Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C25 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #1035 |
| commutator, hypocenter | C25 | C32 |
| Frattini | C5×C8 | AGL(1,𝔽5) |
| Fitting | C8×C25 | C4 |
| socle, prime radical | C2×C5 | #674 |
| cosocle | #87707 | C2 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C8 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=b,b^2=c,c^2=d,d^2=e,f^5=g,f^a=f^2g,g^a=g^2,f^b=f^4g^4,g^b=g^480 conjugacy classes — view the full character table.
| maximal subgroup of | D25⋊C32, #13097828, C2×#11716344, … |
| maximal normal subgroup of | D25⋊C32, #13097828, C2×#11716344, … |
| maximal quotient of | #13097651, C2×#11716344 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 3);