Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #467 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=f,b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^c=g^82596 conjugacy classes — view the full character table.
| maximal subgroup of | #24909390, #24909395, #24909400, … |
| maximal normal subgroup of | #24909390, #24909395, #24909400, … |
| maximal quotient of | #24906825, #24906830, #24906859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 787);