Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#11924174 |
| derived | C3×C72 ⋊ C22×C3×C4 |
| Hall | C3×#3861 ⋊ C22×C4 |
| Sylow | C72 ⋊ C2×C3×C4×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#64423⋊C2 |
| commutator, hypocenter | C3×C72 | C22×C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72 | C23×C3 |
| prime radical | C2×D3×#64424 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
671 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210376, #72222196, C2×D3×#11924174 |
| maximal normal subgroup of | D3×#72210376, C2×D3×#11924174 |
| maximal quotient of | #72222196, C2×D3×#11924174 |
Past the SmallGroups library coverage — no SmallGroups id.