Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D47×#3044 |
| Fitting | C47×#3044 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3044 |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 83 points:
(7,16)(11,25)(15,30)(17,32)(24,35)(26,33)(29,36)(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);(5,8,10,20)(6,12,14,27)(7,15,16,30)(9,22,23,19)(11,24,25,35)(13,28,21,18)(17,34,32,31)(26,36,33,29);(1,2,3,4)(5,7)(6,11)(8,15)(9,17)(10,16)(12,24)(13,26)(14,25)(18,29)(19,31)(20,30)(21,33)(22,34)(23,32)(27,35)(28,36);(2,4)(5,6,10,14)(7,11,16,25)(8,18,20,28)(9,21,23,13)(12,22,27,19)(15,29,30,36)(17,33,32,26)(24,34,35,31);(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, 1036477);