Finite Group DatabasebetaFinite Group Databasebeta| order | 9548 |
| isoclinism | isoclinic class of D77 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic77 |
| unambiguous semidirect product | C7⋊(C31×Dic11) |
| unambiguous semidirect product | C11⋊(Dic7×C31) |
| derived, Hall | C7×C11 ⋊ C4×C31 |
| Hall | C7×C11×C31 ⋊ C4 |
| Hall | C11×C31 ⋊ Dic7 |
| Hall | C7×C31 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic7×C31 |
| Sylow | C7 ⋊ C31×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D77 |
| commutator, hypocenter | C7×C11 | C4×C31 |
| Frattini | C2 | C31×D77 |
| Fitting, socle, prime radical | C2×C7×C11×C31 | C2 |
| cosocle | C2×C7×C11 | C2×C31 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C2×C31 | |
24 conjugacy classes of subgroups.
2480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C31×Dic77, C31×Dic231, C31⋊C3×Dic77, … |
| maximal normal subgroup of | C3×C31×Dic77, C31⋊C3×Dic77, C31×C11⋊(ΓL(1,𝔽8)⋊C4), … |
| maximal quotient of | C3×C31×Dic77, C31×Dic231 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9548, 7);