Finite Group Databasebeta

← Group #165708

Character table — Group #165708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444448888888888888888881616161616111111114444448888888888888888881616161616
order12222222444444444444888888888888224442222222244444444444488888888888822444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ31111111111111111-1-1-1-111111111-1-1-1-1-1-1-11-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-11-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1
χ511111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-11
χ611111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-11
χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1
χ811111111111111-1-1-1-111-1-1-1-111111111-1-11-1-111111111111111-1-1-1-111-1-1-1-111111111-1-11-1-1
χ9222222222-2-22-2-20022000000000000000000-2222222222-2-22-2-20022000000000000000000-2
χ10222222222-2-22-2-200-2-20000000000000000002222222222-2-22-2-200-2-20000000000000000002
χ1122222222-22-2-22-2220000000000000000000-2022222222-22-2-22-2220000000000000000000-20
χ1222222222-22-2-22-2-2-200000000000000000002022222222-22-2-22-2-2-2000000000000000000020
χ1322222222-2-22-2-2200002200000000000000-20022222222-2-22-2-2200002200000000000000-200
χ1422222222-2-22-2-220000-2-20000000000000020022222222-2-22-2-220000-2-200000000000000200
χ15222-22-2-2-20-200202-20000i2i2−i2−i2i2i2−i2−i2000000000222-22-2-2-20-200202-20000i2i2−i2−i2i2i2−i2−i2000000000
χ16222-22-2-2-20-200202-20000−i2−i2i2i2−i2−i2i2i2000000000222-22-2-2-20-200202-20000−i2−i2i2i2−i2−i2i2i2000000000
χ17222-22-2-2-20-20020-220000i2i2−i2−i2−i2−i2i2i2000000000222-22-2-2-20-20020-220000i2i2−i2−i2−i2−i2i2i2000000000
χ18222-22-2-2-20-20020-220000−i2−i2i2i2i2i2−i2−i2000000000222-22-2-2-20-20020-220000−i2−i2i2i2i2i2−i2−i2000000000
χ1922-22-22-2-2-200200002-200i2−i2i2−i20000i2i2−i2−i20000022-22-22-2-2-200200002-200i2−i2i2−i20000i2i2−i2−i200000
χ2022-22-22-2-2-200200002-200−i2i2−i2i20000−i2−i2i2i20000022-22-22-2-2-200200002-200−i2i2−i2i20000−i2−i2i2i200000
χ2122-22-22-2-2-20020000-2200i2−i2i2−i20000−i2−i2i2i20000022-22-22-2-2-20020000-2200i2−i2i2−i20000−i2−i2i2i200000
χ2222-22-22-2-2-20020000-2200−i2i2−i2i20000i2i2−i2−i20000022-22-22-2-2-20020000-2200−i2i2−i2i20000i2i2−i2−i200000
χ232-2-2-222-2200-200200002-200002−22−22−22−2000002-2-2-222-2200-200200002-200002−22−22−22−200000
χ242-2-2-222-2200-200200002-20000−22−22−22−22000002-2-2-222-2200-200200002-20000−22−22−22−2200000
χ252-2-2-222-2200-20020000-2200002−22−2−22−22000002-2-2-222-2200-20020000-2200002−22−2−22−2200000
χ262-2-2-222-2200-20020000-220000−22−222−22−2000002-2-2-222-2200-20020000-220000−22−222−22−200000
χ27444-44-4-4-40400-4000000000000000000000000444-44-4-4-40400-4000000000000000000000000
χ2844-44-44-4-4400-4000000000000000000000000044-44-44-4-4400-40000000000000000000000000
χ2944-4-4-4-4440000000000002-2-22000000000000044-4-4-4-4440000000000002-2-220000000000000
χ3044-4-4-4-444000000000000-222-2000000000000044-4-4-4-444000000000000-222-20000000000000
χ314-444-4-4-440000000000000000000000002-20004-444-4-4-440000000000000000000000002-2000
χ324-444-4-4-44000000000000000000000000-220004-444-4-4-44000000000000000000000000-22000
χ334-44-4-444-4000000000000000000002i−2i−2i2i000004-44-4-444-4000000000000000000002i−2i−2i2i00000
χ344-44-4-444-400000000000000000000−2i2i2i−2i000004-44-4-444-400000000000000000000−2i2i2i−2i00000
χ354-4-444-44-400000000000000002i−2i−2i2i0000000004-4-444-44-400000000000000002i−2i−2i2i000000000
χ364-4-444-44-40000000000000000−2i2i2i−2i0000000004-4-444-44-40000000000000000−2i2i2i−2i000000000
