Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1394 |
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^2=e,c^2=g,d^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^66,d^b=dfg,d^c=dg950 conjugacy classes — view the full character table.
| maximal subgroup of | #30743344, #30743345, #30743347, … |
| maximal normal subgroup of | #30743344, #30743345, #30743347, … |
| maximal quotient of | #30742794, #30742835, #30742862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2637);