Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C25 ⋊ #97 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,d^2=e,f^5=g,b^a=be,f^a=f^4g^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13097718, #13097868, #13097954, … |
| maximal normal subgroup of | #13097718, #13097868, #13097954, … |
| maximal quotient of | #13097660, #13097661, #13097718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 23);