Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #104×C137 ⋊ C2 |
| Sylow | C137 ⋊ #421 |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 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,d^2=f,e^2=f,b^a=bd,d^a=df,c^b=cf,d^b=df,g^c=g^136974 conjugacy classes — view the full character table.
| maximal subgroup of | #421×D137, C2×#22577418, #31789333, … |
| maximal normal subgroup of | #421×D137, C2×#22577418, #31789333, … |
| maximal quotient of | #31779173, #31779175, #31779178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 564);