Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C32 |
| direct product | C22×#10620193 |
| Fitting, socle | C22×C34 ⋊ C8 |
| derived, Sylow | C34 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #10620193 |
| commutator, hypocenter | C34 | C22×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C8 |
| prime radical | C22×C3⋊(C3⋊(C3⋊D3)) | C4 |
| cosocle | #66472 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
1060 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213723, C22×#13049804, #72220306, … |
| maximal normal subgroup of | C2×#72213723, C22×#13049804, #72220306, … |
Past the SmallGroups library coverage — no SmallGroups id.