Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D47×#3234 |
| Fitting | C47×#3234 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3234 |
2050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 points:
(10,16)(14,17)(15,24)(22,23)(25,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27);(1,2)(3,8)(4,6)(5,7)(9,12,13,21)(10,15,16,24)(11,18,19,20)(14,22,17,23);(2,6)(5,8)(9,11,13,19)(10,14,16,17)(12,20,21,18)(15,23,24,22);(2,5)(3,7)(6,8)(9,10)(11,17)(12,15)(13,16)(14,19)(18,23)(20,22)(21,24);(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)(64,65)(66,67)(68,69)(70,71)650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1041667);