Finite Group DatabasebetaFinite Group Databasebeta| order | 558 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D31⋊C3 |
| unambiguous semidirect product | D31⋊C32 |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C3) |
| unambiguous semidirect product | (C3×D31)⋊C3 |
| Fitting, socle | C3×C31 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C32 |
| Hall | C3×C31⋊C3 ⋊ C2 |
| Hall | D31 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 93 |
33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D31⋊C3, C2×C3×D31⋊C3, C9×D31⋊C3, … |
| maximal normal subgroup of | D3×D31⋊C3, C2×C3×D31⋊C3, C9×D31⋊C3, … |
| maximal quotient of | C3×(C31⋊C3)⋊C4, C2×C3×D31⋊C3, C9×D31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(558, 7);