Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#15689398 |
| Sylow | C47 ⋊ C22×#473 |
2630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 83 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)(52,55)(53,60)(54,65)(56,70)(57,72)(58,71)(59,73)(61,69)(62,77)(63,76)(64,78)(66,80)(67,82)(68,81)(74,83)(75,79);(52,54,57,67,58,68,56,66)(53,59,62,74,63,75,61,64)(55,65,72,82,71,81,70,80)(60,73,77,83,76,79,69,78);(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)(52,53,58,63)(54,64,68,74)(55,69,71,77)(56,62,57,61)(59,67,75,66)(60,72,76,70)(65,79,81,73)(78,82,83,80);(50,51);(48,49)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036955);