Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C24×C101 ⋊ C4 |
| Sylow | C101 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^10,d^b=de,d^c=df,g^d=g^100413 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20266077, D101⋊AΣL(1,𝔽16), #27187383, … |
| maximal normal subgroup of | C2×#20266077, D101⋊AΣL(1,𝔽16), #27187383, … |
| maximal quotient of | #27186056, #27186077, #27186110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1449);