Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C52 ⋊ #386 |
808 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|b^2=f,c^2=d,b^a=bf,c^a=ce,g^a=g^4,c^b=ce,h^b=h^4172 conjugacy classes — view the full character table.
| maximal subgroup of | #72223419 |
| maximal normal subgroup of | #72223419 |
| maximal quotient of | #72223414, #72223418, #72226410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3910);