Finite Group Databasebeta

← Group #239404

Character table — Group #239404

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122224444888888888888888888881616161611111111222244448888888888888888888816161616
order12222222222244442244444444448888888844442222222222224444224444444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ9222222222222-2-2-2-222-2-200000000000000000000222222222222-2-2-2-222-2-200000000000000000000
χ10222222222222-2-2-2-2-2-22200000000000000000000222222222222-2-2-2-2-2-22200000000000000000000
χ1122222222-2-2-2-22-22-200000000000000000000200-222222222-2-2-2-22-22-200000000000000000000200-2
χ1222222222-2-2-2-22-22-200000000000000000000-200222222222-2-2-2-22-22-200000000000000000000-2002
χ1322222222-2-2-2-2-22-220000000000000000000002-2022222222-2-2-2-2-22-220000000000000000000002-20
χ1422222222-2-2-2-2-22-22000000000000000000000-22022222222-2-2-2-2-22-22000000000000000000000-220
χ152222-2-2-2-222-2-200002-2000000000022−2−222−2−200002222-2-2-2-222-2-200002-2000000000022−2−222−2−20000
χ162222-2-2-2-222-2-200002-20000000000−2−222−2−22200002222-2-2-2-222-2-200002-20000000000−2−222−2−2220000
χ172222-2-2-2-222-2-20000-22000000000022−2−2−2−22200002222-2-2-2-222-2-20000-22000000000022−2−2−2−2220000
χ182222-2-2-2-222-2-20000-220000000000−2−22222−2−200002222-2-2-2-222-2-20000-220000000000−2−22222−2−20000
χ1922-2-22-2-222-22-20000002i−2i000000002−22−2i2−i2i2−i2000022-2-22-2-222-22-20000002i−2i000000002−22−2i2−i2i2−i20000
χ2022-2-22-2-222-22-20000002i−2i00000000−22−22−i2i2−i2i2000022-2-22-2-222-22-20000002i−2i00000000−22−22−i2i2−i2i20000
χ2122-2-22-2-222-22-2000000−2i2i000000002−22−2−i2i2−i2i2000022-2-22-2-222-22-2000000−2i2i000000002−22−2−i2i2−i2i20000
χ2222-2-22-2-222-22-2000000−2i2i00000000−22−22i2−i2i2−i2000022-2-22-2-222-22-2000000−2i2i00000000−22−22i2−i2i2−i20000
χ2322-2-2-222-22-2-2222-2-200000000000000002i−2i−2i2i000022-2-2-222-22-2-2222-2-200000000000000002i−2i−2i2i0000
χ2422-2-2-222-22-2-2222-2-20000000000000000−2i2i2i−2i000022-2-2-222-22-2-2222-2-20000000000000000−2i2i2i−2i0000
χ2522-2-2-222-22-2-22-2-2220000000000002-2-220000000022-2-2-222-22-2-22-2-2220000000000002-2-2200000000
χ2622-2-2-222-22-2-22-2-222000000000000-222-20000000022-2-2-222-22-2-22-2-222000000000000-222-200000000
χ2722-2-2-222-2-222-22-2-22000000002i2i−2i−2i00000000000022-2-2-222-2-222-22-2-22000000002i2i−2i−2i000000000000
χ2822-2-2-222-2-222-22-2-2200000000−2i−2i2i2i00000000000022-2-2-222-2-222-22-2-2200000000−2i−2i2i2i000000000000
χ2922-2-2-222-2-222-2-222-200002i2i−2i−2i000000000000000022-2-2-222-2-222-2-222-200002i2i−2i−2i0000000000000000
χ3022-2-2-222-2-222-2-222-20000−2i−2i2i2i000000000000000022-2-2-222-2-222-2-222-20000−2i−2i2i2i0000000000000000
χ314444-4-4-4-4-4-44400000000000000000000000000004444-4-4-4-4-4-4440000000000000000000000000000
χ3244-4-44-4-44-44-44000000000000000000000000000044-4-44-4-44-44-440000000000000000000000000000
χ334-44-444-4-40000000000002i−2i2i−2i00000000000000004-44-444-4-40000000000002i−2i2i−2i0000000000000000
χ344-44-444-4-4000000000000−2i2i−2i2i00000000000000004-44-444-4-4000000000000−2i2i−2i2i0000000000000000
χ354-44-4-4-44400000000000000002-22-20000000000004-44-4-4-44400000000000000002-22-2000000000000
χ364-44-4-4-4440000000000000000-22-220000000000004-44-4-4-4440000000000000000-22-22000000000000
χ374-4-444-44-400000000000000002i−2i−2i2i0000000000004-4-444-44-400000000000000002i−2i−2i2i000000000000
χ384-4-444-44-40000000000000000−2i2i2i−2i0000000000004-4-444-44-40000000000000000−2i2i2i−2i000000000000
χ394-4-44-44-440000000000002-2-2200000000000000004-4-44-44-440000000000002-2-220000000000000000
