Finite Group DatabasebetaFinite Group Databasebeta| order | 18099 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C2011⋊C9 |
| derived, Sylow | C2011 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C2011⋊C3 |
| commutator, hypocenter | C2011 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C2011 | C3 |
| LCS | G ▷ C2011 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18099 |
Polycyclic presentation:
3^2,2011|a^3=b,c^a=c^2052019 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D2011⋊C9, C2×C2011⋊C9 |
| maximal normal subgroup of | D2011⋊C9, C2×C2011⋊C9 |
| maximal quotient of | C2×C2011⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18099, 1);