Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3178 |
350 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|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^d=h^66560 conjugacy classes — view the full character table.
| maximal subgroup of | #3178×D67, C2×#22570870, #31725724, … |
| maximal normal subgroup of | #3178×D67, C2×#22570870, #31725724, … |
| maximal quotient of | #30856405, #30860114, #30860134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15171);