Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | D47×#2984 |
| Fitting | C47×#2984 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2984 |
2022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 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)(49,55)(53,54)(57,63)(61,64)(62,71)(69,70);(48,50,51,52)(49,54,55,53)(56,59,60,68)(57,62,63,71)(58,65,66,67)(61,69,64,70);(48,50,51,52)(49,53,55,54)(56,58,60,66)(57,61,63,64)(59,67,68,65)(62,70,71,69);(48,49,52,53,51,55,50,54)(56,57)(58,64)(59,62)(60,63)(61,66)(65,70)(67,69)(68,71);(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)1250 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1034513);