Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C137 ⋊ C4 |
| Sylow | C137 ⋊ #344 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^100,d^b=df,g^d=g^136566 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22578285, #31796499, #31796544, … |
| maximal normal subgroup of | C2×#22578285, #31796499, #31796544, … |
| maximal quotient of | #31795629, #31795631, #31795634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1431);