Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#20255164 |
| Fitting | C2×C47×#444 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3289 |
2620 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)(50,53)(51,59)(52,65)(54,71)(55,68)(56,69)(57,73)(58,60)(61,75)(62,77)(63,79)(64,70)(66,81)(67,80)(72,74)(76,78);(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)(50,53)(51,58)(52,64)(54,68)(55,71)(56,69)(57,72)(59,60)(61,77)(62,75)(63,79)(65,70)(66,80)(67,81)(73,74)(76,78);(50,52,56,67)(51,57,62,74)(53,64,69,81)(54,70,55,66)(58,72,75,73)(59,76,77,79)(60,78,61,63)(65,71,80,68);(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)(50,51,56,62)(52,63,67,78)(53,59,69,77)(54,61,55,60)(57,70,74,66)(58,71,75,68)(64,72,81,73)(65,79,80,76);(48,49)1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045760);