Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20253042 |
| Fitting | C2×C47×#419 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3059 |
2678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 85 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)(57,69)(61,75)(66,80)(70,79)(73,84)(76,82)(77,85)(81,83);(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)(51,53)(54,57)(55,61)(56,66)(58,70)(59,69)(60,73)(62,76)(63,75)(64,77)(65,79)(67,81)(68,80)(71,82)(72,83)(74,84)(78,85);(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)(54,56,65,72,59,68,58,67)(55,60,71,78,63,74,62,64)(57,66,79,83,69,80,70,81)(61,73,82,85,75,84,76,77);(50,51)(52,53)(54,55,59,63)(56,64,68,78)(57,61,69,75)(58,71,65,62)(60,72,74,67)(66,77,80,85)(70,82,79,76)(73,83,84,81);(48,49)1076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036762);