Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (D5⋊AGL(1,𝔽5))⋊C2 |
| commutator, prime radical, cosocle | C2×C5⋊D5 | C23 |
| Fitting, socle | C2×C52 | #41 |
| hypocenter | C52 | #125 |
| LCS | G ▷ C2×C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C2 | |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=e,c^2=e,c^a=ce,f^a=f^2,g^a=g^2,c^b=cd,f^b=g,g^b=f,f^c=g^2,g^c=f^3,f^d=f^4,g^d=g^426 conjugacy classes — view the full character table.
| maximal subgroup of | #13107442, (D5⋊AGL(1,𝔽5))⋊Q8, #13107482, … |
| maximal normal subgroup of | #13107442, (D5⋊AGL(1,𝔽5))⋊Q8, #13107482, … |
| maximal quotient of | #13103357, #13103363, #13103364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 972);