Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#11924176 |
| Hall | C2×#87641 ⋊ C32 |
| Hall | C3×#3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C32×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #64423⋊C2 |
| commutator, cosocle | C2×C72 | C23×C32 |
| Frattini | C2 | C2×C3×#64423⋊C2 |
| Fitting, socle | C22×C3×C72 | C22×C3 |
| hypocenter | C72 | C2×C32×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C22×C3 | |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#72210376, C2×D3×#11924176, C2×#72222111 |
| maximal normal subgroup of | C2×C3×#72210376, C2×D3×#11924176, C2×#72222111 |
Past the SmallGroups library coverage — no SmallGroups id.