Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D5⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C5×C25 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5⋊#1035 |
| commutator, hypocenter | C5×C25 | C42 |
| Frattini | C2×C5 | D5⋊AGL(1,𝔽5) |
| Fitting | C2×C5×C25 | C2×C4 |
| socle | C2×C52 | C2×AGL(1,𝔽5) |
| prime radical, cosocle | C2×C5⋊D25 | C22 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C2 | |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,f^5=g,e^a=e^2,f^a=f^2g,g^a=g^2,e^b=e^4,e^c=e^4,f^c=f^4g^4,g^c=g^468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 258);