Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#13091424 |
| Fitting | C2×#10624869 ⋊ C2 |
| derived | C9×H(3,𝔽3) ⋊ C22×C3 |
| Sylow | #10624869 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊#4207 |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C22×C3 |
| Frattini | C32 | C2×C3×C3⋊(C3⋊D3) |
| Fitting | C2×#10624869 | C2 |
| socle | C2×C32 | C3×C3⋊(C3⋊D3) |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
1227 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221819, C2×#72221823, C2×#72221851 |
| maximal normal subgroup of | C2×#72221823, C2×#72221851 |
Past the SmallGroups library coverage — no SmallGroups id.