Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of AGL(1,𝔽5)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)2 |
| commutator, hypocenter | C52 | C4×C8 |
| Fitting, socle | C2×C52 | C42 |
| prime radical | C2×C5⋊D5 | C2×C4 |
| cosocle | #6036 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,c^2=e,d^2=e,g^a=g^2,f^b=f^2,g^c=g^4,f^d=f^450 conjugacy classes — view the full character table.
| maximal subgroup of | #13107437, #13107438, #13107449, … |
| maximal normal subgroup of | #13107437, #13107438, #13107449, … |
| maximal quotient of | #13103266, #13103267, #13103270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 959);