Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #480 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^82,e^c=ef,g^c=g^82839 conjugacy classes — view the full character table.
| maximal subgroup of | #24906450, #24906451, #24906462, … |
| maximal normal subgroup of | #24906450, #24906451, #24906462, … |
| maximal quotient of | #24907550, #24907653, #24907778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 863);