Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of (D5⋊AGL(1,𝔽5))⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C52 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (D5⋊AGL(1,𝔽5))⋊C2 |
| commutator | C5⋊D5 | C22×C4 |
| Fitting, socle | C2×C52 | #41 |
| prime radical | C2×D52 | C22 |
| cosocle | C2×C5⋊D5 | C23 |
| hypocenter | C52 | #117 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C2 | |
133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
Polycyclic presentation:
2^5,5^2|a^2=d,c^2=e,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^432 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)2⋊C4, (D5⋊AGL(1,𝔽5))⋊Q8, #13107482, … |
| maximal normal subgroup of | AGL(1,𝔽5)2⋊C4, (D5⋊AGL(1,𝔽5))⋊Q8, #13107482, … |
| maximal quotient of | #13103306, #13103307, #13103308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 965);