Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1379 |
136 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 77 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=f,f^2=g,b^a=bc,h^a=h^66,c^b=cg,d^b=dg,h^b=h^661376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1379×D67, C2×#22558299, #30770702, … |
| maximal normal subgroup of | #1379×D67, C2×#22558299, #30770702, … |
| maximal quotient of | #30742671, #30742678, #30742685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2600);