Finite Group Databasebeta

← Group #284884

Character table — Group #284884

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222244444444444444444448888888888888888888888161616161616161616323232
order12222244444422444448888888888882244448888888888888888444444888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1111-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1-11
χ61111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ9111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111-1-11111-1-1-11-1
χ10111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-111-1-1-1-1111-11
χ11111111111111-1-1-1-111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11-1-11-1-11-1-11-11
χ12111111111111-1-1-1-111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-111-111-111-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-111-1111-1-11-1-1
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-11-1-1-111-111
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-11-1-1-111
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1111-1111-1-1
χ1722222222-22-222222-2-2-200000000000022-2-2-2-22200-2-20000000000000000000000
χ1822222222-22-222222-2-2-2000000000000-2-2-2-222-2-200220000000000000000000000
χ1922222222-22-22-2-2-2-2-2-2-20000000000002222-2-2-2-200220000000000000000000000
χ2022222222-22-22-2-2-2-2-2-2-2000000000000-2-222222200-2-20000000000000000000000
χ21222222-2-2-2-2-2-200002-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000002-200002i−2i000
χ22222222-2-2-2-2-2-200002-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000-220000−2i2i000
χ23222222-2-2-2-2-2-200002-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000002-20000−2i2i000
χ24222222-2-2-2-2-2-200002-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000-2200002i−2i000
χ252222-2-22-22-22200002-2-22222-2-2-2-200000000000000000000002200-200200-200000
χ262222-2-22-22-22200002-2-22222-2-2-2-20000000000000000000000-2-200200-200200000
χ272222-2-22-22-22200002-2-2-2-2-2-2222200000000000000000000002200200-200-200000
χ282222-2-22-22-22200002-2-2-2-2-2-222220000000000000000000000-2-200-200200200000
χ292222-2-2-22222-222-2-2-2-2200000000222200-220000-2-20000002200-2-2000000000000
χ302222-2-2-22222-222-2-2-2-2200000000-2-2-2-200-22000022000000-2-20022000000000000
χ312222-2-2-22222-2-2-222-2-22000000002222002-2000022000000-2-200-2-2000000000000
χ322222-2-2-22222-2-2-222-2-2200000000-2-2-2-2002-20000-2-2000000220022000000000000
χ332222-2-2-22-22-2-222-2-222-22i2i−2i−2i−2i−2i2i2i0000002-2000000002i2i−2i−2i000000000000000000
χ342222-2-2-22-22-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i0000002-200000000−2i−2i2i2i000000000000000000
χ352222-2-2-22-22-2-2-2-22222-22i2i−2i−2i−2i−2i2i2i000000-2200000000−2i−2i2i2i000000000000000000
χ362222-2-2-22-22-2-2-2-22222-2−2i−2i2i2i2i2i−2i−2i000000-22000000002i2i−2i−2i000000000000000000
χ3722-2-22-2220-20-22-22-20002−22−22−22−222−2−22-200002-22−2002−22−22−2002−2000000000000
χ3822-2-22-2220-20-22-22-20002−22−22−22−2−2−222-220000-22−22002−22−2−2200−22000000000000
χ3922-2-22-2220-20-22-22-2000−22−22−22−2222−2−2-220000-222−200−22−222−2002−2000000000000
χ4022-2-22-2220-20-22-22-2000−22−22−22−22−2−2222-200002-2−2200−22−22−2200−22000000000000
χ4122-2-22-2220-20-2-22-220002−22−22−22−222−2−2-2200002-2−2200−22−22−22002−2000000000000
χ4222-2-22-2220-20-2-22-220002−22−22−22−2−2−2222-20000-222−200−22−222−200−22000000000000
χ4322-2-22-2220-20-2-22-22000−22−22−22−2222−2−22-20000-22−22002−22−2−22002−2000000000000
χ4422-2-22-2220-20-2-22-22000−22−22−22−22−2−222-2200002-22−2002−22−22−200−22000000000000
χ4522-2-2-22-220-2022-2-22000i2−i2−i2i2−i2i2i2−i222−2−200002i−2i00−222i−2ii2−i2−i2i22−200−22000000000000
χ4622-2-2-22-220-2022-2-22000i2−i2−i2i2−i2i2i2−i2−2−2220000−2i2i002−2−2i2ii2−i2−i2i2−22002−2000000000000
χ4722-2-2-22-220-2022-2-22000−i2i2i2−i2i2−i2−i2i222−2−20000−2i2i00−22−2i2i−i2i2i2−i22−200−22000000000000
χ4822-2-2-22-220-2022-2-22000−i2i2i2−i2i2−i2−i2i2−2−22200002i−2i002−22i−2i−i2i2i2−i2−22002−2000000000000
χ4922-2-2-22-220-202-222-2000i2−i2−i2i2−i2i2i2−i222−2−20000−2i2i002−22i−2i−i2i2i2−i2−2200−22000000000000
χ5022-2-2-22-220-202-222-2000i2−i2−i2i2−i2i2i2−i2−2−22200002i−2i00−22−2i2i−i2i2i2−i22−2002−2000000000000
χ5122-2-2-22-220-202-222-2000−i2i2i2−i2i2−i2−i2i222−2−200002i−2i002−2−2i2ii2−i2−i2i2−2200−22000000000000
χ5222-2-2-22-220-202-222-2000−i2i2i2−i2i2−i2−i2i2−2−2220000−2i2i00−222i−2ii2−i2−i2i22−2002−2000000000000
χ53444444-4-44-44-40000-44-40000000000000000000000000000000000000000000000
χ544444-4-44-4-4-4-440000-4440000000000000000000000000000000000000000000000
χ5544-4-44-4-4-4040400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5644-4-44-4-4-404040000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5744-4-4-444-4040-4000000022−2222−22−2222−222200000000000000000000000000000000000000
χ5844-4-4-444-4040-40000000−2222−222222−2222−2200000000000000000000000000000000000000
χ594-4-44000040-400000000000000002i2−2i22i2−2i200000000000000000022−220000002i−2i000000
χ604-4-44000040-400000000000000002i2−2i22i2−2i2000000000000000000−2222000000−2i2i000000
χ614-4-44000040-40000000000000000−2i22i2−2i22i200000000000000000022−22000000−2i2i000000
χ624-4-44000040-40000000000000000−2i22i2−2i22i2000000000000000000−22220000002i−2i000000
χ638-88-8000000000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ648-88-800000000000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ658-8-880000-808000000000000000000000000000000000000000000000000000000

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