Finite Group DatabasebetaFinite Group Databasebeta| order | 18666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D51×C61⋊C3 |
| unambiguous semidirect product | C3⋊(D17×C61⋊C3) |
| unambiguous semidirect product | C17⋊(D3×C61⋊C3) |
| unambiguous semidirect product | (C61×D51)⋊C3 |
| Fitting, socle, derived | C3×C17×C61 ⋊ C2×C3 |
| Hall | C3×C17×C61⋊C3 ⋊ C2 |
| Hall | C17×C61 ⋊ C3×D3 |
| Hall | C3×C61⋊C3 ⋊ D17 |
| Sylow | C61 ⋊ C3×D51 |
| Sylow | C17 ⋊ D3×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C61 | C2×C3 |
| LCS | G ▷ C3×C17×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3111 |
621 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D61⋊C3, D51⋊(D61⋊C3), D3×D17×C61⋊C3, … |
| maximal normal subgroup of | D51×D61⋊C3, D51⋊(D61⋊C3), D3×D17×C61⋊C3, … |
| maximal quotient of | C61⋊C3×Dic51, C2×D51×C61⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18666, 20);