Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D25⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #87707⋊C5 |
| derived | C25 ⋊ C5×C16 |
| Sylow | 5−1+2 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D25⋊C5 |
| commutator, hypocenter | C25 | C5×C16 |
| Frattini | C5×C8 | C5×D5 |
| Fitting | C8×5−1+2 | C2 |
| socle | C2×C5 | C5×#168 |
| prime radical | C2×C52 | #168 |
| cosocle | C8×C25 | C2×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C8 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2,5,2^3,5^2|a^2=c,c^2=d,d^2=e,f^5=g,f^a=f^4g^4,g^a=g^4,f^b=fg^4176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 52);