Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #2117 |
220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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=e,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^66,d^b=dg,e^b=eg1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30770905, #30770907, #30770956, … |
| maximal normal subgroup of | #30770905, #30770907, #30770956, … |
| maximal quotient of | #30764903, #30764906, #30764975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6138);