Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D47×#2950 |
| Fitting | C47×#2950 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2950 |
2654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 83 points:
(6,13)(8,19)(11,25)(14,21)(15,28)(16,30)(20,32)(31,34)(37,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39);(1,3,4,2)(5,8,10,19)(6,12,13,27)(7,16,18,30)(9,20,23,32)(11,24,25,35)(14,26,21,33)(15,29,28,36)(17,31,22,34);(5,7,10,18)(6,11,13,25)(8,16,19,30)(9,22,23,17)(12,24,27,35)(14,28,21,15)(20,34,32,31)(26,36,33,29);(1,2,4,3)(5,6)(7,15)(8,12)(9,21)(10,13)(11,17)(14,23)(16,29)(18,28)(19,27)(20,33)(22,25)(24,31)(26,32)(30,36)(34,35);(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033708);