Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C89 ⋊ #366 |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=d,b^2=ce,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^881430 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26018430, #26018431, #26018433, … |
| maximal normal subgroup of | #26018430, #26018431, #26018433, … |
| maximal quotient of | #26018324, #26018344, #26018452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 375);