Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C24×C33 |
| direct product | C22⋊A4×C3⋊(C3⋊D3) |
| Fitting, socle, derived | C24×C33 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C33 | C2×C3 |
| LCS | G ▷ C24×C33 | |
| UCS | C1 | |
4690 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 4690 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×C22⋊A4, C3⋊(C3⋊D3)×#1020, #72220648, … |
| maximal normal subgroup of | D3×C3⋊D3×C22⋊A4, C3⋊(C3⋊D3)×#1020, #72220648, … |
Past the SmallGroups library coverage — no SmallGroups id.