Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#13049215 |
| Fitting | C23×C33 ⋊ C2×D3 |
| derived | C3×C22⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13049215 |
| commutator, cosocle, hypocenter | C3×C22⋊H(3,𝔽3) | C23 |
| Frattini | C3 | C2×D3×C3⋊S4 |
| Fitting | C23×C33 | C2×D3 |
| socle | C23×C32 | D32 |
| LCS | G ▷ C3×C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
1438 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 1438 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72222973, C2×D3×((C3⋊S4)⋊C3)⋊C2, #72222989 |
| maximal normal subgroup of | #72222973, C2×D3×((C3⋊S4)⋊C3)⋊C2, #72222989 |
| maximal quotient of | #72222973 |
Past the SmallGroups library coverage — no SmallGroups id.