Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #354 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^82,d^c=df464 conjugacy classes — view the full character table.
| maximal subgroup of | #354×D83, C2×#19127495, #24909125, … |
| maximal normal subgroup of | #354×D83, C2×#19127495, #24909125, … |
| maximal quotient of | C2×#19127495 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 343);