Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #332 |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=e,c^2=f,d^2=ef,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^82839 conjugacy classes — view the full character table.
| maximal subgroup of | #24906551, #24906554, #24906558, … |
| maximal normal subgroup of | #24906551, #24906554, #24906558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 294);