Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20253120 |
| Fitting | C2×C47×#471 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3069 |
2618 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 81 points:
(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)(52,64)(57,72)(62,73)(63,78)(65,66)(71,77)(76,81)(79,80);(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)(50,53)(51,58)(52,63)(54,68)(55,70)(56,69)(57,71)(59,67)(60,75)(61,74)(62,76)(64,78)(65,79)(66,80)(72,77)(73,81);(50,52,54,65,56,64,55,66)(51,57,59,62,61,72,60,73)(53,63,68,79,69,78,70,80)(58,71,67,76,74,77,75,81);(50,51,56,61)(52,62,64,73)(53,67,69,75)(54,60,55,59)(57,66,72,65)(58,70,74,68)(63,77,78,71)(76,80,81,79);(48,49)794 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036977);