Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D47×#2955 |
| Fitting | C47×#2955 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2955 |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 79 points:
(2,10)(8,22)(9,24)(11,19)(12,23)(21,31)(25,29)(26,32)(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);(1,4,6,17,7,18,5,16)(2,9,11,25,10,24,19,29)(3,13,14,27,15,28,20,30)(8,21,23,32,22,31,12,26);(1,3)(2,8)(4,13)(5,20)(6,14)(7,15)(9,21)(10,22)(11,23)(12,19)(16,30)(17,27)(18,28)(24,31)(25,32)(26,29);(1,2,6,11,7,10,5,19)(3,12,14,8,15,23,20,22)(4,9,17,25,18,24,16,29)(13,26,27,21,28,32,30,31);(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, 1033867);