Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #451 |
148 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^136,d^b=df,g^b=g^1361379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779747, #31779748, #31779753, … |
| maximal normal subgroup of | #31779747, #31779748, #31779753, … |
| maximal quotient of | #31779748, #31779765, #31779816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 707);