)21 conjugacy classes — view the full character table.
| maximal quotient of | #72209937, #72227492 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((2,4)(3,5)(7,16)(8,12)(9,14)(10,15)(17,18,22,19)(20,30,27,31)(21,32,36,33)(23,37,26,38)(24,41,28,42)(25,44,29,45)(34,65,69,66)(35,70,72,71)(39,74,48,75)(40,54,49,57)(43,77,50,78)(46,62,51,59)(47,80,52,79)(53,86,56,87)(55,73,58,67)(60,91,63,92)(61,68,64,93)(76,95,83,96)(81,94,84,90)(82,88,85,89), (2,6,7)(3,13,14)(4,15,5)(8,10,11)(9,12,16)(18,23,20)(19,26,27)(21,34,35)(24,43,44)(25,46,47)(28,50,45)(29,51,52)(30,53,54)(31,56,57)(32,42,59)(33,41,62)(36,69,72)(37,40,73)(38,49,67)(39,76,70)(48,83,71)(55,88,81)(58,89,84)(61,91,82)(64,92,85)(65,77,95)(66,78,96)(68,86,94)(87,90,93), (2,8,9)(4,11,10)(5,13,16)(6,14,15)(17,20,21)(18,24,25)(19,28,29)(22,27,36)(23,39,40)(26,48,49)(30,41,55)(31,42,58)(32,60,61)(33,63,64)(34,67,68)(35,57,50)(43,72,54)(46,56,79)(47,81,82)(51,53,80)(52,84,85)(59,90,77)(62,94,78)(65,76,92)(66,83,91)(69,73,93)(70,86,75)(71,87,74), (17,22)(18,19)(20,27)(21,36)(23,26)(24,28)(25,29)(30,31)(32,33)(34,69)(35,72)(37,38)(39,48)(40,49)(41,42)(43,50)(44,45)(46,51)(47,52)(53,56)(54,57)(55,58)(59,62)(60,63)(61,64)(65,66)(67,73)(68,93)(70,71)(74,75)(76,83)(77,78)(79,80)(81,84)(82,85)(86,87)(88,89)(90,94)(91,92)(95,96), (1,2)(3,10)(4,11)(5,12)(6,7)(8,9)(13,16)(14,15), (1,3)(2,10)(4,8)(5,6)(7,12)(9,11)(13,14)(15,16), (1,4)(2,11)(3,8)(5,15)(6,16)(7,13)(9,10)(12,14), (1,5)(2,12)(3,6)(4,15)(7,10)(8,16)(9,13)(11,14));