Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #106×C137 ⋊ C2 |
| Sylow | C137 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^c=g^136974 conjugacy classes — view the full character table.
| maximal subgroup of | #428×D137, C2×#22577442, #31789376, … |
| maximal normal subgroup of | #428×D137, C2×#22577442, #31789376, … |
| maximal quotient of | #31779538, #31779553, #31779571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 588);