Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C101 ⋊ C2 |
| Sylow | C101 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|b^a=bd,c^a=ce,g^a=g^100,e^b=ef,d^c=df866 conjugacy classes — view the full character table.
| maximal subgroup of | #27173114, #27173115, #27173119, … |
| maximal normal subgroup of | #27173114, #27173115, #27173119, … |
| maximal quotient of | #27170050, #27170055, #27170061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 736);