Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #339 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^82,g^b=g^82848 conjugacy classes — view the full character table.
| maximal subgroup of | #339×D83, C2×#19127462, #24907171, … |
| maximal normal subgroup of | #339×D83, C2×#19127462, #24907171, … |
| maximal quotient of | C2×#19127462 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 310);