Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic56⋊C3 |
| unambiguous semidirect product | (C2×Dic56)⋊C3 |
| Hall | C2×Dic56 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×Q32 |
| Sylow | C7 ⋊ C2×C3×Q32 |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1094);