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 ⋊ #3174 |
362 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #3174×D67, C2×#22570833, #31725677, … |
| maximal normal subgroup of | #3174×D67, C2×#22570833, #31725677, … |
| maximal quotient of | #30856390, #30860090, #30860096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15134);