Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#20253786 |
| Fitting | C2×C47×#417 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3142 |
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)(58,62,63,70)(59,66,68,67)(60,71,72,61)(64,69,73,65);(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)(51,55)(54,57)(58,61,62,72,63,71,70,60)(59,65,67,64,68,69,66,73);(50,52,53,56)(51,54,55,57)(58,60,70,71,63,72,62,61)(59,64,66,65,68,73,67,69);(50,51)(52,54)(53,55)(56,57)(58,59)(60,69)(61,64)(62,66)(63,68)(65,72)(67,70)(71,73);(48,49)1076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038863);