Finite Group DatabasebetaFinite Group Databasebeta| order | 3000 |
| isoclinism | isoclinic class of D25⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×D25⋊C5 |
| Fitting | C22×C3×5−1+2 ⋊ C2 |
| derived | C25 ⋊ C23×C3×C5 |
| Hall | C3×5−1+2 ⋊ C23 |
| Sylow | 5−1+2 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D25⋊C5 |
| commutator, cosocle, hypocenter | C25 | C23×C3×C5 |
| Frattini | C5 | C22×C3×C5×D5 |
| Fitting | C22×C3×5−1+2 | C2 |
| socle | C22×C3×C5 | C5×D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C22×C3 | |
212 conjugacy classes of subgroups.
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3×AGL(1,ℤ/25), C2×C3×C4×D25⋊C5 |
| maximal normal subgroup of | C22×C3×AGL(1,ℤ/25), C2×C3×C4×D25⋊C5 |
| maximal quotient of | C2×C3×C4×D25⋊C5 |
Past the SmallGroups library coverage — no SmallGroups id.