Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3183 |
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^c=dg,h^c=h^66,h^d=h^66560 conjugacy classes — view the full character table.
| maximal subgroup of | #30766669, #30766673, #31011074, … |
| maximal normal subgroup of | #30766669, #30766673, #31011074, … |
| maximal quotient of | #30856431, #30860145, #30860162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15234);