Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C137 ⋊ #494 |
122 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=df,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^c=g^136974 conjugacy classes — view the full character table.
| maximal subgroup of | #31782832, #31782833, #31782837, … |
| maximal normal subgroup of | #31782832, #31782833, #31782837, … |
| maximal quotient of | #31780383, #31780385, #31780387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 927);