Finite Group DatabasebetaFinite Group Databasebeta| order | 558 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C31 |
| unambiguous semidirect product | C3⋊(C2×C3×C31) |
| Fitting, socle, Hall | C32×C31 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C31 |
| Sylow | C32 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C31 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C31 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 186 |
279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D31, D32×C31, D3×D93, … |
| maximal normal subgroup of | C3×D3×D31, D32×C31, D3×D93, … |
| maximal quotient of | C3×Dic3×C31, C2×C3×D3×C31, C3×D9×C31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(558, 12);