Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | D47×#3137 |
| Fitting | C47×#3137 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3137 |
2070 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 points:
(11,18)(15,23)(17,24)(19,22)(25,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27);(2,6)(5,8)(9,12,13,16,14,20,21,10)(11,17,19,23,18,24,22,15);(1,3,4,7)(2,5,6,8)(9,11,13,19,14,18,21,22)(10,15,12,17,16,23,20,24);(1,2)(3,5)(4,6)(7,8)(9,10,14,16)(11,17,18,24)(12,13,20,21)(15,22,23,19);(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(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)800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038810);