Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D25⋊C16 |
| derived, Sylow | C25 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #1035 |
| commutator, hypocenter | C25 | C2×C16 |
| Frattini | C4×C5 | C2×AGL(1,𝔽5) |
| Fitting | C8×C25 | C4 |
| socle | C2×C5 | D5⋊C8 |
| prime radical | C2×D25 | C8 |
| cosocle | #6014 | C22 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C8 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,c^2=d,d^2=e,f^5=g,f^a=f^2g,g^a=g^2,f^c=f^4g^4,g^c=g^480 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#1035, #13097830, #13097890, … |
| maximal normal subgroup of | C16×#1035, #13097830, #13097890, … |
| maximal quotient of | D25⋊C32, #13097828, #13097864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 64);