Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #470×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3204 |
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|a^2=g,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^c=h^66,h^d=h^66554 conjugacy classes — view the full character table.
| maximal subgroup of | #30768023, #30768027, #30769183, … |
| maximal normal subgroup of | #30768023, #30768027, #30769183, … |
| maximal quotient of | #30864943, #30866139, #30867122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15417);