Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | Dic3×C3⋊AGL(1,𝔽9) |
| derived, Sylow | C34 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C3⋊AGL(1,𝔽9) |
| commutator, hypocenter | C34 | C4×C8 |
| Fitting, socle | C2×C34 | C2×C8 |
| prime radical | C2×C32×C3⋊D3 | C2×C4 |
| cosocle | C2×C32×#157 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
273 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #72259757 |
| maximal normal subgroup of | #72259757 |
Past the SmallGroups library coverage — no SmallGroups id.