Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#72222160 |
| Fitting, socle | C23×C72 ⋊ C2×C32 |
| derived | C22×C72 ⋊ C22×C32 |
| Hall | C23×C7⋊D7 ⋊ C32 |
| Sylow | C72 ⋊ C22×C3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72222160 |
| commutator, cosocle, hypocenter | C22×C72 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C23×C72 | C2×C32 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C2 | |
660 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
80 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72222160 |
| maximal normal subgroup of | C22×#72222160 |
| maximal quotient of | C22×#72222160 |
Past the SmallGroups library coverage — no SmallGroups id.