Finite Group Databasebeta

← Group #199045

Character table — Group #199045

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444448888888888888888881616161611112222224444444488888888888888888816161616
order12222244444444444444444444448888888844882222224444444444444444444444888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-111-1-11-1ii−i−i1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i1111-1-111-1-11-1ii−i−i1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ101111-1-111-1-11-1ii−i−i1-111-1-1i−iii−i−i-1-111−i−iii-11−ii1111-1-111-1-11-1ii−i−i1-111-1-1i−iii−i−i-1-111−i−iii-11−ii
χ111111-1-111-1-11-1ii−i−i1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii1111-1-111-1-11-1ii−i−i1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii
χ121111-1-111-1-11-1ii−i−i1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i1111-1-111-1-11-1ii−i−i1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i
χ131111-1-111-1-11-1−i−iii1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii1111-1-111-1-11-1−i−iii1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ141111-1-111-1-11-1−i−iii1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i1111-1-111-1-11-1−i−iii1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i
χ151111-1-111-1-11-1−i−iii1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i1111-1-111-1-11-1−i−iii1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i
χ161111-1-111-1-11-1−i−iii1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii1111-1-111-1-11-1−i−iii1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii
χ172222222222-2-22222-2-20000-2-200000000000000002222222222-2-22222-2-20000-2-20000000000000000
χ182222222222-2-2-2-2-2-2-2-200002200000000000000002222222222-2-2-2-2-2-2-2-20000220000000000000000
χ19222222-2-2-2-22-20000-220000002-22-2000000000000222222-2-2-2-22-20000-220000002-22-2000000000000
χ20222222-2-2-2-22-20000-22000000-22-22000000000000222222-2-2-2-22-20000-22000000-22-22000000000000
χ21222222-2-2-2-2-2200002-22-22-2000000000000000000222222-2-2-2-2-2200002-22-22-2000000000000000000
χ22222222-2-2-2-2-2200002-2-22-22000000000000000000222222-2-2-2-2-2200002-2-22-22000000000000000000
χ232222-2-222-2-2-222i2i−2i−2i-220000−2i2i00000000000000002222-2-222-2-2-222i2i−2i−2i-220000−2i2i0000000000000000
χ242222-2-222-2-2-22−2i−2i2i2i-2200002i−2i00000000000000002222-2-222-2-2-22−2i−2i2i2i-2200002i−2i0000000000000000
χ252222-2-2-2-222220000-2-20000002i−2i−2i2i0000000000002222-2-2-2-222220000-2-20000002i−2i−2i2i000000000000
χ262222-2-2-2-222220000-2-2000000−2i2i2i−2i0000000000002222-2-2-2-222220000-2-2000000−2i2i2i−2i000000000000
χ272222-2-2-2-222-2-20000222-2-220000000000000000002222-2-2-2-222-2-20000222-2-22000000000000000000
χ282222-2-2-2-222-2-2000022-222-20000000000000000002222-2-2-2-222-2-2000022-222-2000000000000000000
χ292-2-222-22-2-22002i−2i2i−2i000000000000i2−i2i2−i22−22−200002-2-222-22-2-22002i−2i2i−2i000000000000i2−i2i2−i22−22−20000
χ302-2-222-22-2-22002i−2i2i−2i000000000000−i2i2−i2i2−22−2200002-2-222-22-2-22002i−2i2i−2i000000000000−i2i2−i2i2−22−220000
χ312-2-222-22-2-2200−2i2i−2i2i000000000000i2−i2i2−i2−22−2200002-2-222-22-2-2200−2i2i−2i2i000000000000i2−i2i2−i2−22−220000
χ322-2-222-22-2-2200−2i2i−2i2i000000000000−i2i2−i2i22−22−200002-2-222-22-2-2200−2i2i−2i2i000000000000−i2i2−i2i22−22−20000
χ332-2-22-222-22-2002-2-22000000000000i2−i2−i2i2−i2i2i2−i200002-2-22-222-22-2002-2-22000000000000i2−i2−i2i2−i2i2i2−i20000
χ342-2-22-222-22-2002-2-22000000000000−i2i2i2−i2i2−i2−i2i200002-2-22-222-22-2002-2-22000000000000−i2i2i2−i2i2−i2−i2i20000
χ352-2-22-222-22-200-222-2000000000000i2−i2−i2i2i2−i2−i2i200002-2-22-222-22-200-222-2000000000000i2−i2−i2i2i2−i2−i2i20000
χ362-2-22-222-22-200-222-2000000000000−i2i2i2−i2−i2i2i2−i200002-2-22-222-22-200-222-2000000000000−i2i2i2−i2−i2i2i2−i20000
χ374-4-444-4-444-40000000000000000000000000000004-4-444-4-444-4000000000000000000000000000000
χ384-4-44-44-44-440000000000000000000000000000004-4-44-44-44-44000000000000000000000000000000
χ3988-8-800000000000000000000000000000000000088-8-8000000000000000000000000000000000000
