Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C137 ⋊ C2 |
| Sylow | C137 ⋊ #359 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^136,c^b=ce,e^b=ef,g^b=g^1362198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #359×D137, C2×#22577211, #31782515, … |
| maximal normal subgroup of | #359×D137, C2×#22577211, #31782515, … |
| maximal quotient of | #31778751, #31778754, #31778805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 357);