Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^82,d^b=de,d^c=df587 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D83, C2×#19127488, #24909101, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D83, C2×#19127488, #24909101, … |
| maximal quotient of | C2×#19127488 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 336);