Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#20252292 |
| Fitting | C2×C47×#405 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2955 |
2666 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)(51,59)(57,71)(58,73)(60,68)(61,72)(70,80)(74,78)(75,81);(50,53,55,66,56,67,54,65)(51,58,60,74,59,73,68,78)(52,62,63,76,64,77,69,79)(57,70,72,81,71,80,61,75);(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)(51,57)(53,62)(54,69)(55,63)(56,64)(58,70)(59,71)(60,72)(61,68)(65,79)(66,76)(67,77)(73,80)(74,81)(75,78);(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)(50,51,55,60,56,59,54,68)(52,61,63,57,64,72,69,71)(53,58,66,74,67,73,65,78)(62,75,76,70,77,81,79,80);(48,49)1928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033874);