Finite Group Databasebeta

← Group #165752

Character table — Group #165752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444448888888888888888881616161616111111114444448888888888888888881616161616
order12222222444444444444888888888888444442222222244444444444488888888888844444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111
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
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1
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
χ611111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111-1111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111-11
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
χ811111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1
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
χ1322222222-2-22-2-22000022000000000000-2000022222222-2-22-2-22000022000000000000-20000
χ1422222222-2-22-2-220000-2-20000000000002000022222222-2-22-2-220000-2-200000000000020000
χ1522-22-2-22-20-200202-20000i2i2−i2−i2i2i2−i2−i200000000022-22-2-22-20-200202-20000i2i2−i2−i2i2i2−i2−i2000000000
χ1622-22-2-22-20-200202-20000−i2−i2i2i2−i2−i2i2i200000000022-22-2-22-20-200202-20000−i2−i2i2i2−i2−i2i2i2000000000
χ1722-22-2-22-20-20020-220000i2i2−i2−i2−i2−i2i2i200000000022-22-2-22-20-20020-220000i2i2−i2−i2−i2−i2i2i2000000000
χ1822-22-2-22-20-20020-220000−i2−i2i2i2i2i2−i2−i200000000022-22-2-22-20-20020-220000−i2−i2i2i2i2i2−i2−i2000000000
χ192-22-22-22-2-200200002-200i2−i2i2−i20000i2i2−i2−i2000002-22-22-22-2-200200002-200i2−i2i2−i20000i2i2−i2−i200000
χ202-22-22-22-2-200200002-200−i2i2−i2i20000−i2−i2i2i2000002-22-22-22-2-200200002-200−i2i2−i2i20000−i2−i2i2i200000
χ212-22-22-22-2-20020000-2200i2−i2i2−i20000−i2−i2i2i2000002-22-22-22-2-20020000-2200i2−i2i2−i20000−i2−i2i2i200000
χ222-22-22-22-2-20020000-2200−i2i2−i2i20000i2i2−i2−i2000002-22-22-22-2-20020000-2200−i2i2−i2i20000i2i2−i2−i200000
χ232-2-222-2-2200200-200002-20000i2−i2i2−i2i2−i2i2−i2000002-2-222-2-2200200-200002-20000i2−i2i2−i2i2−i2i2−i200000
χ242-2-222-2-2200200-200002-20000−i2i2−i2i2−i2i2−i2i2000002-2-222-2-2200200-200002-20000−i2i2−i2i2−i2i2−i2i200000
χ252-2-222-2-2200200-20000-220000i2−i2i2−i2−i2i2−i2i2000002-2-222-2-2200200-20000-220000i2−i2i2−i2−i2i2−i2i200000
χ262-2-222-2-2200200-20000-220000−i2i2−i2i2i2−i2i2−i2000002-2-222-2-2200200-20000-220000−i2i2−i2i2i2−i2i2−i200000
χ27444-4-4-4-4400000000000000000000000002i−2i00444-4-4-4-4400000000000000000000000002i−2i00
χ28444-4-4-4-440000000000000000000000000−2i2i00444-4-4-4-440000000000000000000000000−2i2i00
χ2944-44-4-44-40400-400000000000000000000000044-44-4-44-40400-4000000000000000000000000
χ3044-4-444-4-4000000000000000000002-2-220000044-4-444-4-4000000000000000000002-2-2200000
χ3144-4-444-4-400000000000000000000-222-20000044-4-444-4-400000000000000000000-222-200000
χ324-444-44-4-400000000000000002-2-220000000004-444-44-4-400000000000000002-2-22000000000
χ334-444-44-4-40000000000000000-222-20000000004-444-44-4-40000000000000000-222-2000000000
χ344-44-44-44-4400-400000000000000000000000004-44-44-44-4400-40000000000000000000000000
χ354-4-444-4-4400-4004000000000000000000000004-4-444-4-4400-400400000000000000000000000
χ364-4-4-4-44440000000000002-2-2200000000000004-4-4-4-44440000000000002-2-220000000000000
