Finite Group Databasebeta

← Group #324472

Character table — Group #324472

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822224444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ91111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11
χ111111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-11
χ121111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-111-1
χ172222222222-2-2-2-22222-2-2-2-22222-2-2-2-200002-2000022-2-2000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2222200002-20000-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-22222-2-2-2-20000-220000-2-222000000000000000000000000
χ202222222222-2-2-2-222-2-222-2-2-2-2-2-222220000-22000022-2-2000000000000000000000000
χ2122222222-2-22222-2-22222-2-2000000002222-2-2-2-2-2-20000000000000000000000000000
χ2222222222-2-22222-2-22222-2-200000000-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-20000000022-2-222-2-2220000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-200000000-2-2222222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222000000000000-2200000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-222-2-222000000000000-220000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000000002-200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000000002-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2922-2-222-2-20022-2-2002-22-200i2i2−i2−i2i2i2−i2−i20000002i−2i2i−2ii2−i2i2−i2000000002−22−22−22−200000000
χ3022-2-222-2-20022-2-2002-22-200i2i2−i2−i2i2i2−i2−i2000000−2i2i−2i2ii2−i2i2−i200000000−22−22−22−2200000000
χ3122-2-222-2-20022-2-2002-22-200−i2−i2i2i2−i2−i2i2i20000002i−2i2i−2i−i2i2−i2i200000000−22−22−22−2200000000
χ3222-2-222-2-20022-2-2002-22-200−i2−i2i2i2−i2−i2i2i2000000−2i2i−2i2i−i2i2−i2i2000000002−22−22−22−200000000
χ3322-2-222-2-20022-2-200-22-2200i2i2−i2−i2i2i2−i2−i20000002i−2i−2i2i−i2i2−i2i2000000002−22−2−22−2200000000
χ3422-2-222-2-20022-2-200-22-2200i2i2−i2−i2i2i2−i2−i2000000−2i2i2i−2i−i2i2−i2i200000000−22−222−22−200000000
χ3522-2-222-2-20022-2-200-22-2200−i2−i2i2i2−i2−i2i2i20000002i−2i−2i2ii2−i2i2−i200000000−22−222−22−200000000
χ3622-2-222-2-20022-2-200-22-2200−i2−i2i2i2−i2−i2i2i2000000−2i2i2i−2ii2−i2i2−i2000000002−22−2−22−2200000000
χ3722-2-222-2-200-2-222002-2-2200i2i2−i2−i2−i2−i2i2i22-22-2000000i2−i2−i2i200000000i2−i2−i2i2i2−i2−i2i200000000
χ3822-2-222-2-200-2-222002-2-2200i2i2−i2−i2−i2−i2i2i2-22-22000000i2−i2−i2i200000000−i2i2i2−i2−i2i2i2−i200000000
χ3922-2-222-2-200-2-222002-2-2200−i2−i2i2i2i2i2−i2−i22-22-2000000−i2i2i2−i200000000−i2i2i2−i2−i2i2i2−i200000000
χ4022-2-222-2-200-2-222002-2-2200−i2−i2i2i2i2i2−i2−i2-22-22000000−i2i2i2−i200000000i2−i2−i2i2i2−i2−i2i200000000
χ4122-2-222-2-200-2-22200-222-200i2i2−i2−i2−i2−i2i2i22-2-22000000−i2i2i2−i200000000i2−i2−i2i2−i2i2i2−i200000000
χ4222-2-222-2-200-2-22200-222-200i2i2−i2−i2−i2−i2i2i2-222-2000000−i2i2i2−i200000000−i2i2i2−i2i2−i2−i2i200000000
χ4322-2-222-2-200-2-22200-222-200−i2−i2i2i2i2i2−i2−i22-2-22000000i2−i2−i2i200000000−i2i2i2−i2i2−i2−i2i200000000
χ4422-2-222-2-200-2-22200-222-200−i2−i2i2i2i2i2−i2−i2-222-2000000i2−i2−i2i200000000i2−i2−i2i2−i2i2i2−i200000000
χ4522-2-2-2-222222-22-2-2-200002-22i−2i2i−2i2i−2i2i−2i00000000000000000022-2-200000000002i−2i0000
χ4622-2-2-2-222222-22-2-2-200002-22i−2i2i−2i2i−2i2i−2i000000000000000000-2-2220000000000−2i2i0000
χ4722-2-2-2-222222-22-2-2-200002-2−2i2i−2i2i−2i2i−2i2i00000000000000000022-2-20000000000−2i2i0000
χ4822-2-2-2-222222-22-2-2-200002-2−2i2i−2i2i−2i2i−2i2i000000000000000000-2-22200000000002i−2i0000
χ4922-2-2-2-22222-22-22-2-20000-222i−2i2i−2i−2i2i−2i2i0000000000000022-2-20000000000002i−2i000000
χ5022-2-2-2-22222-22-22-2-20000-222i−2i2i−2i−2i2i−2i2i00000000000000-2-222000000000000−2i2i000000
χ5122-2-2-2-22222-22-22-2-20000-22−2i2i−2i2i2i−2i2i−2i0000000000000022-2-2000000000000−2i2i000000
χ5222-2-2-2-22222-22-22-2-20000-22−2i2i−2i2i2i−2i2i−2i00000000000000-2-2220000000000002i−2i000000
χ534444-4-4-4-4004-4-440000000022−22−222222−22−222200000000000000000000000000000000000000
χ544444-4-4-4-4004-4-4400000000−222222−22−222222−2200000000000000000000000000000000000000
χ554444-4-4-4-400-444-40000000022−22−2222−222222−2200000000000000000000000000000000000000
χ564444-4-4-4-400-444-400000000−222222−2222−22−222200000000000000000000000000000000000000
χ5744-4-4-4-444-4-44-44-4440000-440000000000000000000000000000000000000000000000
χ5844-4-4-4-444-4-4-44-444400004-40000000000000000000000000000000000000000000000
χ594-44-44-44-44-400004-4000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ604-44-44-44-44-400004-400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ614-44-44-44-4-440000-4400000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ624-44-44-44-4-440000-440000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ634-4-44-444-44-40000-44000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ644-4-44-444-44-40000-4400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ654-4-44-444-4-4400004-400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ664-4-44-444-4-4400004-40000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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