Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C25×C22⋊Q8 ⋊ C2 |
| Sylow | C25 ⋊ #542 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=f,b^2=f,c^2=e,d^2=f,g^5=h,d^a=df,g^a=g^4h^4,h^a=h^4,c^b=cf,d^b=de,d^c=df190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1302);