Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C52 ⋊ #108 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^4,g^a=g^4206 conjugacy classes — view the full character table.
| maximal subgroup of | #13099291, #13099297, #13099300, … |
| maximal normal subgroup of | #13099291, #13099297, #13099300, … |
| maximal quotient of | #13099490, #13099491, #13099586, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 345);