Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #465×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3346 |
356 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=eg,c^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,c^b=cg,d^b=de,h^b=h^66,f^c=fg,h^c=h^66755 conjugacy classes — view the full character table.
| maximal subgroup of | #3346×D67, C2×#22572700, #31734482, … |
| maximal normal subgroup of | #3346×D67, C2×#22572700, #31734482, … |
| maximal quotient of | #30872155, #30872215, #30873539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17001);