Finite Group DatabasebetaFinite Group Databasebeta| order | 9702 |
| isoclinism | isoclinic class of #64425 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×C11×#64425 |
| Fitting, socle | C3×C72×C11 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C32×C11 |
| Hall | C3×C11×#3862 ⋊ C2 |
| Hall | C11×C7⋊D7 ⋊ C32 |
| Hall | C72×C11 ⋊ C2×C32 |
| Hall | C3×#3862 ⋊ C2×C11 |
| Hall | C7⋊D7 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #64425 |
| commutator, cosocle, hypocenter | C72 | C2×C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C11 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C11 | |
112 conjugacy classes of subgroups.
462 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×#64425, C3×C11×#64422⋊C2, C3×#20266343, … |
| maximal normal subgroup of | C3×D11×#64425, C3×C11×#64422⋊C2, C3×#20266343, … |
| maximal quotient of | C3×C11×#10596875, C2×C3×C11×#64425 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9702, 81);