Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#947 |
| Fitting | C2×C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ #124 |
| Sylow | C3 ⋊ C13×#124 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 624 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(18,20)(21,23,24,28)(22,26,25,27);(21,22,24,25)(23,27,28,26);(15,16)(17,18)(19,20)(22,25)(26,27)312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1035);