Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #103 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^4,g^a=g^4,d^b=de134 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3967, #13101718, #13101719, … |
| maximal normal subgroup of | D5×#3967, #13101718, #13101719, … |
| maximal quotient of | #13099563, Q8⋊#6029, #13099572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 361);