Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D47×#3231 |
| Fitting | C47×#3231 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3231 |
1778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 79 points:
(2,8)(6,9)(7,16)(14,15)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26)(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);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14);(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,22,25)(19,26,28,31)(20,24,21,29)(23,30,32,27);(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)800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1041630);