Finite Group Databasebeta

← Group #247121

Character table — Group #247121

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444444444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1
χ3111111111111111111111111111111-1-1111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111-1-111-1-1-1-11111111111111111-1-11-1-1-1-11-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-11111
χ71111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ81111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-111-1-1-1-1
χ9111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1-111-1-1
χ10111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111111-1-1-1-1-111
χ11111111111111-1-1-1-11111-1-11111-1-111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111
χ12111111111111-1-1-1-11111-1-11111-1-111-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-1-111-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-1-11111-1-1-1-11111111-1-1-1-1-11111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-111111-1-111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-111-1-11-1-1-1-111
χ172222222222-2-2222222-2-2-2-2222222-2-200-2-2-200-2-222000000000000000000000000000000
χ182222222222-2-2222222-2-2-2-2-2-2-2-222-2-200-2220022-2-2000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2222222-2-2-2-20022200-2-2-2-2000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2002-2-2002222000000000000000000000000000000
χ2122222222-2-2222222-2-222220000-2-2-2-222-200220000000000000000000000-20000-2000000
χ2222222222-2-2222222-2-222220000-2-2-2-2-2-2-200-2-20000000000000000000000200002000000
χ2322222222-2-222-2-2-2-2-2-222-2-2000022-2-222200-2-20000000000000000000000-200002000000
χ2422222222-2-222-2-2-2-2-2-222-2-2000022-2-2-2-220022000000000000000000000020000-2000000
χ2522222222-2-2-2-22222-2-2-2-2-2-20000-2-2220020000000000000000000000000002-20002-20000
χ2622222222-2-2-2-22222-2-2-2-2-2-20000-2-222002000000000000000000000000000-22000-220000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-20000000000000000000000000002-2000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-2000000000000000000000000000-220002-20000
χ2922-22-2-22-200-2-222-2-200222-2000000002-20002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ3022-22-2-22-200-2-222-2-200222-2000000002-20002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ3122-22-2-22-200-2-222-2-200222-200000000-22000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ3222-22-2-22-200-2-222-2-200222-200000000-22000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ3322-22-2-22-200-2-2-2-2220022-22000000002-2000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3422-22-2-22-200-2-2-2-2220022-22000000002-2000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ3522-22-2-22-200-2-2-2-2220022-2200000000-220002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ3622-22-2-22-200-2-2-2-2220022-2200000000-220002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ372-2-2222-2-22-2002i−2i2i−2i2-2000022-2-22i−2i000000000002i−2i000000002−22−2i2−i2i2−i200000000002−2i2−i2
χ382-2-2222-2-22-2002i−2i2i−2i2-2000022-2-22i−2i000000000002i−2i00000000−22−22−i2i2−i2i20000000000−22−i2i2
χ392-2-2222-2-22-2002i−2i2i−2i2-20000-2-2222i−2i00000000000−2i2i000000002−22−2i2−i2i2−i20000000000−22−i2i2
χ402-2-2222-2-22-2002i−2i2i−2i2-20000-2-2222i−2i00000000000−2i2i00000000−22−22−i2i2−i2i200000000002−2i2−i2
χ412-2-2222-2-22-200−2i2i−2i2i2-2000022-2-2−2i2i00000000000−2i2i000000002−22−2−i2i2−i2i200000000002−2−i2i2
χ422-2-2222-2-22-200−2i2i−2i2i2-2000022-2-2−2i2i00000000000−2i2i00000000−22−22i2−i2i2−i20000000000−22i2−i2
χ432-2-2222-2-22-200−2i2i−2i2i2-20000-2-222−2i2i000000000002i−2i000000002−22−2−i2i2−i2i20000000000−22i2−i2
χ442-2-2222-2-22-200−2i2i−2i2i2-20000-2-222−2i2i000000000002i−2i00000000−22−22i2−i2i2−i200000000002−2−i2i2
χ452-2-2-22-222-2-22-20000222-2002-22-2002-200000002-20000002-22-200000000000002-20000000
χ462-2-2-22-222-2-22-20000222-2002-22-2002-200000002-2000000-22-220000000000000-220000000
χ472-2-2-22-222-2-22-20000222-200-22-22002-20000000-220000002-22-20000000000000-220000000
χ482-2-2-22-222-2-22-20000222-200-22-22002-20000000-22000000-22-2200000000000002-20000000
χ492-2-2-22-222-2-2-22000022-22002-22-200-220000000-22002-22-20000000000002-2000000000000
χ502-2-2-22-222-2-2-22000022-22002-22-200-220000000-2200-22-22000000000000-22000000000000
χ512-2-2-22-222-2-2-22000022-2200-22-2200-2200000002-2002-22-2000000000000-22000000000000
χ522-2-2-22-222-2-2-22000022-2200-22-2200-2200000002-200-22-220000000000002-2000000000000
χ53444-44-4-4-44-4000000-440000000000000004-4000000000000000000000000000000000000
χ54444-44-4-4-44-4000000-44000000000000000-44000000000000000000000000000000000000
χ55444-44-4-4-4-440000004-400004-4-44000000000000000000000000000000000000000000000
χ56444-44-4-4-4-440000004-40000-444-4000000000000000000000000000000000000000000000
χ5744-44-4-44-4004444-4-400-4-4-440000000000000000000000000000000000000000000000000
χ5844-44-4-44-40044-4-44400-4-44-40000000000000000000000000000000000000000000000000
χ594-444-4-4-4400004i−4i−4i4i0000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ604-444-4-4-4400004i−4i−4i4i000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ614-444-4-4-440000−4i4i4i−4i0000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ624-444-4-4-440000−4i4i4i−4i000000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ634-44-4-444-4004-4000000-440000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ644-44-4-444-4004-4000000-44000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ654-44-4-444-400-440000004-400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ664-44-4-444-400-440000004-40000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ674-4-4444-4-4-44004i−4i4i−4i-4400000000−4i4i0000000000000000000000000000000000000000000
χ684-4-4444-4-4-4400−4i4i−4i4i-44000000004i−4i0000000000000000000000000000000000000000000
χ694-4-4-44-444444-40000-4-44-400000000-4400000000000000000000000000000000000000000
χ704-4-4-44-44444-440000-4-4-44000000004-400000000000000000000000000000000000000000
χ7188-8-8-88-88000000000000000000000000000000000000000000000000000000000000000

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