Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C25 ⋊ C4 |
| Sylow | C25 ⋊ #384 |
279 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,c^2=e,g^5=h,b^a=bf,c^a=ce,g^a=g^2h,h^a=h^2,g^d=g^4h^4,h^d=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #127×#1035, #72275647, #72275693 |
| maximal normal subgroup of | #127×#1035, #72275647, #72275693 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1029);