Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C67 ⋊ #1338 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^66,c^b=ceg,d^b=dg,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1338×D67, C2×#22558192, #30765648, … |
| maximal normal subgroup of | #1338×D67, C2×#22558192, #30765648, … |
| maximal quotient of | #30742614, #30742642, #30742743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2493);