Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | D47×#2884 |
| Fitting | C47×#2884 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2884 |
4818 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)(48,52,53,65)(49,56,57,71)(50,60,61,77)(51,62,63,64)(54,67,58,73)(55,68,69,70)(59,74,75,76)(66,78,72,79);(48,51,53,63)(49,55,57,69)(50,59,61,75)(52,64,65,62)(54,66,58,72)(56,70,71,68)(60,76,77,74)(67,79,73,78);(48,50)(49,54)(51,59)(52,60)(53,61)(55,66)(56,67)(57,58)(62,74)(63,75)(64,76)(65,77)(68,78)(69,72)(70,79)(71,73);(48,49)(50,58,61,54)(51,55)(52,56)(53,57)(59,72,75,66)(60,73,77,67)(62,68)(63,69)(64,70)(65,71)(74,79,76,78);(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, 1033039);