Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C52 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D52 |
| commutator | C2×C52 | C22×C4 |
| Frattini | C22 | C2×D52 |
| Fitting | C2×C4×C52 | C22 |
| socle, cosocle | C22×C52 | C23 |
| prime radical | C22×C5⋊D5 | C22 |
| hypocenter | C52 | #117 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=d,c^2=e,b^a=be,g^a=g^4,f^b=f^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #13099896, #13099898, #13099979, … |
| maximal normal subgroup of | #13099896, #13099898, #13099979, … |
| maximal quotient of | #13100477, #13100478, #13100479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 651);