Finite Group DatabasebetaFinite Group Databasebeta| order | 31518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(D103⋊C17) |
| unambiguous semidirect product | C3⋊(C3×D103⋊C17) |
| unambiguous semidirect product | (C3×D309)⋊C17 |
| Fitting, socle, Hall | C32×C103 ⋊ C2×C17 |
| derived | C3×C103 ⋊ C2×C3×C17 |
| Hall | C32×C103⋊C17 ⋊ C2 |
| Hall | C3×D309 ⋊ C17 |
| Hall | C103⋊C17 ⋊ C3×D3 |
| Sylow | C103 ⋊ C3×D3×C17 |
| Sylow | C32 ⋊ D103⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(D103⋊C17) |
| commutator, cosocle, hypocenter | C3×C103 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C103 | C2×C17 |
| LCS | G ▷ C3×C103 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 618 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31518, 25);