Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1342 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^66,c^b=cf,d^b=defg,e^b=eg,f^b=fg,d^c=dg548 conjugacy classes — view the full character table.
| maximal subgroup of | #1342×D67, C2×#22558203, #30765993, … |
| maximal normal subgroup of | #1342×D67, C2×#22558203, #30765993, … |
| maximal quotient of | #30742534, #30742537, #30742546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2504);