Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D52 |
| commutator | C2×C52 | C2×C8 |
| Fitting, cosocle | C2×C4×C52 | C22 |
| socle | C22×C52 | C2×C4 |
| prime radical | C22×C5⋊D5 | C4 |
| hypocenter | C52 | C22⋊C8 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=cd,c^2=e,b^a=bd,g^a=g^4,f^b=f^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #13099959, #13099960, #13099965, … |
| maximal normal subgroup of | #13099959, #13099960, #13099965, … |
| maximal quotient of | #13099252, #13099255, #13099278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 257);