Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #485 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=f,b^2=f,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 | #485×D83, C2×#19128043, #24917375, … |
| maximal normal subgroup of | #485×D83, C2×#19128043, #24917375, … |
| maximal quotient of | #24907559, #24907664, #24907773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 891);