Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1322 |
108 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 43 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,f^2=g,b^a=bc,c^a=ce,d^b=de,h^b=h^661364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1322×D67, C2×#22558148, #30764963, … |
| maximal normal subgroup of | #1322×D67, C2×#22558148, #30764963, … |
| maximal quotient of | #30742465, #30742467, #30742469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2449);