Finite Group Databasebeta

← Group #258406

Character table — Group #258406

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111-1-111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ81111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-111111-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1111-1-1-1-111-1-1
χ10111111111111-1-1-1-11111-1-111111-1-11-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-1-111
χ11111111111111-1-1-1-11111-1-111111-1-11-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111
χ12111111111111-1-1-1-11111-1-111111-1-11-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11-1-1-1111111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-11-1-11-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-11111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-11-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-11-1-111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-11-1-11-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-11-1-11-111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-111-1-1-1-1-1-111
χ172222222222-2-2222222-2-2-2-22222-222-2-2-2-200-2-22200000000000000000000000000000000
χ182222222222-2-2222222-2-2-2-2-2-2-2-2-222-2-2220022-2-200000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2222222-2-2-2-222200-2-2-2-200000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-22-2-200222200000000000000000000000000000000
χ2122222222-2-2222222-2-222220000-2-2-2-2-20022000022000000000000000000-2-20000000000
χ2222222222-2-2222222-2-222220000-2-2-2-2-200-2-20000-2-2000000000000000000220000000000
χ2322222222-2-222-2-2-2-2-2-222-2-20000-222-2200220000-2-20000000000000000002-20000000000
χ2422222222-2-222-2-2-2-2-2-222-2-20000-222-2200-2-2000022000000000000000000-220000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-200002-2-2220000000000000000000000000000002-22-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-200002-2-222000000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-20000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-2000000000000000000000000000000-222-2000000
χ292-22-222-2-2002-22i2i−2i−2i002-22i−2i000000000002-200002i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000000000
χ302-22-222-2-2002-22i2i−2i−2i002-22i−2i000000000002-200002i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000000000
χ312-22-222-2-2002-22i2i−2i−2i002-22i−2i00000000000-220000−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000000000
χ322-22-222-2-2002-22i2i−2i−2i002-22i−2i00000000000-220000−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000000000
χ332-22-222-2-2002-2−2i−2i2i2i002-2−2i2i000000000002-20000−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000000000
χ342-22-222-2-2002-2−2i−2i2i2i002-2−2i2i000000000002-20000−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000000000
χ352-22-222-2-2002-2−2i−2i2i2i002-2−2i2i00000000000-2200002i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000000000
χ362-22-222-2-2002-2−2i−2i2i2i002-2−2i2i00000000000-2200002i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000000000
χ372-2-222-22-22-22200002-2-2-2002i2i−2i−2i-2002000002i−2i000000002-22-200000000000000002i−2i0000
χ382-2-222-22-22-22200002-2-2-2002i2i−2i−2i-2002000002i−2i00000000-22-220000000000000000−2i2i0000
χ392-2-222-22-22-22200002-2-2-200−2i−2i2i2i-200200000−2i2i000000002-22-20000000000000000−2i2i0000
χ402-2-222-22-22-22200002-2-2-200−2i−2i2i2i-200200000−2i2i00000000-22-2200000000000000002i−2i0000
χ412-2-222-22-22-2-2-200002-222002i2i−2i−2i200-200000−2i2i00002i−2i2i−2i0000000000002-2000000000000
χ422-2-222-22-22-2-2-200002-222002i2i−2i−2i200-200000−2i2i0000−2i2i−2i2i000000000000-22000000000000
χ432-2-222-22-22-2-2-200002-22200−2i−2i2i2i200-2000002i−2i00002i−2i2i−2i000000000000-22000000000000
χ442-2-222-22-22-2-2-200002-22200−2i−2i2i2i200-2000002i−2i0000−2i2i−2i2i0000000000002-2000000000000
χ452-2-22-22-2222002-22-2-2-200002i−2i2i−2i02-2000000002i−2i00000000002−22−22−22−20000000000i2−i2i2−i2
χ462-2-22-22-2222002-22-2-2-200002i−2i2i−2i02-2000000002i−2i0000000000−22−22−22−220000000000−i2i2−i2i2
χ472-2-22-22-2222002-22-2-2-20000−2i2i−2i2i02-200000000−2i2i00000000002−22−22−22−20000000000−i2i2−i2i2
χ482-2-22-22-2222002-22-2-2-20000−2i2i−2i2i02-200000000−2i2i0000000000−22−22−22−220000000000i2−i2i2−i2
χ492-2-22-22-222200-22-22-2-200002i−2i2i−2i0-2200000000−2i2i00000000002−22−2−22−220000000000i2−i2−i2i2
χ502-2-22-22-222200-22-22-2-200002i−2i2i−2i0-2200000000−2i2i0000000000−22−222−22−20000000000−i2i2i2−i2
χ512-2-22-22-222200-22-22-2-20000−2i2i−2i2i0-22000000002i−2i00000000002−22−2−22−220000000000−i2i2i2−i2
χ522-2-22-22-222200-22-22-2-20000−2i2i−2i2i0-22000000002i−2i0000000000−22−222−22−20000000000i2−i2−i2i2
χ534444-4-4-4-44-4000000-4400004-4-44000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4000000-440000-444-4000000000000000000000000000000000000000000000
χ554444-4-4-4-4-440000004-400000000000004-400000000000000000000000000000000000000
χ564444-4-4-4-4-440000004-40000000000000-4400000000000000000000000000000000000000
χ5744-4-44-4-44004-4000000-4400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5844-4-44-4-44004-4000000-440000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5944-4-44-4-4400-440000004-40000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ6044-4-44-4-4400-440000004-4000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ6144-4-4-444-400004i−4i−4i4i0000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ6244-4-4-444-400004i−4i−4i4i000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ6344-4-4-444-40000−4i4i4i−4i0000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ6444-4-4-444-40000−4i4i4i−4i000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ654-44-444-4-400-444i4i−4i−4i00-44−4i4i0000000000000000000000000000000000000000000000000
χ664-44-444-4-400-44−4i−4i4i4i00-444i−4i0000000000000000000000000000000000000000000000000
χ674-4-444-44-4-44440000-44-4-4000000400-400000000000000000000000000000000000000000
χ684-4-444-44-4-44-4-40000-4444000000-400400000000000000000000000000000000000000000
χ694-4-44-44-44-4-4004-44-444000000000-44000000000000000000000000000000000000000000
χ704-4-44-44-44-4-400-44-44440000000004-4000000000000000000000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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