Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C2×H(5,𝔽2)×C11⋊C5 |
| Fitting, Hall | C2×C11×H(5,𝔽2) ⋊ C5 |
| Sylow | C11 ⋊ C2×C5×H(5,𝔽2) |
1796 conjugacy classes of subgroups; only the 1131 normal subgroups are shown.
This group has 1796 conjugacy classes of subgroups — too many to draw. Only its 1131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
238 conjugacy classes — view the full character table.
| maximal subgroup of | C2×H(5,𝔽2)×AGL(1,𝔽11), C11⋊C5×#3484, C2×C11⋊C5×#453, … |
| maximal normal subgroup of | C2×H(5,𝔽2)×AGL(1,𝔽11), C11⋊C5×#3484, C2×C11⋊C5×#453, … |
| maximal quotient of | C11⋊C5×#3484, C11⋊C5×#3498 |
Past the SmallGroups library coverage — no SmallGroups id.