Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #498 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
Polycyclic presentation:
2^6,5^2|a^2=e,b^2=e,c^2=ef,d^2=f,b^a=be,c^a=ce,g^a=g^4,h^a=h^4,c^b=cd,d^b=df,d^c=df190 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#498, #72223075, #72223078, … |
| maximal normal subgroup of | C5⋊D5×#498, #72223075, #72223078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5069);