Finite Group Databasebeta

← Group #323951

Character table — Group #323951

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244448888888822444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-11-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1111111111111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-11-1
χ91111111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ121111111111111111-1-111-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111111111-1-1-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-1-1-1-1111111-1-11-1-11
χ172222222222-2-2-222-222-2-2220000000022-2-2-222-2-2-20000000000000000000000000000
χ182222222222-2-2-222-222-2-22200000000-2-2-222-2-2-2220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-20000000022222-2-22-2-20000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-200000000-2-22-2-2222220000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-22222-2-2-2-200-20000200-2-200002200000000000000000000
χ2222222222-2-2222-2-2222-2-2-2-2-2-2-2-2222200-20000200220000-2-200000000000000000000
χ2322222222-2-2222-2-22-2-2-2-2222222-2-2-2-20020000-200220000-2-200000000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-2-2-222220020000-200-2-200002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000000020000-200002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000000020000-20000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000000-20000200002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000000-2000020000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ29222-2-2-22-22-20002-202-2002-2i2i2−i2−i2i2i2−i2−i20002i−2i0002i−2ii2−i22−22−2i2−i22−22−20000000000000000
χ30222-2-2-22-22-20002-202-2002-2i2i2−i2−i2i2i2−i2−i2000−2i2i000−2i2ii2−i2−22−22i2−i2−22−220000000000000000
χ31222-2-2-22-22-20002-202-2002-2−i2−i2i2i2−i2−i2i2i20002i−2i0002i−2i−i2i2−22−22−i2i2−22−220000000000000000
χ32222-2-2-22-22-20002-202-2002-2−i2−i2i2i2−i2−i2i2i2000−2i2i000−2i2i−i2i22−22−2−i2i22−22−20000000000000000
χ33222-2-2-22-22-20002-20-2200-22i2i2−i2−i2i2i2−i2−i20002i−2i000−2i2i−i2i22−22−2−i2i2−22−220000000000000000
χ34222-2-2-22-22-20002-20-2200-22i2i2−i2−i2i2i2−i2−i2000−2i2i0002i−2i−i2i2−22−22−i2i22−22−20000000000000000
χ35222-2-2-22-22-20002-20-2200-22−i2−i2i2i2−i2−i2i2i20002i−2i000−2i2ii2−i2−22−22i2−i22−22−20000000000000000
χ36222-2-2-22-22-20002-20-2200-22−i2−i2i2i2−i2−i2i2i2000−2i2i0002i−2ii2−i22−22−2i2−i2−22−220000000000000000
χ37222-2-2-22-2-22000-2202-200-22i2i2−i2−i2−i2−i2i2i22-20002-2000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ38222-2-2-22-2-22000-2202-200-22i2i2−i2−i2−i2−i2i2i2-22000-22000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i20000000000000000
χ39222-2-2-22-2-22000-2202-200-22−i2−i2i2i2i2i2−i2−i22-20002-2000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ40222-2-2-22-2-22000-2202-200-22−i2−i2i2i2i2i2−i2−i2-22000-22000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i20000000000000000
χ41222-2-2-22-2-22000-220-22002-2i2i2−i2−i2−i2−i2i2i22-2000-22000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ42222-2-2-22-2-22000-220-22002-2i2i2−i2−i2−i2−i2i2i2-220002-2000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i20000000000000000
χ43222-2-2-22-2-22000-220-22002-2−i2−i2i2i2i2i2−i2−i22-2000-22000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ44222-2-2-22-2-22000-220-22002-2−i2−i2i2i2i2i2−i2−i2-220002-2000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i20000000000000000
χ452-222-2-2-222-222-2-22-2002-2002i−2i2i−2i2i−2i2i−2i000000000000000000000022-2-200002i−2i000000
χ462-222-2-2-222-222-2-22-2002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000-2-2220000−2i2i000000
χ472-222-2-2-222-222-2-22-2002-200−2i2i−2i2i−2i2i−2i2i000000000000000000000022-2-20000−2i2i000000
χ482-222-2-2-222-222-2-22-2002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000-2-22200002i−2i000000
χ492-222-2-2-22-2222-22-2-200-22002i−2i2i−2i−2i2i−2i2i000000000000000000000000002i2i−2i−2i002-20000
χ502-222-2-2-22-2222-22-2-200-22002i−2i2i−2i−2i2i−2i2i00000000000000000000000000−2i−2i2i2i00-220000
χ512-222-2-2-22-2222-22-2-200-2200−2i2i−2i2i2i−2i2i−2i000000000000000000000000002i2i−2i−2i00-220000
χ522-222-2-2-22-2222-22-2-200-2200−2i2i−2i2i2i−2i2i−2i00000000000000000000000000−2i−2i2i2i002-20000
χ5344-4-4-44-44004-4400-400000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ5444-4-4-44-44004-4400-40000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ5544-4-4-44-4400-44-400400000000000000000000000000000000000022−2222−22000000000000
χ5644-4-4-44-4400-44-4004000000000000000000000000000000000000−2222−2222000000000000
χ574-444-4-4-444-4-4-44-44400-44000000000000000000000000000000000000000000000000
χ584-444-4-4-44-44-4-444-44004-4000000000000000000000000000000000000000000000000
χ594-44-444-4-444000-4-4000000022−22−222222−22−222200000000000000000000000000000000000000
χ604-44-444-4-444000-4-40000000−222222−22−222222−2200000000000000000000000000000000000000
χ614-44-444-4-4-4-400044000000022−22−2222−222222−2200000000000000000000000000000000000000
χ624-44-444-4-4-4-4000440000000−222222−2222−22−222200000000000000000000000000000000000000
χ634-4-4-44-444004-4-4004000000000000000000000000000000000000000022−22−222200000000
χ644-4-4-44-444004-4-40040000000000000000000000000000000000000000−222222−2200000000
χ654-4-4-44-44400-44400-400000000000000000000000000000000000022−22−2222000000000000
χ664-4-4-44-44400-44400-4000000000000000000000000000000000000−222222−22000000000000
χ6788-888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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