Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #1604 |
282 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 57 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,c^2=g,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^66,d^b=df,e^b=eg,d^c=dg749 conjugacy classes — view the full character table.
| maximal subgroup of | #30768062, #30768063, #30768073, … |
| maximal normal subgroup of | #30768062, #30768063, #30768073, … |
| maximal quotient of | #30744629, #30744642, #30744701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3479);