Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#20252795 |
| Fitting | C2×C47×#410 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3028 |
4790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 81 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)(50,54,55,66)(51,58,59,65)(52,61,62,76)(53,63,64,78)(56,68,69,75)(57,70,71,77)(60,73,74,81)(67,79,72,80);(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)(50,53)(51,57)(52,60)(54,63)(55,64)(56,67)(58,70)(59,71)(61,73)(62,74)(65,77)(66,78)(68,79)(69,72)(75,80)(76,81);(50,52)(51,56)(53,60)(54,61)(55,62)(57,67)(58,68)(59,69)(63,73)(64,74)(65,75)(66,76)(70,79)(71,72)(77,80)(78,81);(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)(50,51,55,59)(52,56,62,69)(53,57,64,71)(54,65,66,58)(60,72,74,67)(61,75,76,68)(63,77,78,70)(73,79,81,80);(48,49)1070 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036308);