Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20252913 |
| Fitting | C2×C47×#462 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3044 |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 85 points:
(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)(56,65)(60,74)(64,79)(66,81)(73,84)(75,82)(78,85)(80,83);(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)(54,57,59,69)(55,61,63,76)(56,64,65,79)(58,71,72,68)(60,73,74,84)(62,77,70,67)(66,83,81,80)(75,85,82,78);(50,51,52,53)(54,56)(55,60)(57,64)(58,66)(59,65)(61,73)(62,75)(63,74)(67,78)(68,80)(69,79)(70,82)(71,83)(72,81)(76,84)(77,85);(51,53)(54,55,59,63)(56,60,65,74)(57,67,69,77)(58,70,72,62)(61,71,76,68)(64,78,79,85)(66,82,81,75)(73,83,84,80);(48,49)938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036478);