Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×#66897⋊C5 |
| Hall | C2×#66897 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×#100 |
| Sylow | C11 ⋊ C2×C5×#100 |
372 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#100×AGL(1,𝔽11), C2×#72222332, C2×#72222335 |
| maximal normal subgroup of | C2×#100×AGL(1,𝔽11), C2×#72222332, C2×#72222335 |
Past the SmallGroups library coverage — no SmallGroups id.