Finite Group DatabasebetaFinite Group Databasebeta| order | 11520 |
| isoclinism | isoclinic class of #72209669 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| Frattini, Fitting, cosocle | C25 | A6 |
| socle | C24 | SL(2,𝔽9) |
| LCS | G | |
| UCS | C1 | |
117 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 117 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(1,2,6,3)(4,19,16,20)(5,22,27,24)(7,14,8,13)(9,28,32,29)(10,33,23,34)(11,35,39,25)(12,37,44,41)(15,45,21,46)(17,49,40,50)(18,53,38,52)(26,65,63,42)(30,70,47,71)(31,56,62,72)(43,79,61,80)(48,66,73,59)(54,67,78,64)(55,75,74,58)(57,60)(76,77);(2,9,10)(3,15,16)(4,14,21)(5,25,26)(6,8,7)(11,36,37)(12,42,43)(13,32,23)(17,51,52)(18,54,30)(19,55,56)(20,58,59)(22,35,63)(24,50,64)(27,49,67)(28,31,68)(29,48,69)(33,74,72)(34,75,66)(38,65,61)(39,76,53)(40,77,41)(44,78,47)(45,62,57)(46,73,60)(71,79,80);(1,4,22,8,16,5)(2,11,38,13,40,12)(3,17,44,14,39,18)(6,23,27,7,10,24)(9,30,31)(15,47,48)(19,49,68,33,25,57)(20,35,69,34,50,60)(21,61,62)(26,66,77,64,72,36)(28,45)(29,46)(32,43,73)(37,52,53)(42,58,80,65,74,70)(51,67,56,76,63,59)(54,75,79,78,55,71);(1,6)(2,3)(4,16)(5,27)(7,8)(9,32)(10,23)(11,39)(12,44)(13,14)(15,21)(17,40)(18,38)(19,20)(22,24)(25,35)(26,63)(28,29)(30,47)(31,62)(33,34)(37,41)(42,65)(43,61)(45,46)(48,73)(49,50)(52,53)(54,78)(55,74)(56,72)(58,75)(59,66)(64,67)(70,71)(79,80);(1,7)(2,13)(3,14)(4,23)(5,22)(6,8)(9,21)(10,16)(12,38)(15,32)(18,44)(19,33)(20,34)(24,27)(25,35)(30,43)(31,48)(36,76)(37,53)(41,52)(42,78)(47,61)(49,50)(51,77)(54,65)(56,72)(57,60)(59,66)(62,73)(68,69)(70,79)(71,80);(2,3)(9,15)(11,17)(12,18)(13,14)(19,33)(20,34)(21,32)(25,49)(26,67)(28,46)(29,45)(30,47)(31,48)(35,50)(36,51)(38,44)(39,40)(42,78)(43,61)(54,65)(55,58)(56,66)(57,68)(59,72)(60,69)(62,73)(63,64)(70,79)(71,80)(74,75)(76,77);(1,8)(2,14)(3,13)(4,10)(5,24)(6,7)(11,39)(12,18)(16,23)(17,40)(19,34)(20,33)(22,27)(26,64)(28,46)(29,45)(30,43)(31,62)(36,77)(37,52)(38,44)(41,53)(47,61)(48,73)(51,76)(56,66)(57,60)(59,72)(63,67)(68,69)(70,79)(71,80);(1,6)(4,10)(7,8)(9,21)(11,40)(15,32)(16,23)(17,39)(25,50)(26,64)(28,45)(29,46)(30,43)(31,48)(35,49)(36,51)(37,53)(41,52)(42,54)(47,61)(55,75)(56,66)(57,69)(58,74)(59,72)(60,68)(62,73)(63,67)(65,78)(70,71)(76,77)(79,80)21 conjugacy classes — view the full character table.
| maximal quotient of | #72227496 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,6,3)(4,19,16,20)(5,22,27,24)(7,14,8,13)(9,28,32,29)(10,33,23,34)(11,35,39,25)(12,37,44,41)(15,45,21,46)(17,49,40,50)(18,53,38,52)(26,65,63,42)(30,70,47,71)(31,56,62,72)(43,79,61,80)(48,66,73,59)(54,67,78,64)(55,75,74,58)(57,60)(76,77), (2,9,10)(3,15,16)(4,14,21)(5,25,26)(6,8,7)(11,36,37)(12,42,43)(13,32,23)(17,51,52)(18,54,30)(19,55,56)(20,58,59)(22,35,63)(24,50,64)(27,49,67)(28,31,68)(29,48,69)(33,74,72)(34,75,66)(38,65,61)(39,76,53)(40,77,41)(44,78,47)(45,62,57)(46,73,60)(71,79,80), (1,4,22,8,16,5)(2,11,38,13,40,12)(3,17,44,14,39,18)(6,23,27,7,10,24)(9,30,31)(15,47,48)(19,49,68,33,25,57)(20,35,69,34,50,60)(21,61,62)(26,66,77,64,72,36)(28,45)(29,46)(32,43,73)(37,52,53)(42,58,80,65,74,70)(51,67,56,76,63,59)(54,75,79,78,55,71), (1,6)(2,3)(4,16)(5,27)(7,8)(9,32)(10,23)(11,39)(12,44)(13,14)(15,21)(17,40)(18,38)(19,20)(22,24)(25,35)(26,63)(28,29)(30,47)(31,62)(33,34)(37,41)(42,65)(43,61)(45,46)(48,73)(49,50)(52,53)(54,78)(55,74)(56,72)(58,75)(59,66)(64,67)(70,71)(79,80), (1,7)(2,13)(3,14)(4,23)(5,22)(6,8)(9,21)(10,16)(12,38)(15,32)(18,44)(19,33)(20,34)(24,27)(25,35)(30,43)(31,48)(36,76)(37,53)(41,52)(42,78)(47,61)(49,50)(51,77)(54,65)(56,72)(57,60)(59,66)(62,73)(68,69)(70,79)(71,80), (2,3)(9,15)(11,17)(12,18)(13,14)(19,33)(20,34)(21,32)(25,49)(26,67)(28,46)(29,45)(30,47)(31,48)(35,50)(36,51)(38,44)(39,40)(42,78)(43,61)(54,65)(55,58)(56,66)(57,68)(59,72)(60,69)(62,73)(63,64)(70,79)(71,80)(74,75)(76,77), (1,8)(2,14)(3,13)(4,10)(5,24)(6,7)(11,39)(12,18)(16,23)(17,40)(19,34)(20,33)(22,27)(26,64)(28,46)(29,45)(30,43)(31,62)(36,77)(37,52)(38,44)(41,53)(47,61)(48,73)(51,76)(56,66)(57,60)(59,72)(63,67)(68,69)(70,79)(71,80), (1,6)(4,10)(7,8)(9,21)(11,40)(15,32)(16,23)(17,39)(25,50)(26,64)(28,45)(29,46)(30,43)(31,48)(35,49)(36,51)(37,53)(41,52)(42,54)(47,61)(55,75)(56,66)(57,69)(58,74)(59,72)(60,68)(62,73)(63,67)(65,78)(70,71)(76,77)(79,80));