Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| isoclinism | isoclinic class of #72209937 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C22 | #72209614 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C26 | A6 |
| LCS | G | |
| UCS | C1 ◁ C22 | |
596 conjugacy classes of subgroups; only the 8 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 8 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(3,6)(5,9)(8,11)(10,12)(13,14,18,15)(16,26,23,27)(17,28,32,29)(19,33,22,34)(20,37,24,38)(21,40,25,41)(30,61,65,62)(31,66,68,67)(35,70,44,71)(36,50,45,53)(39,73,46,74)(42,58,47,55)(43,76,48,75)(49,82,52,83)(51,69,54,63)(56,87,59,88)(57,64,60,89)(72,91,79,92)(77,90,80,86)(78,84,81,85);(1,2,3)(4,7,8)(5,6,9)(10,11,12)(14,19,16)(15,22,23)(17,30,31)(20,39,40)(21,42,43)(24,46,41)(25,47,48)(26,49,50)(27,52,53)(28,38,55)(29,37,58)(32,65,68)(33,36,69)(34,45,63)(35,72,66)(44,79,67)(51,84,77)(54,85,80)(57,87,78)(60,88,81)(61,73,91)(62,74,92)(64,82,90)(83,86,89);(2,5,6)(7,10,11)(13,16,17)(14,20,21)(15,24,25)(18,23,32)(19,35,36)(22,44,45)(26,37,51)(27,38,54)(28,56,57)(29,59,60)(30,63,64)(31,53,46)(39,68,50)(42,52,75)(43,77,78)(47,49,76)(48,80,81)(55,86,73)(58,90,74)(61,72,88)(62,79,87)(65,69,89)(66,82,71)(67,83,70);(13,18)(14,15)(16,23)(17,32)(19,22)(20,24)(21,25)(26,27)(28,29)(30,65)(31,68)(33,34)(35,44)(36,45)(37,38)(39,46)(40,41)(42,47)(43,48)(49,52)(50,53)(51,54)(55,58)(56,59)(57,60)(61,62)(63,69)(64,89)(66,67)(70,71)(72,79)(73,74)(75,76)(77,80)(78,81)(82,83)(84,85)(86,90)(87,88)(91,92);(1,4)(3,8)(6,11)(9,12);(2,7)(5,10)(6,11)(9,12);(1,4)(3,8)(5,10)(6,11);(2,7)(3,8)(5,10)(9,12);(1,4)(2,7)(3,8)(5,10)(6,11)(9,12)42 conjugacy classes — view the full character table.
| maximal quotient of | #72227900 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((3,6)(5,9)(8,11)(10,12)(13,14,18,15)(16,26,23,27)(17,28,32,29)(19,33,22,34)(20,37,24,38)(21,40,25,41)(30,61,65,62)(31,66,68,67)(35,70,44,71)(36,50,45,53)(39,73,46,74)(42,58,47,55)(43,76,48,75)(49,82,52,83)(51,69,54,63)(56,87,59,88)(57,64,60,89)(72,91,79,92)(77,90,80,86)(78,84,81,85), (1,2,3)(4,7,8)(5,6,9)(10,11,12)(14,19,16)(15,22,23)(17,30,31)(20,39,40)(21,42,43)(24,46,41)(25,47,48)(26,49,50)(27,52,53)(28,38,55)(29,37,58)(32,65,68)(33,36,69)(34,45,63)(35,72,66)(44,79,67)(51,84,77)(54,85,80)(57,87,78)(60,88,81)(61,73,91)(62,74,92)(64,82,90)(83,86,89), (2,5,6)(7,10,11)(13,16,17)(14,20,21)(15,24,25)(18,23,32)(19,35,36)(22,44,45)(26,37,51)(27,38,54)(28,56,57)(29,59,60)(30,63,64)(31,53,46)(39,68,50)(42,52,75)(43,77,78)(47,49,76)(48,80,81)(55,86,73)(58,90,74)(61,72,88)(62,79,87)(65,69,89)(66,82,71)(67,83,70), (13,18)(14,15)(16,23)(17,32)(19,22)(20,24)(21,25)(26,27)(28,29)(30,65)(31,68)(33,34)(35,44)(36,45)(37,38)(39,46)(40,41)(42,47)(43,48)(49,52)(50,53)(51,54)(55,58)(56,59)(57,60)(61,62)(63,69)(64,89)(66,67)(70,71)(72,79)(73,74)(75,76)(77,80)(78,81)(82,83)(84,85)(86,90)(87,88)(91,92), (1,4)(3,8)(6,11)(9,12), (2,7)(5,10)(6,11)(9,12), (1,4)(3,8)(5,10)(6,11), (2,7)(3,8)(5,10)(9,12), (1,4)(2,7)(3,8)(5,10)(6,11)(9,12));