Finite Group Databasebeta

← Group #255463

Character table — Group #255463

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444222244444424444444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111-1-1-1-1-1-1111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ811111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111-111-1-1-1-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-1-1-111-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-1-111
χ12111111111111-1-1-1-111111111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-11-1-1111111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-11111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-111-1-111-1-1-1-111111111-1-1-1-1-111111-1-1-1-1-1-111
χ172222222222-2-2222222-2-22222-2-222-2-2-2-2-2-2-2220000000000000000000000000000000000
χ182222222222-2-2222222-2-2-2-2-2-2-2-222-2-2-22222-2-20000000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2222222-2-2-2-2222-2-2-2-20000000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-2-2-22-2-222220000000000000000000000000000000000
χ2122222222-2-2222222-2-222000022-2-2-2-2-200000022220000000000000000-200-20000000000
χ2222222222-2-2222222-2-222000022-2-2-2-2-2000000-2-2-2-2000000000000000020020000000000
χ2322222222-2-222-2-2-2-2-2-2220000-2-222-2-2200000022-2-20000000000000000-20020000000000
χ2422222222-2-222-2-2-2-2-2-2220000-2-222-2-22000000-2-2220000000000000000200-20000000000
χ2522222222-2-2-2-22222-2-2-2-20000-2-2-2-22220000000000000000000000000000002-22-2000000
χ2622222222-2-2-2-22222-2-2-2-20000-2-2-2-2222000000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-20000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-2000000000000000000000000000000-222-2000000
χ2922-2-2-222-2002-22i2i−2i−2i002-200002i−2i000000000002-22i−2ii2i2−i2−i222−2−2i2i2−i2−i222−2−200000000000000
χ3022-2-2-222-2002-22i2i−2i−2i002-200002i−2i000000000002-22i−2i−i2−i2i2i2−2−222−i2−i2i2i2−2−22200000000000000
χ3122-2-2-222-2002-22i2i−2i−2i002-200002i−2i00000000000-22−2i2ii2i2−i2−i222−2−2−i2−i2i2i2−2−22200000000000000
χ3222-2-2-222-2002-22i2i−2i−2i002-200002i−2i00000000000-22−2i2i−i2−i2i2i2−2−222i2i2−i2−i222−2−200000000000000
χ3322-2-2-222-2002-2−2i−2i2i2i002-20000−2i2i000000000002-2−2i2ii2i2−i2−i2−2−222i2i2−i2−i2−2−22200000000000000
χ3422-2-2-222-2002-2−2i−2i2i2i002-20000−2i2i000000000002-2−2i2i−i2−i2i2i222−2−2−i2−i2i2i222−2−200000000000000
χ3522-2-2-222-2002-2−2i−2i2i2i002-20000−2i2i00000000000-222i−2ii2i2−i2−i2−2−222−i2−i2i2i222−2−200000000000000
χ3622-2-2-222-2002-2−2i−2i2i2i002-20000−2i2i00000000000-222i−2i−i2−i2i2i222−2−2i2i2−i2−i2−2−22200000000000000
χ372-222-2-22-22-2002i−2i2i−2i2-20022-2-2002i−2i00000002i−2i000000000000i2−i2i2−i22−22−20000000000i2−i22−2
χ382-222-2-22-22-2002i−2i2i−2i2-20022-2-2002i−2i00000002i−2i000000000000−i2i2−i2i2−22−220000000000−i2i2−22
χ392-222-2-22-22-2002i−2i2i−2i2-200-2-222002i−2i0000000−2i2i000000000000i2−i2i2−i22−22−20000000000−i2i2−22
χ402-222-2-22-22-2002i−2i2i−2i2-200-2-222002i−2i0000000−2i2i000000000000−i2i2−i2i2−22−220000000000i2−i22−2
χ412-222-2-22-22-200−2i2i−2i2i2-20022-2-200−2i2i0000000−2i2i000000000000i2−i2i2−i2−22−220000000000i2−i2−22
χ422-222-2-22-22-200−2i2i−2i2i2-20022-2-200−2i2i0000000−2i2i000000000000−i2i2−i2i22−22−20000000000−i2i22−2
χ432-222-2-22-22-200−2i2i−2i2i2-200-2-22200−2i2i00000002i−2i000000000000i2−i2i2−i2−22−220000000000−i2i22−2
χ442-222-2-22-22-200−2i2i−2i2i2-200-2-22200−2i2i00000002i−2i000000000000−i2i2−i2i22−22−20000000000i2−i2−22
χ452-2-22-22-22222-20000-2-2-222-22-200002-20002-20000002i−2i2i−2i00000000000002i−2i00000000000
χ462-2-22-22-22222-20000-2-2-222-22-200002-20002-2000000−2i2i−2i2i0000000000000−2i2i00000000000
χ472-2-22-22-22222-20000-2-2-22-22-2200002-2000-220000002i−2i2i−2i0000000000000−2i2i00000000000
χ482-2-22-22-22222-20000-2-2-22-22-2200002-2000-22000000−2i2i−2i2i00000000000002i−2i00000000000
χ492-2-22-22-2222-220000-2-22-22-22-20000-22000-2200000000002i−2i2i−2i00000000000000002i−2i0000
χ502-2-22-22-2222-220000-2-22-22-22-20000-22000-220000000000−2i2i−2i2i0000000000000000−2i2i0000
χ512-2-22-22-2222-220000-2-22-2-22-220000-220002-200000000002i−2i2i−2i0000000000000000−2i2i0000
χ522-2-22-22-2222-220000-2-22-2-22-220000-220002-20000000000−2i2i−2i2i00000000000000002i−2i0000
χ5344-444-4-4-44-4000000-44004-4-4400000000000000000000000000000000000000000000000
χ5444-444-4-4-44-4000000-4400-444-400000000000000000000000000000000000000000000000
χ5544-444-4-4-4-440000004-400000000000004-400000000000000000000000000000000000000
χ5644-444-4-4-4-440000004-40000000000000-4400000000000000000000000000000000000000
χ5744-4-4-444-400-444i4i−4i−4i00-440000−4i4i000000000000000000000000000000000000000000000
χ5844-4-4-444-400-44−4i−4i4i4i00-4400004i−4i000000000000000000000000000000000000000000000
χ594-444-4-44-4-44004i−4i4i−4i-4400000000−4i4i0000000000000000000000000000000000000000000
χ604-444-4-44-4-4400−4i4i−4i4i-44000000004i−4i0000000000000000000000000000000000000000000
χ614-44-444-4-40044000000-4-400000000000000000000022−22−222200000000000000000000000000
χ624-44-444-4-40044000000-4-4000000000000000000000−222222−2200000000000000000000000000
χ634-44-444-4-400-4-40000004400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ644-44-444-4-400-4-4000000440000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ654-4-44-44-44-4-44-4000044-4400000000-4400000000000000000000000000000000000000000
χ664-4-44-44-44-4-4-440000444-4000000004-400000000000000000000000000000000000000000
χ674-4-4-44-44400004-4-440000000000000000000000000000000002-2-222-2-2200000000000000
χ684-4-4-44-44400004-4-44000000000000000000000000000000000-222-2-222-200000000000000
χ694-4-4-44-4440000-444-40000000000000000000000000000000002-2-22-222-200000000000000
χ704-4-4-44-4440000-444-4000000000000000000000000000000000-222-22-2-2200000000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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