Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C89 ⋊ #368 |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=d,b^2=ce,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^b=g^88638 conjugacy classes — view the full character table.
| maximal subgroup of | #368×D89, C2×#19151427, #26022045, … |
| maximal normal subgroup of | #368×D89, C2×#19151427, #26022045, … |
| maximal quotient of | #26018323, #26018325, #26018345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 378);