Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×(C2×#261)⋊C4 |
| Fitting | C2×C3×C4×C13 ⋊ C4 |
| Hall | C3×C13 ⋊ #95 |
| Sylow | C13 ⋊ C3×#95 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 312 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,8,11,15,9,13,14,6,10,16,12,7)(17,18,19,20)(22,24);(5,6,7,9)(8,11,12,16)(10,14,15,13)(21,22)(23,24)132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 463);