Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D47×#3321 |
| Fitting | C47×#3321 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3321 |
2178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 points:
(3,8)(5,7)(9,11,14,13)(10,15,17,22)(12,18,21,20)(16,23,24,19)(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);(9,12,14,21)(10,16,17,24)(11,18,13,20)(15,23,22,19);(1,3)(2,5)(4,8)(6,7)(9,11,14,13)(10,15,17,22)(12,20,21,18)(16,19,24,23);(1,2,4,6)(3,7,8,5)(9,10,14,17)(11,15,13,22)(12,19,21,23)(16,20,24,18);(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)725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1046310);