Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #480 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^136,e^c=ef,g^c=g^1361379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779776, #31779777, #31779788, … |
| maximal normal subgroup of | #31779776, #31779777, #31779788, … |
| maximal quotient of | #31780876, #31780979, #31781104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 863);