Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D47×#3046 |
| Fitting | C47×#3046 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3046 |
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:
(5,7,9,14)(6,11,13,18)(8,15,16,20)(10,17,12,19)(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);(6,10)(8,16)(11,17)(12,13)(15,20)(18,19);(1,2,3,4)(7,14)(11,18)(15,20)(17,19);(2,4)(5,6,9,13)(7,11,14,18)(8,10,16,12)(15,17,20,19);(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)800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036499);