Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C25 ⋊ C4×Q8 |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=d,c^2=de,f^5=g,f^a=f^4g^4,g^a=g^4,c^b=cd140 conjugacy classes — view the full character table.
| maximal subgroup of | #13097855, #13098035, #13098041, … |
| maximal normal subgroup of | #13097855, #13098035, #13098041, … |
| maximal quotient of | #13097923, #13097925, #13097929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 108);