Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#11717581 |
| Sylow | C101 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^10,c^b=ce,g^d=g^100278 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4⋊#11717581, D101⋊(D4⋊C8), #27186423, … |
| maximal normal subgroup of | C2×D4⋊#11717581, D101⋊(D4⋊C8), #27186423, … |
| maximal quotient of | #27185948, #27185950, #27185968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1396);