Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | D33×A4 |
| Fitting, socle, derived | C22×C33 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C33 | C23×C3 |
| LCS | G ▷ C22×C33 | |
| UCS | C1 | |
1880 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10595527⋊C3, D32×A4×S4, D33×S4 |
| maximal normal subgroup of | D33×S4 |
| maximal quotient of | D3×#10595527⋊C3, D32×A4×S4 |
Past the SmallGroups library coverage — no SmallGroups id.