Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C67 ⋊ #2897 |
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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=f,e^2=g,b^a=be,e^a=eg,h^a=h^66,e^b=eg,d^c=dg1166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30871806, #30871813, #30871824, … |
| maximal normal subgroup of | #30871806, #30871813, #30871824, … |
| maximal quotient of | #30822213, #30822308, #30822409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13036);