Finite Group DatabasebetaFinite Group Databasebeta| order | 7370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D67⋊C11) |
| unambiguous semidirect product | D335⋊C11 |
| unambiguous semidirect product | (C67⋊C11)⋊D5 |
| Fitting, socle, derived, Hall | C5×C67 ⋊ C2×C11 |
| Hall | C5×C67⋊C11 ⋊ C2 |
| Hall | C67⋊C11 ⋊ D5 |
| Hall | D335 ⋊ C11 |
| Sylow | C67 ⋊ D5×C11 |
| Sylow | C5 ⋊ D67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C67 | C2×C11 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,67|b^a=b^4,d^a=d^66,d^c=d^6459 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7370, 13);