Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C3×C3⋊#1020 |
| Fitting, socle | C26×C32 ⋊ D3 |
| derived | C3×C22⋊A4 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C3⋊#1020 |
| commutator, cosocle, hypocenter | C3×C22⋊A4 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C26×C32 | D3 |
| LCS | G ▷ C3×C22⋊A4 | |
| UCS | C1 ◁ C22×C3 | |
7258 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 7258 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213301, C22×#72213207, C22×#72213251, … |
| maximal normal subgroup of | C3×A4×C3⋊#1020 |
| maximal quotient of | C3×#72215523, C22×#72220148 |
Past the SmallGroups library coverage — no SmallGroups id.