Finite Group DatabasebetaFinite Group Databasebeta| order | 18666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D153 |
| unambiguous semidirect product | C9⋊(D17×C61) |
| unambiguous semidirect product | C17⋊(D9×C61) |
| Fitting, Hall | C9×C17×C61 ⋊ C2 |
| derived, Hall | C9×C17 ⋊ C2×C61 |
| Hall | C17×C61 ⋊ D9 |
| Hall | C9×C61 ⋊ D17 |
| Sylow | C17 ⋊ D9×C61 |
| Sylow | C9 ⋊ D17×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D153 |
| commutator, cosocle, hypocenter | C9×C17 | C2×C61 |
| Frattini | C3 | C61×D51 |
| Fitting | C9×C17×C61 | C2 |
| socle | C3×C17×C61 | D3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C61 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9333 |
4758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D153, D9×D17×C61, D153⋊D61, … |
| maximal normal subgroup of | D61×D153, D9×D17×C61, D153⋊D61, … |
| maximal quotient of | C61×Dic153, C2×C61×D153 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18666, 8);