Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #99×C137 ⋊ C2 |
| Sylow | C137 ⋊ #410 |
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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=e,c^2=f,b^a=bd,d^a=df,e^b=ef,g^c=g^136770 conjugacy classes — view the full character table.
| maximal subgroup of | #31782427, #31782429, #31782437, … |
| maximal normal subgroup of | #31782427, #31782429, #31782437, … |
| maximal quotient of | #31779100, #31779102, #31779108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 521);