Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C137 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 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,e^2=f,b^a=bd,g^a=g^100,g^c=g^136,g^e=g^136584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795626, #31795631, #31795651, … |
| maximal normal subgroup of | #31795626, #31795631, #31795651, … |
| maximal quotient of | #31796015, #31796018, #31796021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1517);