Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C52 ⋊ #365 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^4,h^a=h^4,d^b=df256 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#365, #72253104, #72253107, … |
| maximal normal subgroup of | C5⋊D5×#365, #72253104, #72253107, … |
| maximal quotient of | #72242187, C2×#13099547 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1899);