Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #346 |
123 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=bf,h^a=h^4,g^b=g^2,g^c=g^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #72242231, #72242301, #72242305 |
| maximal normal subgroup of | #72242231, #72242301, #72242305 |
| maximal quotient of | #72242225 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2157);