Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #135×C83 ⋊ C2 |
| Sylow | C83 ⋊ #509 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^82590 conjugacy classes — view the full character table.
| maximal subgroup of | #24909358, #24909361, #24909409, … |
| maximal normal subgroup of | #24909358, #24909361, #24909409, … |
| maximal quotient of | #24909175, #24909178, #24909252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 984);