Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3104 |
384 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^66,f^c=fg962 conjugacy classes — view the full character table.
| maximal subgroup of | #30825721, #30825723, #30825754, … |
| maximal normal subgroup of | #30825721, #30825723, #30825754, … |
| maximal quotient of | #30855841, #30858821, #30858823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14547);