Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20255193 |
| Fitting | C2×C47×#443 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3293 |
2598 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)(50,54)(51,59)(52,64)(53,67)(55,73)(56,70)(57,71)(58,74)(60,78)(61,76)(62,77)(63,79)(65,80)(66,81)(68,75)(69,72);(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)(50,53,57,58)(51,52,62,66)(54,67,71,74)(55,68,56,63)(59,64,77,81)(60,65,61,72)(69,78,80,76)(70,79,73,75);(50,52,57,66)(51,58,62,53)(54,69,71,80)(55,72,56,65)(59,75,77,79)(60,68,61,63)(64,73,81,70)(67,76,74,78);(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)(50,51,57,62)(52,63,66,68)(53,65,58,72)(54,59,71,77)(55,61,56,60)(64,79,81,75)(67,80,74,69)(70,78,73,76);(48,49)1346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045800);