Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D47×#3276 |
| Fitting | C47×#3276 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3276 |
2742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 67 points:
(5,9)(6,8)(7,12)(10,14)(11,13)(15,16)(17,20)(18,19)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(2,4)(5,8,11,10)(6,13,14,9)(7,16,18,17)(12,15,19,20);(5,7,11,18)(6,12,14,19)(8,17,10,16)(9,15,13,20);(1,2)(3,4)(5,6,11,14)(7,15,18,20)(8,13,10,9)(12,16,19,17);(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)(64,65)(66,67)725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1044706);