Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #359 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^88,c^b=ce,e^b=ef,g^b=g^881430 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #359×D89, C2×#19151406, #26021978, … |
| maximal normal subgroup of | #359×D89, C2×#19151406, #26021978, … |
| maximal quotient of | #26018214, #26018217, #26018268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 357);