Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D47×#3179 |
| Fitting | C47×#3179 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3179 |
2034 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 points:
(1,3,4,7)(2,6,5,8)(9,12,13,10)(11,19,18,15)(14,21,22,16)(17,20,24,23)(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);(9,11,14,20,13,18,22,23)(10,15,16,17,12,19,21,24);(2,5)(6,8)(10,12)(11,18)(16,21)(20,23);(1,2)(3,6)(4,5)(7,8)(9,10,13,12)(11,17,18,24)(14,21,22,16)(15,23,19,20);(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)800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1039444);