Finite Group DatabasebetaFinite Group Databasebeta| order | 2500 |
| isoclinism | isoclinic class of AGL(1,ℤ/25) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×AGL(1,ℤ/25) |
| Fitting, Sylow | C5×5−1+2 ⋊ C4 |
| derived | C25 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | AGL(1,ℤ/25) |
| commutator, hypocenter | C25 | C4×C52 |
| Frattini | C5 | C52×AGL(1,𝔽5) |
| Fitting | C5×5−1+2 | C4 |
| socle | C52 | C5×AGL(1,𝔽5) |
| prime radical | C5×D25⋊C5 | C2 |
| cosocle | D25 | C2×C52 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C5 | |
86 conjugacy classes of subgroups.
130 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×AGL(1,ℤ/25), #72228833, D5×AGL(1,ℤ/25), … |
| maximal normal subgroup of | C2×C5×AGL(1,ℤ/25), #72228833, D5×AGL(1,ℤ/25) |
| maximal quotient of | C2×C5×AGL(1,ℤ/25), #72228833 |
Past the SmallGroups library coverage — no SmallGroups id.