Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D101⋊#101 |
| Sylow | C101 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=e,b^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^10,e^b=ef,g^c=g^100,g^e=g^100272 conjugacy classes — view the full character table.
| maximal subgroup of | #27186228, #101×#87938, #27186979, … |
| maximal normal subgroup of | #27186228, #101×#87938, #27186979, … |
| maximal quotient of | D101⋊#324, #27186375, #27186376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1534);