Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C2×C36 |
| direct product | C32×Ω+(4,𝔽3) |
| Fitting | C32×H(5,𝔽2) ⋊ C32 |
| derived, Sylow | H(5,𝔽2) ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C32 | A42 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C34 |
| Frattini | C2 | C32×A42 |
| Fitting | C32×H(5,𝔽2) | C32 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C32 | |
1320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
225 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.