Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D47×#3289 |
| Fitting | C47×#3289 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3289 |
2620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 79 points:
(1,4)(2,10)(3,16)(5,22)(6,19)(7,20)(8,24)(9,11)(12,26)(13,28)(14,30)(15,21)(17,32)(18,31)(23,25)(27,29)(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)(3,15)(5,19)(6,22)(7,20)(8,23)(10,11)(12,28)(13,26)(14,30)(16,21)(17,31)(18,32)(24,25)(27,29);(1,3,7,18)(2,8,13,25)(4,15,20,32)(5,21,6,17)(9,23,26,24)(10,27,28,30)(11,29,12,14)(16,22,31,19);(1,2,7,13)(3,14,18,29)(4,10,20,28)(5,12,6,11)(8,21,25,17)(9,22,26,19)(15,23,32,24)(16,30,31,27);(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)650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045753);