Finite Group DatabasebetaFinite Group Databasebeta| order | 9230 |
| isoclinism | isoclinic class of D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D65 |
| unambiguous semidirect product | C5⋊(D13×C71) |
| unambiguous semidirect product | C13⋊(D5×C71) |
| Fitting, socle, Hall | C5×C13×C71 ⋊ C2 |
| derived, Hall | C5×C13 ⋊ C2×C71 |
| Hall | C13×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ D13 |
| Sylow | C13 ⋊ D5×C71 |
| Sylow | C5 ⋊ D13×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D65 |
| commutator, hypocenter | C5×C13 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C71 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
2414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C71×#63122, C71⋊#63122, C71×#63121, … |
| maximal normal subgroup of | C71×#63122, C71⋊#63122, C71×#63121, … |
| maximal quotient of | C71×Dic65, C2×C71×D65, C3×C71×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9230, 8);