Finite Group DatabasebetaFinite Group Databasebeta| order | 6496 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | #127×C29⋊C7 |
| Fitting, Hall | C29×#127 ⋊ C7 |
| Sylow | C29 ⋊ C7×#127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C29⋊C7 |
| commutator, socle, cosocle | C22×C29 | C23×C7 |
| Fitting | C29×#127 | C7 |
| hypercenter | #127 | C29⋊C7 |
| hypocenter | C29 | C7×#127 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #127 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #127×D29⋊C7 |
| maximal normal subgroup of | #127×D29⋊C7 |
Past the SmallGroups library coverage — no SmallGroups id.