Finite Group Databasebeta

← Group #138558

Character table — Group #138558

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order1222444444448888244444488888888161616161616161624888161616161616161616161616444488882488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ5111111111111111111-1-11-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111-1-11-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ8111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ91111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1iiii−i−i−i−i-1-1111ii−i−iiiii−i−i−i−iii−i−i11-1-11-1i−i
χ101111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1iiii−i−i−i−i-1-1111ii−i−iiiii−i−i−i−i−i−iii-1-111-11−ii
χ111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1−i−i−i−iiiii-1-1111−i−iii−i−i−i−iiiiiii−i−i-1-111-11i−i
χ121111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1−i−i−i−iiiii-1-1111−i−iii−i−i−i−iiiii−i−iii11-1-11-1−ii
χ131111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiiiii−i−i11-1-1-11−ii
χ141111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiii−i−iii-1-1111-1i−i
χ151111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−iii−i−i-1-1111-1−ii
χ161111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−i−i−iii11-1-1-11i−i
χ17222222222222-2-2-2-22222222-2-2-2-2-2-2-2-20000000022-2-2-2000000000000000000000000
χ18222222222222-2-2-2-222-2-22-2-2-2-2-2-2222200000000-2-2-222000000000000000000000000
χ1922222222-2-2222222-2-200-20022-2-200002222222200-200-2-2-2-200000000000000000000
χ2022222222-2-2222222-2-200-20022-2-20000-2-2-2-2-2-2-2-200-200222200000000000000000000
χ2122222222-2-222-2-2-2-2-2-200-200-2-2220000000000000020000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222-2-222-2-2-2-2-2-200-200-2-222000000000000002000000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-222-2-20000-2222-2-2-200000000i2i2−i2−i2i2i2−i2−i2-22000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ24222222-2-222-2-20000-2222-2-2-200000000−i2−i2i2i2−i2−i2i2i2-22000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ25222222-2-222-2-20000-22-2-2-22200000000i2i2−i2−i2i2i2−i2−i22-2000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ26222222-2-222-2-20000-22-2-2-22200000000−i2−i2i2i2−i2−i2i2i22-2000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ27222222-2-2-2-2-2-200002-20020000002i2i−2i−2ii2i2−i2−i2i2i2−i2−i20002i−2i−i2i2−i2i22−2−222−2−22000000000000
χ28222222-2-2-2-2-2-200002-20020000002i2i−2i−2i−i2−i2i2i2−i2−i2i2i20002i−2ii2−i2i2−i2−222−2−222−2000000000000
χ29222222-2-2-2-2-2-200002-2002000000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2000−2i2i−i2i2−i2i2−222−2−222−2000000000000
χ30222222-2-2-2-2-2-200002-2002000000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000−2i2ii2−i2i2−i22−2−222−2−22000000000000
χ312222-2-22222-2-22222-2-222222-2-222222200000000-2-2-2-2-2000000000000000000000000
χ322222-2-22222-2-22222-2-2-2-22-2-2-2-222-2-2-2-20000000022-222000000000000000000000000
χ332222-2-222-2-2-2-222222200-200-2-2-2-200000000000000200000022-2-2-2-222000000000000
χ342222-2-222-2-2-2-222222200-200-2-2-2-2000000000000002000000-2-22222-2-2000000000000
χ352222-2-222-2-2-2-2-2-2-2-22200-200222200002i2i2i2i−2i−2i−2i−2i00-200−2i−2i2i2i00000000000000000000
χ362222-2-222-2-2-2-2-2-2-2-22200-20022220000−2i−2i−2i−2i2i2i2i2i00-2002i2i−2i−2i00000000000000000000
χ372222-2-2-2-2222200002-222-2-2-20000000022−2−2−2−2222-20002−2−222−22−2−22−22000000000000
χ382222-2-2-2-2222200002-222-2-2-200000000−2−22222−2−22-2000−222−2−22−222−22−2000000000000
χ392222-2-2-2-2222200002-2-2-2-2220000000022−2−2−2−222-220002−2−22−22−222−22−2000000000000
χ402222-2-2-2-2222200002-2-2-2-22200000000−2−22222−2−2-22000−222−22−22−2−22−22000000000000
χ412222-2-2-2-2-2-2220000-220020000002i2i−2i−2i22−2−2−2−222000−2i2i−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ422222-2-2-2-2-2-2220000-220020000002i2i−2i−2i−2−22222−2−2000−2i2i2−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ432222-2-2-2-2-2-2220000-22002000000−2i−2i2i2i22−2−2−2−2220002i−2i−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ442222-2-2-2-2-2-2220000-22002000000−2i−2i2i2i−2−22222−2−20002i−2i2−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ4522-2-22i−2i2-2002i−2i2i2i−2i−2i00000002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000001−i−1+i1+i−1−ii2−i22−20000
χ4622-2-22i−2i2-2002i−2i2i2i−2i−2i00000002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000−1+i1−i−1−i1+i−i2i2−220000
χ4722-2-22i−2i2-2002i−2i2i2i−2i−2i00000002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000001−i−1+i1+i−1−i−i2i2−220000
χ4822-2-22i−2i2-2002i−2i2i2i−2i−2i00000002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000−1+i1−i−1−i1+ii2−i22−20000
χ4922-2-2−2i2i2-200−2i2i−2i−2i2i2i00000002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000001+i−1−i1−i−1+ii2−i2−220000
χ5022-2-2−2i2i2-200−2i2i−2i−2i2i2i00000002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000−1−i1+i−1+i1−i−i2i22−20000
χ5122-2-2−2i2i2-200−2i2i−2i−2i2i2i00000002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000001+i−1−i1−i−1+i−i2i22−20000
χ5222-2-2−2i2i2-200−2i2i−2i−2i2i2i00000002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000−1−i1+i−1+i1−ii2−i2−220000
χ5344-4-44i−4i4-4004i−4i−4i−4i4i4i0000000-440000000000000000000000000000000000000000000
χ5444-4-44i−4i-4400−4i4i00000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000
χ5544-4-44i−4i-4400−4i4i0000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000
χ5644-4-4−4i4i4-400−4i4i4i4i−4i−4i0000000-440000000000000000000000000000000000000000000
χ5744-4-4−4i4i-44004i−4i00000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000
χ5844-4-4−4i4i-44004i−4i0000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000
χ594-44-400004-4002i2−2i22i2−2i2000004i−4i002i2−2i222−2222−220000000000000000000000000000000000000
χ604-44-400004-4002i2−2i22i2−2i200000−4i4i002i2−2i2−2222−22220000000000000000000000000000000000000
χ614-44-400004-400−2i22i2−2i22i2000004i−4i00−2i22i2−2222−22220000000000000000000000000000000000000
χ624-44-400004-400−2i22i2−2i22i200000−4i4i00−2i22i222−2222−220000000000000000000000000000000000000
χ634-44-40000-44002i2−2i22i2−2i2004-400000−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ644-44-40000-44002i2−2i22i2−2i200-4400000−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000
χ654-44-40000-4400−2i22i2−2i22i2004-4000002i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ664-44-40000-4400−2i22i2−2i22i200-44000002i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.