Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#20252478 |
| Sylow | C47 ⋊ C2×#2984 |
2022 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)(51,57)(55,56)(59,65)(63,66)(64,73)(71,72);(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)(50,52,53,54)(51,56,57,55)(58,61,62,70)(59,64,65,73)(60,67,68,69)(63,71,66,72);(50,52,53,54)(51,55,57,56)(58,60,62,68)(59,63,65,66)(61,69,70,67)(64,72,73,71);(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)(50,51,54,55,53,57,52,56)(58,59)(60,66)(61,64)(62,65)(63,68)(67,72)(69,71)(70,73);(48,49)1388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1034518);