Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1458 |
264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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,c^2=f,e^2=g,b^a=bd,d^a=df,e^b=ef,h^c=h^66770 conjugacy classes — view the full character table.
| maximal subgroup of | #30764914, #30764916, #30764922, … |
| maximal normal subgroup of | #30764914, #30764916, #30764922, … |
| maximal quotient of | #30743767, #30743775, #30743822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2821);