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^a=g^881430 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26018436, #26018437, #26018442, … |
| maximal normal subgroup of | #26018436, #26018437, #26018442, … |
| maximal quotient of | #26018324, #26018326, #26018346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 379);