Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1413 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=f,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^66,c^b=cf,d^b=def,e^b=eg,d^c=dfg,e^d=eg542 conjugacy classes — view the full character table.
| maximal subgroup of | #30743677, #30743678, #30743680, … |
| maximal normal subgroup of | #30743677, #30743678, #30743680, … |
| maximal quotient of | #30743222, #30743240, #30743371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2683);