Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×C3⋊D231 |
| unambiguous semidirect product | C3⋊(C7×D231) |
| unambiguous semidirect product | C7⋊(C7×C3⋊D33) |
| unambiguous semidirect product | C11⋊(C7×C3⋊D21) |
| Fitting, socle, Hall | C32×C72×C11 ⋊ C2 |
| derived | C32×C7×C11 ⋊ C2×C7 |
| Hall | C72×C11 ⋊ C3⋊D3 |
| Hall | C32×C72 ⋊ D11 |
| Hall | C32×C11 ⋊ C7×D7 |
| Sylow | C72 ⋊ C3⋊D33 |
| Sylow | C11 ⋊ C7×C3⋊D21 |
| Sylow | C32 ⋊ C7×D77 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊D231 |
| commutator, cosocle, hypocenter | C32×C7×C11 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C11 | C2 |
| LCS | G ▷ C32×C7×C11 | |
| UCS | C1 ◁ C7 | |
132 conjugacy classes of subgroups.
2436 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D11×C3⋊D21, C7×D7×C3⋊D33, C7×C3⋊D3×D77, … |
| maximal normal subgroup of | C7×D11×C3⋊D21, C7×D7×C3⋊D33, C7×C3⋊D3×D77, … |
| maximal quotient of | C7×C3⋊Dic231, C2×C7×C3⋊D231 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 134);