Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊(C67⋊C16) |
| Sylow | C67 ⋊ D4⋊C16 |
110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 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,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^66,c^b=ce1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C16×D67, C2×D4⋊(C67⋊C16), #30765532, … |
| maximal normal subgroup of | D4⋊C16×D67, C2×D4⋊(C67⋊C16), #30765532, … |
| maximal quotient of | #30742480, #30742483, #30742486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2465);