Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1982 |
428 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=f,b^2=dfg,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^66,d^b=dg,f^b=fg,h^b=h^66962 conjugacy classes — view the full character table.
| maximal subgroup of | #30747740, #30747741, #30747782, … |
| maximal normal subgroup of | #30747740, #30747741, #30747782, … |
| maximal quotient of | #30754788, #30754806, #30754875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5438);