Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D47×#2916 |
| Fitting | C47×#2916 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2916 |
2586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 79 points:
(4,17)(9,23)(13,27)(18,19)(21,31)(24,30)(25,32)(28,29)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,4)(2,9)(3,13)(5,18)(6,19)(7,17)(8,21)(10,24)(11,23)(12,25)(14,28)(15,29)(16,27)(20,30)(22,31)(26,32);(1,3,5,14,7,16,6,15)(2,8,10,12,11,22,20,26)(4,13,18,28,17,27,19,29)(9,21,24,25,23,31,30,32);(1,2,6,10,7,11,5,20)(3,12,15,22,16,26,14,8)(4,9,19,24,17,23,18,30)(13,25,29,31,27,32,28,21);(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)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033262);