Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #103×C137 ⋊ C2 |
| Sylow | C137 ⋊ #468 |
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 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|b^2=d,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^136,c^b=cf,g^b=g^136,g^c=g^136968 conjugacy classes — view the full character table.
| maximal subgroup of | #468×D137, C2×#22577652, #31790397, … |
| maximal normal subgroup of | #468×D137, C2×#22577652, #31790397, … |
| maximal quotient of | #31780257, #31780264, #31780291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 798);