Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C11 · Schur multiplier (H2) = C7 |
| direct product | C72×C11×D9 |
| unambiguous semidirect product | C9⋊(C2×C72×C11) |
| Fitting, Hall | C72×C9×C11 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C72×C11 |
| Hall | C72×C9 ⋊ C2×C11 |
| Hall | C9×C11 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72×C11 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C72×C11 |
| Frattini | C3 | D3×C72×C11 |
| Fitting | C72×C9×C11 | C2 |
| socle | C3×C72×C11 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C72×C11 | |
120 conjugacy classes of subgroups.
3234 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×D9×D11, C7×C11×D7×D9, C7×D9×D77, … |
| maximal normal subgroup of | C72×D9×D11, C7×C11×D7×D9, C7×D9×D77, … |
| maximal quotient of | C72×C11×Dic9, C2×C72×C11×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 61);