Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D47×#3335 |
| Fitting | C47×#3335 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3335 |
2158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 63 points:
(3,8)(6,7)(17,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19);(1,4,5,2)(3,7,8,6)(10,13)(11,16)(14,15);(1,3)(2,6)(4,7)(5,8);(1,2,5,4)(3,7,8,6)(9,10,12,15)(11,13,16,14);(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)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1047983);