Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | D47×#3156 |
| Fitting | C47×#3156 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3156 |
3150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 83 points:
(8,20)(12,26)(17,31)(21,30)(24,35)(27,33)(28,36)(32,34)(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);(1,2,3,4)(5,8)(6,12)(7,17)(9,21)(10,20)(11,24)(13,27)(14,26)(15,28)(16,30)(18,32)(19,31)(22,33)(23,34)(25,35)(29,36);(5,7,16,23,10,19,9,18)(6,11,22,29,14,25,13,15)(8,17,30,34,20,31,21,32)(12,24,33,36,26,35,27,28);(2,4)(5,6,10,14)(7,15,19,29)(8,12,20,26)(9,22,16,13)(11,23,25,18)(17,28,31,36)(21,33,30,27)(24,34,35,32);(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)800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1039062);