Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#20251999 |
| Sylow | C47 ⋊ C2×#2916 |
2586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 81 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(53,66)(58,72)(62,76)(67,68)(70,80)(73,79)(74,81)(77,78);(50,53)(51,58)(52,62)(54,67)(55,68)(56,66)(57,70)(59,73)(60,72)(61,74)(63,77)(64,78)(65,76)(69,79)(71,80)(75,81);(50,52,54,63,56,65,55,64)(51,57,59,61,60,71,69,75)(53,62,67,77,66,76,68,78)(58,70,73,74,72,80,79,81);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(50,51,55,59,56,60,54,69)(52,61,64,71,65,75,63,57)(53,58,68,73,66,72,67,79)(62,74,78,80,76,81,77,70);(48,49)1928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033266);