Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D47×#3041 |
| Fitting | C47×#3041 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3041 |
3074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 67 points:
(7,14)(10,18)(15,20)(17,19)(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);(6,11)(8,16)(10,17)(12,13)(15,20)(18,19);(1,2,3,4)(5,7)(6,10)(8,15)(9,14)(11,17)(12,19)(13,18)(16,20);(2,4)(5,6)(7,10)(8,11)(9,13)(12,16)(14,18)(15,17)(19,20);(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, 1036447);