Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #2198 |
246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=g,c^2=g,b^a=bd,c^a=ce,f^a=fg,e^b=efg,h^b=h^66,d^c=df,h^c=h^66,e^d=eg548 conjugacy classes — view the full character table.
| maximal subgroup of | #30776552, #30776553, #30776557, … |
| maximal normal subgroup of | #30776552, #30776553, #30776557, … |
| maximal quotient of | #30767868, #30767898, #30768040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6505);