Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×SD16×C137 ⋊ C2 |
| Sylow | C137 ⋊ #577 |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,137|a^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,d^c=df,g^d=g^136974 conjugacy classes — view the full character table.
| maximal subgroup of | #31792554, #31792555, #31792561, … |
| maximal normal subgroup of | #31792554, #31792555, #31792561, … |
| maximal quotient of | #31789310, #31789317, #31789380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1355);