Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#20254429 |
| Fitting | C2×C47×#452 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3219 |
2198 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)(58,61,62,63)(59,66,64,67)(60,69,70,71)(65,68,72,73);(52,57)(54,56)(58,60)(59,65)(61,69)(62,70)(63,71)(64,72)(66,68)(67,73);(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)(50,52,53,57)(51,54,55,56)(59,64)(65,72)(66,67)(68,73);(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)(60,68)(61,67)(62,64)(63,66)(65,69)(70,73)(71,72);(48,49)926 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1040875);