Finite Group Databasebeta

← Group #278953

Character table — Group #278953

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888824444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-11-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ91111111111111111-1-111-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1-11
χ101111111111111111-1-111-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-111-1
χ111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-111-1
χ121111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ17222222222-2-2222-2-222-2-2-2-22222-2-2-2-22-200000000-2-200002200000000000000000000
χ18222222222-2-2222-2-222-2-2-2-2-2-2-2-222222-200000000220000-2-200000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2222222-2-2-2-2-2200000000220000-2-200000000000000000000
χ20222222222-2-2222-2-2-2-2-2-222-2-2-2-22222-2200000000-2-200002200000000000000000000
χ2122222222-222-2-2-22222-2-22200000000-2-22222-2-2-2-20000000000000000000000000000
χ2222222222-222-2-2-22222-2-22200000000-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-222-2-2-222-2-2-2-2-2-2000000002222-2-222-2-20000000000000000000000000000
χ2422222222-222-2-2-222-2-2-2-2-2-20000000022-2-222-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-2200000000002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-220000000000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000002-200000000002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000000002-20000000000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2922-2-222-2-202-20002-22i−2i002i−2ii2i2−i2−i2i2i2−i2−i20000002-22i−2i2−2i2−i2i2−i22−22−22−20000000000000000
χ3022-2-222-2-202-20002-22i−2i002i−2ii2i2−i2−i2i2i2−i2−i2000000-22−2i2i2−2−i2i2−i2i22−2−22−220000000000000000
χ3122-2-222-2-202-20002-22i−2i002i−2i−i2−i2i2i2−i2−i2i2i20000002-22i−2i−22−i2i2−i2i2−22−22−220000000000000000
χ3222-2-222-2-202-20002-22i−2i002i−2i−i2−i2i2i2−i2−i2i2i2000000-22−2i2i−22i2−i2i2−i2−222−22−20000000000000000
χ3322-2-222-2-202-20002-2−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i20000002-2−2i2i−22i2−i2i2−i2−22−22−220000000000000000
χ3422-2-222-2-202-20002-2−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i2000000-222i−2i−22−i2i2−i2i2−222−22−20000000000000000
χ3522-2-222-2-202-20002-2−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i20000002-2−2i2i2−2−i2i2−i2i22−22−22−20000000000000000
χ3622-2-222-2-202-20002-2−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i2000000-222i−2i2−2i2−i2i2−i22−2−22−220000000000000000
χ3722-2-222-2-20-22000-222i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2002-22i−2i0000−222−2−222−2−i2i2i2−i20000000000000000
χ3822-2-222-2-20-22000-222i−2i00−2i2ii2i2−i2−i2−i2−i2i2i200-22−2i2i0000−22−222−22−2i2−i2−i2i20000000000000000
χ3922-2-222-2-20-22000-222i−2i00−2i2i−i2−i2i2i2i2i2−i2−i2002-22i−2i00002−2−222−2−22i2−i2−i2i20000000000000000
χ4022-2-222-2-20-22000-222i−2i00−2i2i−i2−i2i2i2i2i2−i2−i200-22−2i2i00002−22−2−22−22−i2i2i2−i20000000000000000
χ4122-2-222-2-20-22000-22−2i2i002i−2ii2i2−i2−i2−i2−i2i2i2002-2−2i2i00002−2−222−2−22−i2i2i2−i20000000000000000
χ4222-2-222-2-20-22000-22−2i2i002i−2ii2i2−i2−i2−i2−i2i2i200-222i−2i00002−22−2−22−22i2−i2−i2i20000000000000000
χ4322-2-222-2-20-22000-22−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2002-2−2i2i0000−222−2−222−2i2−i2−i2i20000000000000000
χ4422-2-222-2-20-22000-22−2i2i002i−2i−i2−i2i2i2i2i2−i2−i200-222i−2i0000−22−222−22−2−i2i2i2−i20000000000000000
χ452-2-222-2-22-2222-22-2-2002-2002-22-22-22-2000000000000000000000000002i2i−2i−2i002i−2i0000
χ462-2-222-2-22-2222-22-2-2002-2002-22-22-22-200000000000000000000000000−2i−2i2i2i00−2i2i0000
χ472-2-222-2-22-2222-22-2-2002-200-22-22-22-22000000000000000000000000002i2i−2i−2i00−2i2i0000
χ482-2-222-2-22-2222-22-2-2002-200-22-22-22-2200000000000000000000000000−2i−2i2i2i002i−2i0000
χ492-2-222-2-22-2-2-22-222200-22002-22-2-22-22000000000000000000000022-2-200002-2000000
χ502-2-222-2-22-2-2-22-222200-22002-22-2-22-220000000000000000000000-2-2220000-22000000
χ512-2-222-2-22-2-2-22-222200-2200-22-222-22-2000000000000000000000022-2-20000-22000000
χ522-2-222-2-22-2-2-22-222200-2200-22-222-22-20000000000000000000000-2-22200002-2000000
χ534444-4-4-4-4400-4-440000000000000000000000000000000000000022−2222−22000000000000
χ544444-4-4-4-4400-4-4400000000000000000000000000000000000000−2222−2222000000000000
χ554444-4-4-4-4-40044-400000000000000000000000000000000000000000022−2222−2200000000
χ564444-4-4-4-4-40044-4000000000000000000000000000000000000000000−2222−222200000000
χ574-44-44-44-404-4000-440000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-44-44-44-404-4000-44000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-44-44-44-40-440004-40000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-44-44-44-40-440004-4000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-444-4-44444-44-4-4-400-44000000000000000000000000000000000000000000000000
χ624-4-444-4-444-4-4-44-444004-4000000000000000000000000000000000000000000000000
χ634-4-44-444-44004-4-40000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ644-4-44-444-44004-4-4000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ654-4-44-444-4-400-4440000000000000000000000000000000000000022−22−2222000000000000
χ664-4-44-444-4-400-44400000000000000000000000000000000000000−222222−22000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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