Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3243 |
320 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^66,f^c=fg653 conjugacy classes — view the full character table.
| maximal subgroup of | #3243×D67, C2×#22571488, #31728076, … |
| maximal normal subgroup of | #3243×D67, C2×#22571488, #31728076, … |
| maximal quotient of | #30865378, #30865595, #30866424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15789);