Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1326 |
158 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 37 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,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^66,c^b=cg,d^b=de,h^b=h^66,d^c=dg752 conjugacy classes — view the full character table.
| maximal subgroup of | #1326×D67, C2×#22558158, #30765004, … |
| maximal normal subgroup of | #1326×D67, C2×#22558158, #30765004, … |
| maximal quotient of | #30742471, #30742478, #30742626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2459);