Finite Group DatabasebetaFinite Group Databasebeta| order | 11520 |
| isoclinism | isoclinic class of #72209667 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | #72209614 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C25 | A6 |
| LCS | G | |
| UCS | C1 ◁ C2 | |
186 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 186 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)(4,14,11,15)(5,16,20,17)(7,21,10,22)(8,25,12,26)(9,28,13,29)(18,49,53,50)(19,54,56,55)(23,58,32,59)(24,38,33,41)(27,61,34,62)(30,46,35,43)(31,64,36,63)(37,70,40,71)(39,57,42,51)(44,75,47,76)(45,52,48,77)(60,79,67,80)(65,78,68,74)(66,72,69,73);(2,7,4)(3,10,11)(5,18,19)(8,27,28)(9,30,31)(12,34,29)(13,35,36)(14,37,38)(15,40,41)(16,26,43)(17,25,46)(20,53,56)(21,24,57)(22,33,51)(23,60,54)(32,67,55)(39,72,65)(42,73,68)(45,75,66)(48,76,69)(49,61,79)(50,62,80)(52,70,78)(71,74,77);(1,4,5)(2,8,9)(3,12,13)(6,11,20)(7,23,24)(10,32,33)(14,25,39)(15,26,42)(16,44,45)(17,47,48)(18,51,52)(19,41,34)(27,56,38)(30,40,63)(31,65,66)(35,37,64)(36,68,69)(43,74,61)(46,78,62)(49,60,76)(50,67,75)(53,57,77)(54,70,59)(55,71,58);(5,20)(8,12)(14,15)(16,17)(19,56)(21,22)(24,33)(28,29)(37,40)(43,46)(49,50)(52,77)(65,68)(70,71)(72,73)(79,80);(1,6)(4,11)(5,20)(16,17)(21,22)(28,29)(30,35)(37,40)(44,47)(45,48)(54,55)(58,59)(63,64)(70,71)(72,73)(79,80);(4,11)(5,20)(7,10)(9,13)(16,17)(18,53)(25,26)(30,35)(37,40)(38,41)(45,48)(54,55)(60,67)(66,69)(70,71)(74,78);(2,3)(5,20)(7,10)(9,13)(14,15)(16,17)(19,56)(23,32)(31,36)(37,40)(43,46)(52,77)(60,67)(66,69)(70,71)(75,76);(1,6)(2,3)(4,11)(5,20)(7,10)(8,12)(9,13)(14,15)(16,17)(18,53)(19,56)(21,22)(23,32)(24,33)(25,26)(27,34)(28,29)(30,35)(31,36)(37,40)(38,41)(39,42)(43,46)(44,47)(45,48)(49,50)(51,57)(52,77)(54,55)(58,59)(60,67)(61,62)(63,64)(65,68)(66,69)(70,71)(72,73)(74,78)(75,76)(79,80)22 conjugacy classes — view the full character table.
| maximal quotient of | #72209937, #72227488 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,6,3)(4,14,11,15)(5,16,20,17)(7,21,10,22)(8,25,12,26)(9,28,13,29)(18,49,53,50)(19,54,56,55)(23,58,32,59)(24,38,33,41)(27,61,34,62)(30,46,35,43)(31,64,36,63)(37,70,40,71)(39,57,42,51)(44,75,47,76)(45,52,48,77)(60,79,67,80)(65,78,68,74)(66,72,69,73), (2,7,4)(3,10,11)(5,18,19)(8,27,28)(9,30,31)(12,34,29)(13,35,36)(14,37,38)(15,40,41)(16,26,43)(17,25,46)(20,53,56)(21,24,57)(22,33,51)(23,60,54)(32,67,55)(39,72,65)(42,73,68)(45,75,66)(48,76,69)(49,61,79)(50,62,80)(52,70,78)(71,74,77), (1,4,5)(2,8,9)(3,12,13)(6,11,20)(7,23,24)(10,32,33)(14,25,39)(15,26,42)(16,44,45)(17,47,48)(18,51,52)(19,41,34)(27,56,38)(30,40,63)(31,65,66)(35,37,64)(36,68,69)(43,74,61)(46,78,62)(49,60,76)(50,67,75)(53,57,77)(54,70,59)(55,71,58), (5,20)(8,12)(14,15)(16,17)(19,56)(21,22)(24,33)(28,29)(37,40)(43,46)(49,50)(52,77)(65,68)(70,71)(72,73)(79,80), (1,6)(4,11)(5,20)(16,17)(21,22)(28,29)(30,35)(37,40)(44,47)(45,48)(54,55)(58,59)(63,64)(70,71)(72,73)(79,80), (4,11)(5,20)(7,10)(9,13)(16,17)(18,53)(25,26)(30,35)(37,40)(38,41)(45,48)(54,55)(60,67)(66,69)(70,71)(74,78), (2,3)(5,20)(7,10)(9,13)(14,15)(16,17)(19,56)(23,32)(31,36)(37,40)(43,46)(52,77)(60,67)(66,69)(70,71)(75,76), (1,6)(2,3)(4,11)(5,20)(7,10)(8,12)(9,13)(14,15)(16,17)(18,53)(19,56)(21,22)(23,32)(24,33)(25,26)(27,34)(28,29)(30,35)(31,36)(37,40)(38,41)(39,42)(43,46)(44,47)(45,48)(49,50)(51,57)(52,77)(54,55)(58,59)(60,67)(61,62)(63,64)(65,68)(66,69)(70,71)(72,73)(74,78)(75,76)(79,80));