Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,ℤ/25) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (D25⋊C5)⋊C8 |
| unambiguous semidirect product | (D25⋊C8)⋊C5 |
| derived | C25 ⋊ C2×C5×C8 |
| Sylow | 5−1+2 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | AGL(1,ℤ/25) |
| commutator, hypocenter | C25 | C2×C5×C8 |
| Frattini, socle | C2×C5 | C2×C5×AGL(1,𝔽5) |
| Fitting | C4×5−1+2 | C4 |
| prime radical | C2×D25⋊C5 | C4 |
| cosocle | Dic25 | C22×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C4 | |
69 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^2,5,2^2,5^2|a^2=d,b^2=e,d^2=e,f^5=g,f^a=f^2g,g^a=g^2,f^c=fg,f^d=f^4g^4,g^d=g^4104 conjugacy classes — view the full character table.
| maximal subgroup of | #72275728, C8×AGL(1,ℤ/25), #72275733, … |
| maximal normal subgroup of | #72275728, C8×AGL(1,ℤ/25), #72275733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 286);