χ374-4-4-4-4444000000000000-222-200000000000004-4-4-4-4444000000000000-222-20000000000000
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
χ3911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1
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
χ411111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-11
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
χ4311111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111-1-11-1
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
χ4511111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11111
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
χ5022222222-2-22-2-22000022000000000000-20000-2-2-2-2-2-2-2-222-222-20000-2-200000000000020000
χ5122222222-2-22-2-220000-2-200000000000020000-2-2-2-2-2-2-2-222-222-2000022000000000000-20000
χ5222-22-2-22-20-200202-20000i2i2−i2−i2i2i2−i2−i2000000000-2-22-222-220200-20-220000−i2−i2i2i2−i2−i2i2i2000000000
χ5322-22-2-22-20-200202-20000−i2−i2i2i2−i2−i2i2i2000000000-2-22-222-220200-20-220000i2i2−i2−i2i2i2−i2−i2000000000
χ5422-22-2-22-20-20020-220000i2i2−i2−i2−i2−i2i2i2000000000-2-22-222-220200-202-20000−i2−i2i2i2i2i2−i2−i2000000000
χ5522-22-2-22-20-20020-220000−i2−i2i2i2i2i2−i2−i2000000000-2-22-222-220200-202-20000i2i2−i2−i2−i2−i2i2i2000000000
χ562-22-22-22-2-200200002-200i2−i2i2−i20000i2i2−i2−i200000-22-22-22-22200-20000-2200−i2i2−i2i20000−i2−i2i2i200000
χ572-22-22-22-2-200200002-200−i2i2−i2i20000−i2−i2i2i200000-22-22-22-22200-20000-2200i2−i2i2−i20000i2i2−i2−i200000
χ582-22-22-22-2-20020000-2200i2−i2i2−i20000−i2−i2i2i200000-22-22-22-22200-200002-200−i2i2−i2i20000i2i2−i2−i200000
χ592-22-22-22-2-20020000-2200−i2i2−i2i20000i2i2−i2−i200000-22-22-22-22200-200002-200i2−i2i2−i20000−i2−i2i2i200000
χ602-2-222-2-2200200-200002-20000i2−i2i2−i2i2−i2i2−i200000-222-2-222-200-20020000-220000−i2i2−i2i2−i2i2−i2i200000
χ612-2-222-2-2200200-200002-20000−i2i2−i2i2−i2i2−i2i200000-222-2-222-200-20020000-220000i2−i2i2−i2i2−i2i2−i200000
χ622-2-222-2-2200200-20000-220000i2−i2i2−i2−i2i2−i2i200000-222-2-222-200-200200002-20000−i2i2−i2i2i2−i2i2−i200000
χ632-2-222-2-2200200-20000-220000−i2i2−i2i2i2−i2i2−i200000-222-2-222-200-200200002-20000i2−i2i2−i2−i2i2−i2i200000
χ64444-4-4-4-4400000000000000000000000002i−2i00-4-4-44444-40000000000000000000000000−2i2i00
χ65444-4-4-4-440000000000000000000000000−2i2i00-4-4-44444-400000000000000000000000002i−2i00
χ6644-44-4-44-40400-4000000000000000000000000-4-44-444-440-4004000000000000000000000000
χ6744-4-444-4-4000000000000000000002-2-2200000-4-444-4-44400000000000000000000-222-200000
χ6844-4-444-4-400000000000000000000-222-200000-4-444-4-444000000000000000000002-2-2200000
χ694-444-44-4-400000000000000002-2-22000000000-44-4-44-4440000000000000000-222-2000000000
χ704-444-44-4-40000000000000000-222-2000000000-44-4-44-44400000000000000002-2-22000000000
χ714-44-44-44-4400-40000000000000000000000000-44-44-44-44-40040000000000000000000000000
χ724-4-444-4-4400-400400000000000000000000000-444-4-444-400400-400000000000000000000000
χ734-4-4-4-44440000000000002-2-220000000000000-44444-4-4-4000000000000-222-20000000000000
χ744-4-4-4-4444000000000000-222-20000000000000-44444-4-4-40000000000002-2-220000000000000

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