Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #466×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3203 |
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^d=h^66752 conjugacy classes — view the full character table.
| maximal subgroup of | #30767970, #30767974, #30767987, … |
| maximal normal subgroup of | #30767970, #30767974, #30767987, … |
| maximal quotient of | #30864941, #30866144, #30867160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15406);