χ404-4-44-44-44000000000000-222-200000000000000004-4-44-44-44000000000000-222-20000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ421111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ451111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1
χ461111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11
χ471111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ481111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1
χ49222222222222-2-2-2-222-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000
χ50222222222222-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000000000
χ5122222222-2-2-2-22-22-200000000000000000000200-2-2-2-2-2-2-2-2-22222-22-2200000000000000000000-2002
χ5222222222-2-2-2-22-22-200000000000000000000-2002-2-2-2-2-2-2-2-22222-22-2200000000000000000000200-2
χ5322222222-2-2-2-2-22-220000000000000000000002-20-2-2-2-2-2-2-2-222222-22-2000000000000000000000-220
χ5422222222-2-2-2-2-22-22000000000000000000000-220-2-2-2-2-2-2-2-222222-22-20000000000000000000002-20
χ552222-2-2-2-222-2-200002-2000000000022−2−222−2−20000-2-2-2-22222-2-2220000-220000000000−2−222−2−2220000
χ562222-2-2-2-222-2-200002-20000000000−2−222−2−2220000-2-2-2-22222-2-2220000-22000000000022−2−222−2−20000
χ572222-2-2-2-222-2-20000-22000000000022−2−2−2−2220000-2-2-2-22222-2-22200002-20000000000−2−22222−2−20000
χ582222-2-2-2-222-2-20000-220000000000−2−22222−2−20000-2-2-2-22222-2-22200002-2000000000022−2−2−2−2220000
χ5922-2-22-2-222-22-20000002i−2i000000002−22−2i2−i2i2−i20000-2-222-222-2-22-22000000−2i2i00000000−22−22−i2i2−i2i20000
χ6022-2-22-2-222-22-20000002i−2i00000000−22−22−i2i2−i2i20000-2-222-222-2-22-22000000−2i2i000000002−22−2i2−i2i2−i20000
χ6122-2-22-2-222-22-2000000−2i2i000000002−22−2−i2i2−i2i20000-2-222-222-2-22-220000002i−2i00000000−22−22i2−i2i2−i20000
χ6222-2-22-2-222-22-2000000−2i2i00000000−22−22i2−i2i2−i20000-2-222-222-2-22-220000002i−2i000000002−22−2−i2i2−i2i20000
χ6322-2-2-222-22-2-2222-2-200000000000000002i−2i−2i2i0000-2-2222-2-22-222-2-2-2220000000000000000−2i2i2i−2i0000
χ6422-2-2-222-22-2-2222-2-20000000000000000−2i2i2i−2i0000-2-2222-2-22-222-2-2-22200000000000000002i−2i−2i2i0000
χ6522-2-2-222-22-2-22-2-2220000000000002-2-2200000000-2-2222-2-22-222-222-2-2000000000000-222-200000000
χ6622-2-2-222-22-2-22-2-222000000000000-222-200000000-2-2222-2-22-222-222-2-20000000000002-2-2200000000
χ6722-2-2-222-2-222-22-2-22000000002i2i−2i−2i000000000000-2-2222-2-222-2-22-222-200000000−2i−2i2i2i000000000000
χ6822-2-2-222-2-222-22-2-2200000000−2i−2i2i2i000000000000-2-2222-2-222-2-22-222-2000000002i2i−2i−2i000000000000
χ6922-2-2-222-2-222-2-222-200002i2i−2i−2i0000000000000000-2-2222-2-222-2-222-2-220000−2i−2i2i2i0000000000000000
χ7022-2-2-222-2-222-2-222-20000−2i−2i2i2i0000000000000000-2-2222-2-222-2-222-2-2200002i2i−2i−2i0000000000000000
χ714444-4-4-4-4-4-4440000000000000000000000000000-4-4-4-4444444-4-40000000000000000000000000000
χ7244-4-44-4-44-44-440000000000000000000000000000-4-444-444-44-44-40000000000000000000000000000
χ734-44-444-4-40000000000002i−2i2i−2i0000000000000000-44-44-4-444000000000000−2i2i−2i2i0000000000000000
χ744-44-444-4-4000000000000−2i2i−2i2i0000000000000000-44-44-4-4440000000000002i−2i2i−2i0000000000000000
χ754-44-4-4-44400000000000000002-22-2000000000000-44-4444-4-40000000000000000-22-22000000000000
χ764-44-4-4-4440000000000000000-22-22000000000000-44-4444-4-400000000000000002-22-2000000000000
χ774-4-444-44-400000000000000002i−2i−2i2i000000000000-444-4-44-440000000000000000−2i2i2i−2i000000000000
χ784-4-444-44-40000000000000000−2i2i2i−2i000000000000-444-4-44-4400000000000000002i−2i−2i2i000000000000
χ794-4-44-44-440000000000002-2-220000000000000000-444-44-44-4000000000000-222-20000000000000000
χ804-4-44-44-44000000000000-222-20000000000000000-444-44-44-40000000000002-2-220000000000000000

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