Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11765324 |
| Fitting | C2×C4×C5×C7 ⋊ C2×C4 |
| Hall | C5×C7 ⋊ C2×C4×D4 |
| Sylow | C7 ⋊ C2×D4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#6456 |
852 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
134 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72217707, C2×D4×D7×AGL(1,𝔽5), #72218554, … |
| maximal normal subgroup of | C2×#72217707, C2×D4×D7×AGL(1,𝔽5), #72218554, … |
| maximal quotient of | #72218554, #72218605 |
Past the SmallGroups library coverage — no SmallGroups id.