Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×#64423 |
| Fitting, socle | C22×C3×C72 ⋊ C22×C3 |
| derived | C3×C72 ⋊ C24×C3 |
| Hall | C3×#3861 ⋊ C24 |
| Sylow | C72 ⋊ C23×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#64423 |
| commutator, cosocle, hypocenter | C3×C72 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C72 | C22×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C22 | |
1343 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1343 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#64423⋊C2, C2×D3×#11924207, C2×D3×#11924176 |
| maximal normal subgroup of | C22×D3×#64423⋊C2, C2×D3×#11924207, C2×D3×#11924176 |
| maximal quotient of | C2×D3×#11924207 |
Past the SmallGroups library coverage — no SmallGroups id.