Finite Group DatabasebetaFinite Group Databasebeta| order | 18660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C311⋊C5 |
| unambiguous semidirect product | C3⋊(C22×C311⋊C5) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C311⋊C5) |
| unambiguous semidirect product | (C2×D3×C311)⋊C5 |
| Fitting, socle | C2×C3×C311 ⋊ C2×C5 |
| derived, Hall | C3×C311 ⋊ C22×C5 |
| Hall | C3×C311⋊C5 ⋊ C22 |
| Hall | C2×D3×C311 ⋊ C5 |
| Sylow | C311 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ C22×C311⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C311⋊C5 |
| commutator, cosocle, hypocenter | C3×C311 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C311 | C2×C5 |
| LCS | G ▷ C3×C311 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1866 |
402 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18660, 18);