Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×#66869⋊C5 |
| Fitting | C2×C42×C11 ⋊ C2×C5 |
| Hall | C2×#66869 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×#104 |
| Sylow | C11 ⋊ C2×C5×#104 |
340 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#104×AGL(1,𝔽11), C2×#72222331, C2×#72222335 |
| maximal normal subgroup of | C2×#104×AGL(1,𝔽11), C2×#72222331, C2×#72222335 |
Past the SmallGroups library coverage — no SmallGroups id.