Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊AGL(1,𝔽5) |
| Sylow | C52 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)2 |
| commutator, Fitting, socle | C2×C52 | C42 |
| prime radical, cosocle | C2×D52 | C22 |
| hypocenter | C52 | #95 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,b^a=be,g^a=g^2,f^b=f^2,g^c=g^4,f^d=f^438 conjugacy classes — view the full character table.
| maximal subgroup of | #13107439, #13107440, #13107444, … |
| maximal normal subgroup of | #13107439, #13107440, #13107444, … |
| maximal quotient of | #13103254, #13103255, #13103256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 957);