Finite Group DatabasebetaFinite Group Databasebeta| order | 9230 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C5×C13×D71 |
| Fitting, socle, Hall | C5×C13×C71 ⋊ C2 |
| derived, Sylow | C71 ⋊ C2×C5×C13 |
| Hall | C13×C71 ⋊ C2×C5 |
| Hall | C5×C71 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | D71 |
| commutator, hypocenter | C71 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C71 | C2 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C5×C13 | |
16 conjugacy classes of subgroups.
2405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D13×D71, D5×C13×D71, D65×D71, … |
| maximal normal subgroup of | C5×D13×D71, D5×C13×D71, D65×D71, … |
| maximal quotient of | C5×C13×Dic71, C2×C5×C13×D71, C3×C5×C13×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9230, 3);