Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D5×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C5×C25 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D5×D25 |
| commutator, hypocenter | C5×C25 | C2×C8 |
| Frattini | C4×C5 | D52 |
| Fitting, cosocle | C4×C5×C25 | C22 |
| socle | C2×C52 | C4×D5 |
| prime radical | C2×C5⋊D25 | C4 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=c,c^2=d,f^5=g,f^a=f^4g^4,g^a=g^4,e^b=e^4224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 74);