Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C11⋊C5×#585 |
| Fitting, Hall | C11×#585 ⋊ C5 |
| Sylow | C11 ⋊ C5×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C24×C11⋊C5 |
| commutator, socle, cosocle | C2×C11 | C25×C5 |
| Frattini | C2 | C25×C11⋊C5 |
| Fitting | C11×#585 | C5 |
| hypercenter | #585 | C11⋊C5 |
| hypocenter | C11 | C5×#585 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
238 conjugacy classes — view the full character table.
| maximal subgroup of | #585×AGL(1,𝔽11), C11⋊C5×#3585, #72269585 |
| maximal normal subgroup of | #585×AGL(1,𝔽11), C11⋊C5×#3585, #72269585 |
Past the SmallGroups library coverage — no SmallGroups id.