Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1323 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1323×D67, C2×#22558150, #30764973, … |
| maximal normal subgroup of | #1323×D67, C2×#22558150, #30764973, … |
| maximal quotient of | #30742472, #30742474, #30742476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2451);