Finite Group DatabasebetaFinite Group Databasebeta| order | 18666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C61 · Schur multiplier (H2) = C3 |
| direct product | C32×D17×C61 |
| unambiguous semidirect product | C17⋊(C2×C32×C61) |
| Fitting, socle, Hall | C32×C17×C61 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C32×C61 |
| Hall | C17×C61 ⋊ C2×C32 |
| Hall | C32×C17 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C61 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C32×C61 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C61 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C32×C61 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9333 |
5490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C61×#595, C32×#16861897, C32×D17×D61, … |
| maximal normal subgroup of | C32×C61×#595, C32×#16861897, C32×D17×D61, … |
| maximal quotient of | C32×C61×Dic17, C2×C32×D17×C61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18666, 31);