Finite Group DatabasebetaFinite Group Databasebeta| order | 18294 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D3049⋊C3 |
| unambiguous semidirect product | (C3049⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C3049 ⋊ C2×C3 |
| Hall | C3049⋊C3 ⋊ C2 |
| Hall | D3049 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3049 | C2×C3 |
| LCS | G ▷ C3049 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3049 |
Polycyclic presentation:
2,3,3049|c^a=c^3048,c^b=c^2516514 conjugacy classes — view the full character table.
| maximal subgroup of | #27131906⋊C3, C2×D3049⋊C3 |
| maximal normal subgroup of | #27131906⋊C3, C2×D3049⋊C3 |
| maximal quotient of | Dic3049⋊C3, C2×D3049⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18294, 1);