Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20253107 |
| Fitting | C2×C47×#413 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3067 |
2650 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)(50,54,56,55)(51,59,61,60)(52,64,66,65)(53,68,69,70)(57,72,73,62)(58,74,75,67)(63,78,79,80)(71,81,77,76);(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)(50,53)(51,58)(52,63)(54,68)(55,70)(56,69)(57,71)(59,74)(60,67)(61,75)(62,76)(64,78)(65,80)(66,79)(72,81)(73,77);(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)(50,52,54,64,56,66,55,65)(51,57,60,62,61,73,59,72)(53,63,68,78,69,79,70,80)(58,71,67,76,75,77,74,81);(50,51)(52,62)(53,67)(54,59)(55,60)(56,61)(57,64)(58,68)(63,77)(65,73)(66,72)(69,74)(70,75)(71,79)(76,78)(80,81);(48,49)1076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036962);