Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#20253707 |
| Fitting | C2×C47×#486 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3131 |
2222 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)(58,62,64,63)(59,67,69,68)(60,61,71,70)(65,72,73,66);(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)(51,55)(54,57)(58,61,62,71,64,70,63,60)(59,66,68,73,69,72,67,65);(50,52,53,56)(51,54,55,57)(58,60,63,70,64,71,62,61)(59,65,67,72,69,73,68,66);(50,51)(52,54)(53,55)(56,57)(58,59)(60,66)(61,65)(62,67)(63,68)(64,69)(70,73)(71,72);(48,49)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038767);