Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | D7×#95⋊C3 |
| Fitting, derived | C7×#95 ⋊ C2×C3 |
| Hall | D7×#95 ⋊ C3 |
| Sylow | C7 ⋊ C2×#95⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7×C42⋊C3 |
| commutator, Fitting, cosocle, hypocenter | C7×#95 | C2×C3 |
| Frattini | C23 | A4×D7 |
| socle | C23×C7 | C2×A4 |
| LCS | G ▷ C7×#95 | |
| UCS | C1 ◁ C2 | |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1440);