Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×#157⋊D3 |
| Fitting, socle | C22×C34 ⋊ D4 |
| Sylow | C34 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #157⋊D3 |
| commutator, cosocle | C3×C3⋊D3 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | D4 |
| hypocenter | C33 | C22×C3×D4 |
| LCS | G ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C22×C3 | |
1946 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C22×(#157⋊D3)⋊D3 |
| maximal normal subgroup of | C22×(#157⋊D3)⋊D3 |
Past the SmallGroups library coverage — no SmallGroups id.