Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#20254346 |
| Fitting | C2×C47×#431 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3210 |
2186 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)(51,55)(54,56)(58,61,63,62)(59,65,66,70)(60,68,69,71)(64,72,73,67);(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)(52,57)(54,56)(58,60)(59,64)(61,68)(62,71)(63,69)(65,72)(66,73)(67,70);(50,52,53,57)(51,54,55,56);(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)(52,56)(53,55)(54,57)(58,59,63,66)(60,67,69,72)(61,65,62,70)(64,71,73,68);(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, 1040780);