Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3×#92281 |
| Fitting | C2×C3×#6909 ⋊ C2 |
| Sylow | C3×#6909 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C22×C33 |
| Frattini | C32 | C2×C33×D3 |
| Fitting | C2×C3×#6909 | C2 |
| hypercenter | C2×C33 | (C3⋊D3)⋊C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C2×C32 ◁ C2×C33 | |
1270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
204 conjugacy classes — view the full character table.
| maximal quotient of | C2×#72221881 |
Past the SmallGroups library coverage — no SmallGroups id.