Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #418 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^82,c^b=cf,d^b=df842 conjugacy classes — view the full character table.
| maximal subgroup of | #24907430, #24907433, #24907841, … |
| maximal normal subgroup of | #24907430, #24907433, #24907841, … |
| maximal quotient of | #24907182, #24907288, #24907394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 554);