Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1993 |
276 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 109 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,b^2=def,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^66,c^b=cg1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30748227, #30748229, #30750744, … |
| maximal normal subgroup of | #30748227, #30748229, #30750744, … |
| maximal quotient of | #30755850, #30755866, #30755914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5483);