Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C32 |
| direct product | C2×#13049399 |
| derived, Sylow | C34 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊D3×#157 |
| commutator, hypocenter | C34 | C22×C8 |
| Frattini | C2 | C2×C3⋊D3×#157 |
| Fitting, socle | C22×C34 | C2×C4 |
| prime radical | C22×C3⋊(C3⋊(C3⋊D3)) | C4 |
| cosocle | C32×C3⋊Dic3 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
1484 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 1484 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220201, #72252796, C2×#72220228, … |
| maximal normal subgroup of | C2×#72220201, #72252796, C2×#72220228, … |
Past the SmallGroups library coverage — no SmallGroups id.