Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#20252782 |
| Fitting | C2×C47×#410 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3025 |
5086 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 65 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)(50,53,54,60)(51,56,57,63)(52,58,59,64)(55,62,61,65);(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)(50,52)(51,55)(53,58)(54,59)(56,62)(57,61)(60,64)(63,65);(50,51)(52,55)(53,56)(54,57)(58,62)(59,61)(60,63)(64,65);(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)(55,61)(62,65);(48,49)1076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036292);