Finite Group DatabasebetaFinite Group Databasebeta| order | 18666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D61⋊C9) |
| unambiguous semidirect product | (C61⋊C9)⋊D17 |
| unambiguous semidirect product | D1037⋊C9 |
| derived, Hall | C17×C61 ⋊ C2×C9 |
| Hall | C17×C61⋊C9 ⋊ C2 |
| Hall | D1037 ⋊ C9 |
| Hall | C61⋊C9 ⋊ D17 |
| Sylow | C61 ⋊ C9×D17 |
| Sylow | C17 ⋊ D61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C17⋊(D61⋊C3) |
| commutator, hypocenter | C17×C61 | C2×C9 |
| Fitting, socle, cosocle | C3×C17×C61 | C2×C3 |
| prime radical | C3×D1037 | C3 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9333 |
Polycyclic presentation:
2,3,17,61,3|b^3=e,c^a=c^16,d^a=d^60,d^b=d^47600 conjugacy classes — view the full character table.
| maximal subgroup of | #16861895⋊C9, #16861896⋊C9, D17×D61⋊C9, … |
| maximal normal subgroup of | #16861895⋊C9, #16861896⋊C9, D17×D61⋊C9, … |
| maximal quotient of | Dic1037⋊C9, C2×C17⋊(D61⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18666, 12);