Finite Group DatabasebetaFinite Group Databasebeta| order | 18666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C17×C61 ⋊ C2×C3 |
| derived, Hall | C17×C61 ⋊ C2×C32 |
| Hall | C3×C17×C61⋊C3 ⋊ C2 |
| Hall | D1037 ⋊ C32 |
| Hall | C3×C61⋊C3 ⋊ D17 |
| Sylow | C61 ⋊ C32×D17 |
| Sylow | C17 ⋊ C3×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C17⋊(D61⋊C3) |
| commutator, cosocle, hypocenter | C17×C61 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C61 | C2×C3 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3111 |
600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#16861895⋊C3, C3×#16861896⋊C3, C3×D17×D61⋊C3, … |
| maximal normal subgroup of | C3×#16861895⋊C3, C3×#16861896⋊C3, C3×D17×D61⋊C3, … |
| maximal quotient of | C3×Dic1037⋊C3, C2×C3×C17⋊(D61⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18666, 15);