Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #451×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3223 |
364 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^66,f^c=fg653 conjugacy classes — view the full character table.
| maximal subgroup of | #3223×D67, C2×#22571288, #31727239, … |
| maximal normal subgroup of | #3223×D67, C2×#22571288, #31727239, … |
| maximal quotient of | #30865212, #30865621, #30866424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15589);