Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3179 |
374 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=dg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #3179×D67, C2×#22570888, #31725723, … |
| maximal normal subgroup of | #3179×D67, C2×#22570888, #31725723, … |
| maximal quotient of | #30856408, #30860125, #30860139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15189);