Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #481 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|c^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^82,e^c=ef839 conjugacy classes — view the full character table.
| maximal subgroup of | #24906481, #24906482, #24906492, … |
| maximal normal subgroup of | #24906481, #24906482, #24906492, … |
| maximal quotient of | #24907553, #24907656, #24907780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 867);