Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D47×#3293 |
| Fitting | C47×#3293 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3293 |
2598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 79 points:
(1,5)(2,10)(3,15)(4,18)(6,24)(7,21)(8,22)(9,25)(11,29)(12,27)(13,28)(14,30)(16,31)(17,32)(19,26)(20,23)(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);(1,4,8,9)(2,3,13,17)(5,18,22,25)(6,19,7,14)(10,15,28,32)(11,16,12,23)(20,29,31,27)(21,30,24,26);(1,3,8,17)(2,9,13,4)(5,20,22,31)(6,23,7,16)(10,26,28,30)(11,19,12,14)(15,24,32,21)(18,27,25,29);(1,2,8,13)(3,14,17,19)(4,16,9,23)(5,10,22,28)(6,12,7,11)(15,30,32,26)(18,31,25,20)(21,29,24,27);(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)725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045795);