Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C22×C47⋊#564 |
| Sylow | C47 ⋊ C22×#564 |
6374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 12032 |
A minimal faithful permutation representation — 6 generators on 83 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)(53,59)(57,66)(58,62)(65,67)(68,71,72,81)(69,74,75,79)(70,78,77,80)(73,82,76,83);(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)(52,55,56,64)(53,58,59,62)(54,60,61,63)(57,65,66,67)(70,77)(73,76)(78,80)(82,83);(52,54,56,61)(53,57,59,66)(55,63,64,60)(58,67,62,65)(68,70)(69,73)(71,80)(72,77)(74,83)(75,76)(78,81)(79,82);(52,53)(54,57)(55,62)(56,59)(58,64)(60,67)(61,66)(63,65)(68,69,72,75)(70,76,77,73)(71,79,81,74)(78,82,80,83);(50,51);(48,49)1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1076464);