Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#72222008 |
| derived, Sylow | C72 ⋊ C22×C32×C4 |
| Hall | C2×#87639 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ C22×C4 |
680 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
196 conjugacy classes — view the full character table.
| maximal quotient of | #72245201 |
Past the SmallGroups library coverage — no SmallGroups id.