χ408-88-80000000000000000000000000000000000008-88-8000000000000000000000000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ421111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ43111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ44111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1
χ45111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ46111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ47111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ48111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ491111-1-111-1-11-1ii−i−i1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i-1-1-1-111-1-111-11−i−iii-11-1-111−ii−i−iii-1-111−i−iii-11−ii
χ501111-1-111-1-11-1ii−i−i1-111-1-1i−iii−i−i-1-111−i−iii-11−ii-1-1-1-111-1-111-11−i−iii-11-1-111−ii−i−iii11-1-1ii−i−i1-1i−i
χ511111-1-111-1-11-1ii−i−i1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii-1-1-1-111-1-111-11−i−iii-1111-1-1−iiii−i−i-1-111−i−iii1-1i−i
χ521111-1-111-1-11-1ii−i−i1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i-1-1-1-111-1-111-11−i−iii-1111-1-1−iiii−i−i11-1-1ii−i−i-11−ii
χ531111-1-111-1-11-1−i−iii1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii-1-1-1-111-1-111-11ii−i−i-11-1-111i−iii−i−i-1-111ii−i−i-11i−i
χ541111-1-111-1-11-1−i−iii1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i-1-1-1-111-1-111-11ii−i−i-11-1-111i−iii−i−i11-1-1−i−iii1-1−ii
χ551111-1-111-1-11-1−i−iii1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i-1-1-1-111-1-111-11ii−i−i-1111-1-1i−i−i−iii-1-111ii−i−i1-1−ii
χ561111-1-111-1-11-1−i−iii1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii-1-1-1-111-1-111-11ii−i−i-1111-1-1i−i−i−iii11-1-1−i−iii-11i−i
χ572222222222-2-22222-2-20000-2-20000000000000000-2-2-2-2-2-2-2-2-2-222-2-2-2-2220000220000000000000000
χ582222222222-2-2-2-2-2-2-2-20000220000000000000000-2-2-2-2-2-2-2-2-2-2222222220000-2-20000000000000000
χ59222222-2-2-2-22-20000-220000002-22-2000000000000-2-2-2-2-2-22222-2200002-2000000-22-22000000000000
χ60222222-2-2-2-22-20000-22000000-22-22000000000000-2-2-2-2-2-22222-2200002-20000002-22-2000000000000
χ61222222-2-2-2-2-2200002-22-22-2000000000000000000-2-2-2-2-2-222222-20000-22-22-22000000000000000000
χ62222222-2-2-2-2-2200002-2-22-22000000000000000000-2-2-2-2-2-222222-20000-222-22-2000000000000000000
χ632222-2-222-2-2-222i2i−2i−2i-220000−2i2i0000000000000000-2-2-2-222-2-2222-2−2i−2i2i2i2-200002i−2i0000000000000000
χ642222-2-222-2-2-22−2i−2i2i2i-2200002i−2i0000000000000000-2-2-2-222-2-2222-22i2i−2i−2i2-20000−2i2i0000000000000000
χ652222-2-2-2-222220000-2-20000002i−2i−2i2i000000000000-2-2-2-22222-2-2-2-2000022000000−2i2i2i−2i000000000000
χ662222-2-2-2-222220000-2-2000000−2i2i2i−2i000000000000-2-2-2-22222-2-2-2-20000220000002i−2i−2i2i000000000000
χ672222-2-2-2-222-2-20000222-2-22000000000000000000-2-2-2-22222-2-2220000-2-2-222-2000000000000000000
χ682222-2-2-2-222-2-2000022-222-2000000000000000000-2-2-2-22222-2-2220000-2-22-2-22000000000000000000
χ692-2-222-22-2-22002i−2i2i−2i000000000000i2−i2i2−i22−22−20000-222-2-22-222-200−2i2i−2i2i000000000000−i2i2−i2i2−22−220000
χ702-2-222-22-2-22002i−2i2i−2i000000000000−i2i2−i2i2−22−220000-222-2-22-222-200−2i2i−2i2i000000000000i2−i2i2−i22−22−20000
χ712-2-222-22-2-2200−2i2i−2i2i000000000000i2−i2i2−i2−22−220000-222-2-22-222-2002i−2i2i−2i000000000000−i2i2−i2i22−22−20000
χ722-2-222-22-2-2200−2i2i−2i2i000000000000−i2i2−i2i22−22−20000-222-2-22-222-2002i−2i2i−2i000000000000i2−i2i2−i2−22−220000
χ732-2-22-222-22-2002-2-22000000000000i2−i2−i2i2−i2i2i2−i20000-222-22-2-22-2200-222-2000000000000−i2i2i2−i2i2−i2−i2i20000
χ742-2-22-222-22-2002-2-22000000000000−i2i2i2−i2i2−i2−i2i20000-222-22-2-22-2200-222-2000000000000i2−i2−i2i2−i2i2i2−i20000
χ752-2-22-222-22-200-222-2000000000000i2−i2−i2i2i2−i2−i2i20000-222-22-2-22-22002-2-22000000000000−i2i2i2−i2−i2i2i2−i20000
χ762-2-22-222-22-200-222-2000000000000−i2i2i2−i2−i2i2i2−i20000-222-22-2-22-22002-2-22000000000000i2−i2−i2i2i2−i2−i2i20000
χ774-4-444-4-444-4000000000000000000000000000000-444-4-444-4-44000000000000000000000000000000
χ784-4-44-44-44-44000000000000000000000000000000-444-44-44-44-4000000000000000000000000000000
χ7988-8-8000000000000000000000000000000000000-8-888000000000000000000000000000000000000
χ808-88-8000000000000000000000000000000000000-88-88000000000000000000000000000000000000

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