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 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^82596 conjugacy classes — view the full character table.
| maximal subgroup of | #24909341, #24909342, #24909346, … |
| maximal normal subgroup of | #24909341, #24909342, #24909346, … |
| maximal quotient of | #24909168, #24909170, #24909245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 979);