Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | D47×#3027 |
| Fitting | C47×#3027 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3027 |
5110 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)(48,51,52,58)(49,54,55,61)(50,56,57,62)(53,60,59,63);(48,50)(49,53)(51,56)(52,57)(54,60)(55,59)(58,62)(61,63);(48,49)(50,53)(51,54)(52,55)(56,60)(57,59)(58,61)(62,63);(51,58)(53,59)(54,61)(56,62);(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)725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036299);