Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C32 |
| direct product | A42×C3⋊D3 |
| Fitting, socle, derived | C24×C32 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C32 | C2×C32 |
| LCS | G ▷ C24×C32 | |
| UCS | C1 | |
1132 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72220505, C3⋊D3×A4⋊S4, D32×A42, … |
| maximal normal subgroup of | C3⋊D3×A4⋊S4, D32×A42, #72220734, … |
| maximal quotient of | C2×A42×C3⋊D3 |
Past the SmallGroups library coverage — no SmallGroups id.