Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #356 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=f,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^100,c^b=cf,d^b=def,d^c=df,g^d=g^136353 conjugacy classes — view the full character table.
| maximal subgroup of | #31795914, #31795915, C2×#22578313, … |
| maximal normal subgroup of | #31795914, #31795915, C2×#22578313, … |
| maximal quotient of | #31795719, #31795732, #31795773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1459);