Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #448×C67 ⋊ C2 |
| Sylow | C67 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,e^d=eg,h^d=h^66662 conjugacy classes — view the full character table.
| maximal subgroup of | D4×SD16×D67, C2×#22571898, #31731119, … |
| maximal normal subgroup of | D4×SD16×D67, C2×#22571898, #31731119, … |
| maximal quotient of | #30845296, #30845301, #30845311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16199);