Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #442×C67 ⋊ C2 |
| Sylow | C67 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^66,e^b=eg,h^c=h^66,h^d=h^66770 conjugacy classes — view the full character table.
| maximal subgroup of | C4×AGL(1,ℤ/8)×D67, C2×#22569020, C4×#16864192, … |
| maximal normal subgroup of | C4×AGL(1,ℤ/8)×D67, C2×#22569020, C4×#16864192, … |
| maximal quotient of | #30825248, #30825417, #30825433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13321);