Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#20253497 |
| Fitting | C2×C4×#41×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3111 |
2182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 73 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)(50,52,53,56)(51,55,54,57)(58,61,62,63)(59,66,67,65)(60,69,70,71)(64,73,68,72);(59,65)(61,63)(64,72)(66,67)(68,73)(69,71);(51,54)(55,57)(58,60,62,70)(59,64,67,68)(61,69,63,71)(65,72,66,73);(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)(50,51)(52,55)(53,54)(56,57)(58,59)(60,68)(61,66)(62,67)(63,65)(64,70)(69,72)(71,73);(48,49)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1037748);