Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D25⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D25⋊C5 |
| unambiguous semidirect product | (C8×D25)⋊C5 |
| Fitting | C8×5−1+2 ⋊ C2 |
| derived | C25 ⋊ C2×C5×C8 |
| Sylow | 5−1+2 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D25⋊C5 |
| commutator, hypocenter | C25 | C2×C5×C8 |
| Frattini | C4×C5 | C2×C5×D5 |
| Fitting | C8×5−1+2 | C2 |
| socle | C2×C5 | C4×C5×D5 |
| prime radical | C2×D25⋊C5 | C4 |
| cosocle | C4×C25 | C22×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | M16×D25⋊C5, C8×AGL(1,ℤ/25), #72275733, … |
| maximal normal subgroup of | M16×D25⋊C5, C8×AGL(1,ℤ/25), #72275733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 130);