Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #413 |
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,89|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^88902 conjugacy classes — view the full character table.
| maximal subgroup of | #26020051, #26020053, #26020201, … |
| maximal normal subgroup of | #26020051, #26020053, #26020201, … |
| maximal quotient of | #26018564, #26018568, #26018584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 531);