Finite Group DatabasebetaFinite Group Databasebeta| order | 7370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×D67 |
| unambiguous semidirect product | C67⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C11×D67)⋊C5 |
| Fitting, socle, derived, Hall | C11×C67 ⋊ C2×C5 |
| Hall | C11⋊C5×C67 ⋊ C2 |
| Hall | C11×D67 ⋊ C5 |
| Sylow | C67 ⋊ C2×C11⋊C5 |
| Sylow | C11 ⋊ C5×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C67 | C2×C5 |
| LCS | G ▷ C11×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7370, 14);