Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1608 |
228 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 53 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=g,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^66,d^b=df,e^b=eg,h^b=h^66,d^c=dg749 conjugacy classes — view the full character table.
| maximal subgroup of | #30768554, #30768555, #30768560, … |
| maximal normal subgroup of | #30768554, #30768555, #30768560, … |
| maximal quotient of | #30744862, #30744890, #30744958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3503);