Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2246 |
216 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^662150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743463, #30743465, #30743475, … |
| maximal normal subgroup of | #30743463, #30743465, #30743475, … |
| maximal quotient of | #30770484, #30770517, #30770543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6760);