Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3⋊D3×#1020 |
| Fitting, socle | C25×C32 ⋊ C2×D3 |
| derived | C32×C22⋊A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D3×#1020 |
| commutator, cosocle, hypocenter | C32×C22⋊A4 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C25×C32 | C2×D3 |
| LCS | G ▷ C32×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
8778 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 8778 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#1020, C2×#72210357 |
| maximal normal subgroup of | C2×#72210357 |
| maximal quotient of | D3×C3⋊D3×#1020 |
Past the SmallGroups library coverage — no SmallGroups id.