Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1361 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,c^2=fg,d^2=efg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^66,c^b=cf,d^b=defg,e^b=eg,f^b=fg755 conjugacy classes — view the full character table.
| maximal subgroup of | #1361×D67, C2×#22558255, #30767073, … |
| maximal normal subgroup of | #1361×D67, C2×#22558255, #30767073, … |
| maximal quotient of | #30742556, #30742562, #30742564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2556);