Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#101×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1785 |
584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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,c^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^66,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #30771341, #30771343, #30771349, … |
| maximal normal subgroup of | #30771341, #30771343, #30771349, … |
| maximal quotient of | #30747164, #30747168, #30747178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4437);