Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#11724114 |
| Sylow | C34 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×GO+(4,𝔽2) |
| commutator, cosocle | C2×C3×C3⋊D3 | C23×C3 |
| Frattini | C2 | C3×D3×GO+(4,𝔽2) |
| Fitting, socle | C2×C34 | C2×D4 |
| hypocenter | C33 | C3×#121 |
| LCS | G ▷ C2×C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C2×C3 | |
856 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13180139 |
| maximal normal subgroup of | C3×#13180139 |
Past the SmallGroups library coverage — no SmallGroups id.