Finite Group DatabasebetaFinite Group Databasebeta| order | 9734 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C157 · Schur multiplier (H2) = C1 |
| direct product | D31×C157 |
| unambiguous semidirect product | C31⋊(C2×C157) |
| Fitting, socle, Hall | C31×C157 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C157 | D31 |
| commutator, cosocle, hypocenter | C31 | C2×C157 |
| Frattini | C1 | G |
| Fitting, socle | C31×C157 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C157 | |
8 conjugacy classes of subgroups.
2669 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D157, C2×D31×C157, C3×D31×C157, … |
| maximal normal subgroup of | D31×D157, C2×D31×C157, C3×D31×C157, … |
| maximal quotient of | Dic31×C157, C2×D31×C157, C3×D31×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9734, 1);