Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C137 ⋊ C2 |
| Sylow | C137 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^a=bd,c^a=ce,g^a=g^136,e^b=ef,d^c=df1172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31782771, #31782772, #31782776, … |
| maximal normal subgroup of | #31782771, #31782772, #31782776, … |
| maximal quotient of | #31779707, #31779712, #31779718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 736);