Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of AGL(1,ℤ/25) |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6016⋊C5 |
| derived | C25 ⋊ C5×C8 |
| Sylow | 5−1+2 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,ℤ/25) |
| commutator, hypocenter | C25 | C5×C8 |
| Frattini, socle | C2×C5 | C5×AGL(1,𝔽5) |
| Fitting | C2×5−1+2 | C4 |
| prime radical | C2×C52 | AGL(1,𝔽5) |
| cosocle | Dic25 | C2×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2,5,2^2,5^2|a^2=c,c^2=d,e^5=f,e^a=e^2f,f^a=f^2,e^b=ef^4,e^c=e^4f^4,f^c=f^452 conjugacy classes — view the full character table.
| maximal subgroup of | (D25⋊C5)⋊C8, #87735⋊C5, C2×#6016⋊C5, … |
| maximal normal subgroup of | (D25⋊C5)⋊C8, #87735⋊C5, C2×#6016⋊C5, … |
| maximal quotient of | #87709⋊C5, C2×#6016⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 27);