Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D39 |
| Fitting | C2×C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C22×Q8 |
| Sylow | C13 ⋊ C2×D3×Q8 |
| Sylow | C3 ⋊ C2×Q8×D13 |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1419);