Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3233 |
332 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^66,f^c=fg659 conjugacy classes — view the full character table.
| maximal subgroup of | #3233×D67, C2×#22571385, #31727917, … |
| maximal normal subgroup of | #3233×D67, C2×#22571385, #31727917, … |
| maximal quotient of | #30865337, #30865526, #30866373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15686);