Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #465×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3350 |
348 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,c^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,c^b=cg,d^b=de,h^b=h^66,f^c=fg,h^c=h^66755 conjugacy classes — view the full character table.
| maximal subgroup of | #3350×D67, C2×#22572760, #31734496, … |
| maximal normal subgroup of | #3350×D67, C2×#22572760, #31734496, … |
| maximal quotient of | #30872170, #30872230, #30873555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17061);