Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#20255749 |
| Fitting | C2×C47×#485 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3336 |
1866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 73 points:
(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)(52,57)(55,56);(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)(50,53,54,51)(52,56,57,55)(59,64)(61,69)(63,70)(65,66)(67,73)(71,72);(50,52)(51,55)(53,56)(54,57)(58,60,62,68)(59,63,66,72)(61,67,69,73)(64,70,65,71);(50,51,54,53)(52,56,57,55)(58,59)(60,63)(61,64)(62,66)(65,69)(67,70)(68,72)(71,73);(48,49)944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1047996);