Finite Group DatabasebetaFinite Group Databasebeta| order | 18666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3 |
| Fitting, socle | C2×C3×C17×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C2×C32×C17 |
| Hall | C2×C17×C61 ⋊ C32 |
| Hall | C17×C61 ⋊ C2×C32 |
| Hall | C2×C61 ⋊ C32×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C17 | C61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C2×C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C17×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C3×C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6222 |
2346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×Dic61⋊C3, C3×Dic1037⋊C3, C3×Dic17×C61⋊C3, … |
| maximal normal subgroup of | C3×C17×Dic61⋊C3, C3×Dic1037⋊C3, C3×Dic17×C61⋊C3, … |
| maximal quotient of | C3×C4×C17×C61⋊C3, C22×C3×C17×C61⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18666, 21);