Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×AΓL(1,𝔽25) |
| Fitting, socle | C2×C52 ⋊ ΓL(1,𝔽25) |
| Hall | C52⋊C3 ⋊ C2×M16 |
| Sylow | C52 ⋊ C2×ΓL(1,𝔽25) |
163 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
40 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(2,𝔽5), C22×AΓL(1,𝔽25), D3×AΓL(1,𝔽25), … |
| maximal normal subgroup of | C22×AΓL(1,𝔽25), C4×AΓL(1,𝔽25) |
| maximal quotient of | C22×AΓL(1,𝔽25), D3×AΓL(1,𝔽25), C4×AΓL(1,𝔽25) |
Past the SmallGroups library coverage — no SmallGroups id.