Finite Group DatabasebetaFinite Group Databasebeta| order | 7040 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C11⋊C5×#3498 |
| Fitting, Hall | C11×#3498 ⋊ C5 |
| Sylow | C11 ⋊ C5×#3498 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×C11⋊C5 |
| commutator, socle, cosocle | C22×C11 | C25×C5 |
| Fitting | C11×#3498 | C5 |
| hypercenter | #3498 | C11⋊C5 |
| hypocenter | C11 | C5×#3498 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #3498 | |
3496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽11)×#3498 |
| maximal normal subgroup of | AGL(1,𝔽11)×#3498 |
Past the SmallGroups library coverage — no SmallGroups id.