Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C32 |
| direct product | C22×C3⋊#6258 |
| Fitting | C24×C33 ⋊ D3 |
| derived | C3×C22⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C3⋊(C3⋊S4) |
| commutator, cosocle, hypocenter | C3×C22⋊H(3,𝔽3) | C23 |
| Frattini | C3 | C22×C3⋊(C3⋊S4) |
| Fitting | C24×C33 | D3 |
| socle | C24×C32 | C3⋊D3 |
| LCS | G ▷ C3×C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
2478 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 2478 conjugacy classes of subgroups — too many to draw. Only its 201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
156 conjugacy classes — view the full character table.
| maximal subgroup of | #72220531, C22×((C3⋊S4)⋊C3)⋊D3, #72222948, … |
| maximal normal subgroup of | #72220531, C22×((C3⋊S4)⋊C3)⋊D3, #72222948, … |
Past the SmallGroups library coverage — no SmallGroups id.