Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#20252272 |
| Sylow | C47 ⋊ C2×#2952 |
2806 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 69 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)(54,58,60,56)(55,63,64,66)(57,65,59,67)(61,62,69,68);(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)(50,52,53,51)(54,57,60,59)(55,62,64,68)(56,65,58,67)(61,66,69,63);(54,56,60,58)(55,61,64,69)(57,65,59,67)(62,66,68,63);(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)(50,51,53,52)(54,55,60,64)(56,63,58,66)(57,62,59,68)(61,67,69,65);(48,49)1376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033732);