Finite Group DatabasebetaFinite Group Databasebeta| order | 7370 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D55 |
| unambiguous semidirect product | C5⋊(D11×C67) |
| unambiguous semidirect product | C11⋊(D5×C67) |
| Fitting, socle, Hall | C5×C11×C67 ⋊ C2 |
| derived, Hall | C5×C11 ⋊ C2×C67 |
| Hall | C11×C67 ⋊ D5 |
| Hall | C5×C67 ⋊ D11 |
| Sylow | C11 ⋊ D5×C67 |
| Sylow | C5 ⋊ D11×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D55 |
| commutator, hypocenter | C5×C11 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C67 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C67 | |
16 conjugacy classes of subgroups.
1943 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D55×D67, D5×D11×C67, D55⋊D67, … |
| maximal normal subgroup of | D55×D67, D5×D11×C67, D55⋊D67, … |
| maximal quotient of | C67×Dic55, C2×C67×D55, C3×C67×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7370, 9);