Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1293 |
184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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=fg,d^2=fg,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^66,d^b=dg1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742528, #30742529, #30742531, … |
| maximal normal subgroup of | #30742528, #30742529, #30742531, … |
| maximal quotient of | #30742369, #30742371, #30742434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2387);