Finite Group DatabasebetaFinite Group Databasebeta| order | 25664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D401⋊#100 |
| Sylow | C401 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3208 |
Polycyclic presentation:
2^6,401|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^20,e^b=ef,g^c=g^400,g^e=g^4001022 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25664, 1532);