Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C214 |
| direct product | C22×#6548⋊C3 |
| Fitting | C23×C7×D4 ⋊ C2×C3 |
| Hall | C22×#6548 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C22×H(5,𝔽2) |
| Sylow | C7 ⋊ C22×C3×H(5,𝔽2) |
13120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | C22×H(5,𝔽2)×AGL(1,𝔽7), #72277927, #72277956 |
| maximal normal subgroup of | C22×H(5,𝔽2)×AGL(1,𝔽7), #72277927, #72277956 |
| maximal quotient of | #72277632 |
Past the SmallGroups library coverage — no SmallGroups id.