χ374-4-4-444-4400400-4000000000000000000000004-4-4-444-4400400-400000000000000000000000
χ381111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1
χ401111111111111111-1-1-1-111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-11
χ411111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-11
χ4211111111111111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1
χ4311111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-111-1
χ4411111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-111
χ4511111111111111-1-1-1-111-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-111
χ46222222222-2-22-2-20022000000000000000000-2-2-2-2-2-2-2-2-2-222-22200-2-20000000000000000002
χ47222222222-2-22-2-200-2-20000000000000000002-2-2-2-2-2-2-2-2-222-2220022000000000000000000-2
χ4822222222-22-2-22-2220000000000000000000-20-2-2-2-2-2-2-2-22-222-22-2-2000000000000000000020
χ4922222222-22-2-22-2-2-2000000000000000000020-2-2-2-2-2-2-2-22-222-22220000000000000000000-20
χ5022222222-2-22-2-2200002200000000000000-200-2-2-2-2-2-2-2-222-222-20000-2-200000000000000200
χ5122222222-2-22-2-220000-2-200000000000000200-2-2-2-2-2-2-2-222-222-200002200000000000000-200
χ52222-22-2-2-20-200202-20000i2i2−i2−i2i2i2−i2−i2000000000-2-2-22-22220200-20-220000−i2−i2i2i2−i2−i2i2i2000000000
χ53222-22-2-2-20-200202-20000−i2−i2i2i2−i2−i2i2i2000000000-2-2-22-22220200-20-220000i2i2−i2−i2i2i2−i2−i2000000000
χ54222-22-2-2-20-20020-220000i2i2−i2−i2−i2−i2i2i2000000000-2-2-22-22220200-202-20000−i2−i2i2i2i2i2−i2−i2000000000
χ55222-22-2-2-20-20020-220000−i2−i2i2i2i2i2−i2−i2000000000-2-2-22-22220200-202-20000i2i2−i2−i2−i2−i2i2i2000000000
χ5622-22-22-2-2-200200002-200i2−i2i2−i20000i2i2−i2−i200000-2-22-22-222200-20000-2200−i2i2−i2i20000−i2−i2i2i200000
χ5722-22-22-2-2-200200002-200−i2i2−i2i20000−i2−i2i2i200000-2-22-22-222200-20000-2200i2−i2i2−i20000i2i2−i2−i200000
χ5822-22-22-2-2-20020000-2200i2−i2i2−i20000−i2−i2i2i200000-2-22-22-222200-200002-200−i2i2−i2i20000i2i2−i2−i200000
χ5922-22-22-2-2-20020000-2200−i2i2−i2i20000i2i2−i2−i200000-2-22-22-222200-200002-200i2−i2i2−i20000−i2−i2i2i200000
χ602-2-2-222-2200-200200002-200002−22−22−22−200000-2222-2-22-200200-20000-220000−22−22−22−2200000
χ612-2-2-222-2200-200200002-20000−22−22−22−2200000-2222-2-22-200200-20000-2200002−22−22−22−200000
χ622-2-2-222-2200-20020000-2200002−22−2−22−2200000-2222-2-22-200200-200002-20000−22−222−22−200000
χ632-2-2-222-2200-20020000-220000−22−222−22−200000-2222-2-22-200200-200002-200002−22−2−22−2200000
χ64444-44-4-4-40400-4000000000000000000000000-4-4-44-44440-4004000000000000000000000000
χ6544-44-44-4-4400-40000000000000000000000000-4-44-44-444-40040000000000000000000000000
χ6644-4-4-4-4440000000000002-2-220000000000000-4-44444-4-4000000000000-222-20000000000000
χ6744-4-4-4-444000000000000-222-20000000000000-4-44444-4-40000000000002-2-220000000000000
χ684-444-4-4-440000000000000000000000002-2000-44-4-4444-4000000000000000000000000-22000
χ694-444-4-4-44000000000000000000000000-22000-44-4-4444-40000000000000000000000002-2000
χ704-44-4-444-4000000000000000000002i−2i−2i2i00000-44-444-4-4400000000000000000000−2i2i2i−2i00000
χ714-44-4-444-400000000000000000000−2i2i2i−2i00000-44-444-4-44000000000000000000002i−2i−2i2i00000
χ724-4-444-44-400000000000000002i−2i−2i2i000000000-444-4-44-440000000000000000−2i2i2i−2i000000000
χ734-4-444-44-40000000000000000−2i2i2i−2i000000000-444-4-44-4400000000000000002i−2i−2i2i000000000
χ744-4-4-444-4400400-400000000000000000000000-4444-4-44-400-400400000000000000000000000

Here i is the imaginary unit (i² = −1).