Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C2×C33 |
| direct product | C9×Ω+(4,𝔽3) |
| Fitting | C9×H(5,𝔽2) ⋊ C32 |
| derived, Sylow | H(5,𝔽2) ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | A42 |
| commutator, hypocenter | H(5,𝔽2) | C32×C9 |
| Frattini, socle | C2×C3 | C3×A42 |
| Fitting | C9×H(5,𝔽2) | C32 |
| prime radical | C3×Ω+(4,𝔽3) | C3 |
| cosocle | C3×H(5,𝔽2) | C33 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C9 | |
348 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
225 conjugacy classes — view the full character table.
| maximal quotient of | #72276184 |
Past the SmallGroups library coverage — no SmallGroups id.