Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#11724055 |
| Fitting | C24×C33 ⋊ D3 |
| derived | C32⋊(C22⋊A4) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊#1020 |
| commutator, cosocle, hypocenter | C32⋊(C22⋊A4) | C2×C3 |
| Frattini | C3 | C3×C3⋊#1020 |
| Fitting | C24×C33 | D3 |
| socle | C24×C32 | C3⋊D3 |
| LCS | G ▷ C32⋊(C22⋊A4) | |
| UCS | C1 ◁ C32 | |
1004 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
138 conjugacy classes — view the full character table.
| maximal subgroup of | #72220513, #72220612 |
| maximal normal subgroup of | #72220612 |
Past the SmallGroups library coverage — no SmallGroups id.