Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | D47×#2883 |
| Fitting | C47×#2883 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2883 |
5338 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 752 |
A minimal faithful permutation representation — 5 generators on 63 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(51,59)(54,61)(57,63)(60,62);(48,51)(49,54)(50,57)(52,59)(53,60)(55,61)(56,62)(58,63);(48,50)(49,53)(51,57)(52,58)(54,60)(55,56)(59,63)(61,62);(48,49)(50,56,58,53)(51,54)(52,55)(57,62,63,60)(59,61);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(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)1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033034);