Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C67 ⋊ #2254 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^66764 conjugacy classes — view the full character table.
| maximal subgroup of | #30776750, #30776751, #2254×D67, … |
| maximal normal subgroup of | #30776750, #30776751, #2254×D67, … |
| maximal quotient of | #30772266, #30773864, #30773865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6791);