Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #334 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^4,h^a=h^4412 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#334, #72242180, #72242187, … |
| maximal normal subgroup of | C5⋊D5×#334, #72242180, #72242187, … |
| maximal quotient of | #72242187 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1842);