Finite Group DatabasebetaFinite Group Databasebeta| order | 12642 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C2×C49×C43⋊C3 |
| Fitting, Hall | C2×C43×C49 ⋊ C3 |
| derived, Sylow | C43 ⋊ C2×C3×C49 |
| Hall | C43×C49 ⋊ C2×C3 |
| Hall | C2×C43 ⋊ C3×C49 |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 94 |
| transitive degree | μt(G) = 4214 |
A minimal faithful permutation representation — 2 generators on 94 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,33)(18,26,31)(21,29,28)(23,32,25)(27,36,40)(30,37,39)(34,41,35)(38,42,43)(44,48,56,68,80,88,92,46,52,62,75,85,91,65,49,57,69,81,89,59,72,53,63,76,86,54,66,78,58,70,82,50,60,73,83,64,77,47,55,67,79,87,71,45,51,61,74,84,90)(93,94);(1,2,4,8,15,20,5,9,16,25,35,32,12,19,28,24,34,41,22,31,39,36,14,23,33,40,43,42,26,7,13,21,30,38,37,17,3,6,11,18,27,29,10)1666 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12642, 20);