Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27×C3 |
| direct product | C22×C3⋊D3×C22⋊A4 |
| Fitting, socle | C26×C32 ⋊ C2×C3 |
| derived | C24×C32 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊D3×C22⋊A4 |
| commutator, cosocle, hypocenter | C24×C32 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C26×C32 | C2×C3 |
| LCS | G ▷ C24×C32 | |
| UCS | C1 ◁ C22 | |
59824 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 59824 conjugacy classes of subgroups — too many to draw. Only its 328 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213266 |
| maximal normal subgroup of | C22×#72213266 |
Past the SmallGroups library coverage — no SmallGroups id.