Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | D47×#2889 |
| Fitting | C47×#2889 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2889 |
4770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 79 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(51,62)(55,68)(59,73)(63,75)(66,72)(69,78)(74,76)(77,79);(48,51)(49,55)(50,59)(52,63)(53,62)(54,66)(56,68)(57,69)(58,72)(60,74)(61,73)(64,76)(65,75)(67,77)(70,78)(71,79);(48,50,53,61)(49,54,56,58)(51,59,62,73)(52,64,65,60)(55,66,68,72)(57,71,70,67)(63,76,75,74)(69,79,78,77);(48,49,52,57,53,56,65,70)(50,58,60,71,61,54,64,67)(51,55,63,69,62,68,75,78)(59,72,74,79,73,66,76,77);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033064);