Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C52 ⋊ Q32 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^4,g^a=g^4203 conjugacy classes — view the full character table.
| maximal subgroup of | #13099243, #13099246, #13099482, … |
| maximal normal subgroup of | #13099243, #13099246, #13099482, … |
| maximal quotient of | #13099538, #13099543, C2×#11716668 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 327);