Finite Group Databasebeta

← Group #258413

Character table — Group #258413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422444444444888888888888888822444444448888
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
χ3111111111111111111111111111111-1-1111111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1111-1-1-1-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1111-1-1-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111
χ12111111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1111111-1-1
χ13111111111111-1-1-1-11111-1-1-1-11-1-1-1-1111-1-11111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-11111-1-111
χ14111111111111-1-1-1-11111-1-1-1-11-1-1-1-1111-1-11111-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-11-111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1111-111-1-1-1-1-1-111
χ172222222222-2-2222222-2-222-2-2-20000-22200000022-2000000000000000000-2-20000000000
χ182222222222-2-2222222-2-222-2-2-20000-2-2-2000000-2-2-2000000000000000000220000000000
χ192222222222-2-2-2-2-2-222-2-2-2-222-20000-222000000-2-220000000000000000002-20000000000
χ202222222222-2-2-2-2-2-222-2-2-2-222-20000-2-2-2000000222000000000000000000-220000000000
χ2122222222-2-2222222-2-222-2-222-22222-200-2-222-2-200-2000000000000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-2-20022-2-22200-2000000000000000000000000000000
χ2322222222-2-222-2-2-2-2-2-22222-2-2-22222-200-2-2-2-222002000000000000000000000000000000
χ2422222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2002222-2-2002000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-220000200000000002000000000000000000002-22-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-22000020000000000200000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222000020000000000-2000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222000020000000000-200000000000000000000-222-2000000
χ2922-2-22-22-2002-22i2i−2i−2i002-2002i−2i022-2-2000002i−2i000000000000022−2−2i2i2−i2−i200000000002−2i2−i2
χ3022-2-22-22-2002-22i2i−2i−2i002-2002i−2i022-2-2000002i−2i0000000000000−2−222−i2−i2i2i20000000000−22−i2i2
χ3122-2-22-22-2002-22i2i−2i−2i002-2002i−2i0-2-22200000−2i2i000000000000022−2−2i2i2−i2−i20000000000−22−i2i2
χ3222-2-22-22-2002-22i2i−2i−2i002-2002i−2i0-2-22200000−2i2i0000000000000−2−222−i2−i2i2i200000000002−2i2−i2
χ3322-2-22-22-2002-2−2i−2i2i2i002-200−2i2i022-2-200000−2i2i000000000000022−2−2−i2−i2i2i200000000002−2−i2i2
χ3422-2-22-22-2002-2−2i−2i2i2i002-200−2i2i022-2-200000−2i2i0000000000000−2−222i2i2−i2−i20000000000−22i2−i2
χ3522-2-22-22-2002-2−2i−2i2i2i002-200−2i2i0-2-222000002i−2i000000000000022−2−2−i2−i2i2i20000000000−22i2−i2
χ3622-2-22-22-2002-2−2i−2i2i2i002-200−2i2i0-2-222000002i−2i0000000000000−2−222i2i2−i2−i200000000002−2−i2i2
χ372-222-2-22-22-2002i−2i2i−2i2-2002i−2i000000002-20000002i−2i022−2−2i2i2−i2−i22−22−2i2−i2i2−i200000000000000
χ382-222-2-22-22-2002i−2i2i−2i2-2002i−2i000000002-20000002i−2i0−2−222−i2−i2i2i2−22−22−i2i2−i2i200000000000000
χ392-222-2-22-22-2002i−2i2i−2i2-2002i−2i00000000-22000000−2i2i022−2−2i2i2−i2−i2−22−22−i2i2−i2i200000000000000
χ402-222-2-22-22-2002i−2i2i−2i2-2002i−2i00000000-22000000−2i2i0−2−222−i2−i2i2i22−22−2i2−i2i2−i200000000000000
χ412-222-2-22-22-200−2i2i−2i2i2-200−2i2i000000002-2000000−2i2i022−2−2−i2−i2i2i22−22−2−i2i2−i2i200000000000000
χ422-222-2-22-22-200−2i2i−2i2i2-200−2i2i000000002-2000000−2i2i0−2−222i2i2−i2−i2−22−22i2−i2i2−i200000000000000
χ432-222-2-22-22-200−2i2i−2i2i2-200−2i2i00000000-220000002i−2i022−2−2−i2−i2i2i2−22−22i2−i2i2−i200000000000000
χ442-222-2-22-22-200−2i2i−2i2i2-200−2i2i00000000-220000002i−2i0−2−222i2i2−i2−i22−22−2−i2i2−i2i200000000000000
χ452-22-222-2-2222-20000-2-2-220000-22i−2i2i−2i2002i−2i000000000002-22-200000000000000002i−2i0000
χ462-22-222-2-2222-20000-2-2-220000-22i−2i2i−2i2002i−2i00000000000-22-220000000000000000−2i2i0000
χ472-22-222-2-2222-20000-2-2-220000-2−2i2i−2i2i200−2i2i000000000002-22-20000000000000000−2i2i0000
χ482-22-222-2-2222-20000-2-2-220000-2−2i2i−2i2i200−2i2i00000000000-22-2200000000000000002i−2i0000
χ492-22-222-2-2-2-22-2000022-22000022i−2i2i−2i-200−2i2i00000002i−2i2i−2i0000000000002-2000000000000
χ502-22-222-2-2-2-22-2000022-22000022i−2i2i−2i-200−2i2i0000000−2i2i−2i2i000000000000-22000000000000
χ512-22-222-2-2-2-22-2000022-2200002−2i2i−2i2i-2002i−2i00000002i−2i2i−2i000000000000-22000000000000
χ522-22-222-2-2-2-22-2000022-2200002−2i2i−2i2i-2002i−2i0000000−2i2i−2i2i0000000000002-2000000000000
χ53444-4-4-4-444-4000000-440000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ54444-4-4-4-444-4000000-44000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ55444-4-4-4-44-440000004-4000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ56444-4-4-4-44-440000004-400000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5744-4-44-44-400-444i4i−4i−4i00-4400−4i4i00000000000000000000000000000000000000000000000
χ5844-4-44-44-400-44−4i−4i4i4i00-44004i−4i00000000000000000000000000000000000000000000000
χ594-444-4-44-4-44004i−4i4i−4i-4400−4i4i0000000000000000000000000000000000000000000000000
χ604-444-4-44-4-4400−4i4i−4i4i-44004i−4i0000000000000000000000000000000000000000000000000
χ614-44-444-4-444-440000-4-44-4000040000-400000000000000000000000000000000000000000
χ624-44-444-4-4-4-4-440000444-40000-40000400000000000000000000000000000000000000000
χ634-4-444-4-440044000000-4-4000004i−4i−4i4i000000000000000000000000000000000000000000
χ644-4-444-4-440044000000-4-400000−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-444-4-4400-4-40000004400000000000000004-4000000000000000000000000000000000
χ664-4-444-4-4400-4-4000000440000000000000000-44000000000000000000000000000000000
χ674-4-4-4-444400004-4-440000000000000000000000000000000002-2-222-2-2200000000000000
χ684-4-4-4-444400004-4-44000000000000000000000000000000000-222-2-222-200000000000000
χ694-4-4-4-44440000-444-40000000000000000000000000000000002-2-22-222-200000000000000
χ704-4-4-4-44440000-444-4000000000000000000000000000000000-222-22-2-2200000000000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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