Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C137 ⋊ C2 |
| Sylow | C137 ⋊ #459 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^136,e^c=ef1379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779843, #31779845, #31779854, … |
| maximal normal subgroup of | #31779843, #31779845, #31779854, … |
| maximal quotient of | #31780130, #31780144, #31780154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 744);