Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | (C3⋊D3)⋊C3×#626 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D32×(C3⋊D3)⋊C3 |
| commutator, cosocle | C2×C34 | C23×C3 |
| Frattini | C2×C3 | C3×D33 |
| Fitting | C2×C32×H(3,𝔽3) | C23 |
| socle | C2×C33 | C22×C3×D3 |
| hypocenter | C34 | C2×C3×D4 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 | |
1504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #626×PSU(3,𝔽2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.