Finite Group DatabasebetaFinite Group Databasebeta| order | 18162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #22583794⋊C2 |
| Fitting, socle, derived, Sylow | C1009 ⋊ C2×C9 |
| Hall | #22583794 ⋊ C2 |
| Hall | D1009 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1009 | C2×C9 |
| prime radical | D1009⋊C3 | C3 |
| cosocle | C1009⋊C3 | C2×C3 |
| LCS | G ▷ C1009 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1009 |
Polycyclic presentation:
2,3^2,1009|b^3=c,d^a=d^1008,d^b=d^759,d^c=d^37474 conjugacy classes — view the full character table.
| maximal subgroup of | #49138047, C2×#22583794⋊C2 |
| maximal normal subgroup of | #49138047, C2×#22583794⋊C2 |
| maximal quotient of | #49138035, C2×#22583794⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18162, 8);