Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #106×C137 ⋊ C2 |
| Sylow | C137 ⋊ #481 |
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,137|c^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^136,g^b=g^136,e^c=ef971 conjugacy classes — view the full character table.
| maximal subgroup of | #481×D137, C2×#22577723, #31790706, … |
| maximal normal subgroup of | #481×D137, C2×#22577723, #31790706, … |
| maximal quotient of | #31780878, #31780980, #31781105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 869);