Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25×C3 |
| direct product | D3×#10593630 |
| Fitting | C32×#120 ⋊ C2×D3 |
| derived | C32×C22⋊A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C22⋊A4 | C23 |
| Frattini | C22 | C2×D3×C3⋊S4 |
| Fitting | C32×#120 | C2×D3 |
| socle | C22×C32 | C22×S4 |
| LCS | G ▷ C32×C22⋊A4 | |
| UCS | C1 | |
2297 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 2297 conjugacy classes of subgroups — too many to draw. Only its 76 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 | D3×#13166068, #72220967, D32×#1020⋊C2 |
| maximal normal subgroup of | D32×#1020⋊C2 |
| maximal quotient of | D3×#13166068, #72220967 |
Past the SmallGroups library coverage — no SmallGroups id.