Finite Group Databasebeta

← Group #138552

Character table — Group #138552

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order12222244444488884448888161616161616161616161616161616162444888881616161616161616444488882488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-1-1-111-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-1ii−i−iii−i−iii−i−i11-1-11-1i−i
χ101111-1-1-1-111-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-1ii−i−iii−i−i−i−iii-1-111-11−ii
χ111111-1-1-1-111-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-111ii−i−i−i−iiiii−i−i11-1-1-11−ii
χ121111-1-1-1-111-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-111ii−i−i−i−iii−i−iii-1-1111-1i−i
χ131111-1-1-1-111-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-111−i−iiiii−i−iii−i−i-1-1111-1−ii
χ141111-1-1-1-111-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-111−i−iiiii−i−i−i−iii11-1-1-11i−i
χ151111-1-1-1-111-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-1−i−iii−i−iiiii−i−i-1-111-11i−i
χ161111-1-1-1-111-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-1−i−iii−i−iii−i−iii11-1-11-1−ii
χ17222222222222-2-2-2-2222-2-2-2-200000000000000002222-2-2-2-2-200000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-20000000000000000-2-2-2-2-2222200000000000000000000
χ1922222222-2-2-2-20000-22-20000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000002i−2i2i−2ii2−i2i2−i22−22−2000000000000
χ2022222222-2-2-2-20000-22-20000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000−2i2i−2i2ii2−i2i2−i2−22−22000000000000
χ2122222222-2-2-2-20000-22-20000−i2−i2i2i2−i2−i2i2i222−2−222−2−200000−2i2i−2i2i−i2i2−i2i22−22−2000000000000
χ2222222222-2-2-2-20000-22-20000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000002i−2i2i−2i−i2i2−i2i2−22−22000000000000
χ23222222-2-222-2-222222-2-222-2-200000000222222220000-200000000-2-2-2-2000000000000
χ24222222-2-222-2-222222-2-222-2-200000000-2-2-2-2-2-2-2-20000-2000000002222000000000000
χ25222222-2-222-2-2-2-2-2-22-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000020000−2i−2i2i2i0000000000000000
χ26222222-2-222-2-2-2-2-2-22-2-2-2-222−2i−2i−2i−2i2i2i2i2i000000000000200002i2i−2i−2i0000000000000000
χ27222222-2-2-2-2220000-2-22000022−2−2−2−22222−2−222−2−22-2-2200000−222−2−22−22000000000000
χ28222222-2-2-2-2220000-2-22000022−2−2−2−222−2−222−2−222-222-200000−222−22−22−2000000000000
χ29222222-2-2-2-2220000-2-220000−2−22222−2−222−2−222−2−2-222-2000002−2−22−22−22000000000000
χ30222222-2-2-2-2220000-2-220000−2−22222−2−2−2−222−2−2222-2-22000002−2−222−22−2000000000000
χ312222-2-22222222222-2-2-2-2-22222222222000000000000-20000-2-2-2-20000000000000000
χ322222-2-22222222222-2-2-2-2-222-2-2-2-2-2-2-2-2000000000000-2000022220000000000000000
χ332222-2-2222222-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i0000200000000−2i−2i2i2i000000000000
χ342222-2-2222222-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i00002000000002i2i−2i−2i000000000000
χ352222-2-222-2-2-2-200002-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-22-200000−i2i2−i2i2−i2i2i2−i2000000000000
χ362222-2-222-2-2-2-200002-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-22-2200000−i2i2−i2i2i2−i2−i2i2000000000000
χ372222-2-222-2-2-2-200002-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-22-2200000i2−i2i2−i2−i2i2i2−i2000000000000
χ382222-2-222-2-2-2-200002-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-22-200000i2−i2i2−i2i2−i2−i2i2000000000000
χ392222-2-2-2-222-2-22222-222-2-2-2-2000000000000000022-2-22-2-22200000000000000000000
χ402222-2-2-2-222-2-22222-222-2-2-2-20000000000000000-2-222222-2-200000000000000000000
χ412222-2-2-2-2-2-222000022-2000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000−2i2i2i−2i2−2−22i2−i2−i2i2000000000000
χ422222-2-2-2-2-2-222000022-2000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000002i−2i−2i2i2−2−22−i2i2i2−i2000000000000
χ432222-2-2-2-2-2-222000022-20000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000002i−2i−2i2i−222−2i2−i2−i2i2000000000000
χ442222-2-2-2-2-2-222000022-20000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000−2i2i2i−2i−222−2−i2i2i2−i2000000000000
χ4522-2-2002i−2i2-22i−2i2i2i−2i−2i000002-22ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ600000000000000000000000001+i−1−i1−i−1+i2−2i2−i20000
χ4622-2-2002i−2i2-22i−2i2i2i−2i−2i000002-22ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60000000000000000000000000−1−i1+i−1+i1−i−22−i2i20000
χ4722-2-2002i−2i2-22i−2i2i2i−2i−2i000002-2−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ600000000000000000000000001+i−1−i1−i−1+i−22−i2i20000
χ4822-2-2002i−2i2-22i−2i2i2i−2i−2i000002-2−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ60000000000000000000000000−1−i1+i−1+i1−i2−2i2−i20000
χ4922-2-200−2i2i2-2−2i2i−2i−2i2i2i000002-22ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ200000000000000000000000001−i−1+i1+i−1−i−22i2−i20000
χ5022-2-200−2i2i2-2−2i2i−2i−2i2i2i000002-22ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ20000000000000000000000000−1+i1−i−1−i1+i2−2−i2i20000
χ5122-2-200−2i2i2-2−2i2i−2i−2i2i2i000002-2−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ200000000000000000000000001−i−1+i1+i−1−i2−2−i2i20000
χ5222-2-200−2i2i2-2−2i2i−2i−2i2i2i000002-2−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ20000000000000000000000000−1+i1−i−1−i1+i−22i2−i20000
χ5344-4-4004i−4i4-44i−4i−4i−4i4i4i00000-44000000000000000000000000000000000000000000000
χ5444-4-4004i−4i-44−4i4i000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ5544-4-4004i−4i-44−4i4i00000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ5644-4-400−4i4i4-4−4i4i4i4i−4i−4i00000-44000000000000000000000000000000000000000000000
χ5744-4-400−4i4i-444i−4i000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ5844-4-400−4i4i-444i−4i00000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ594-4-444-400000022−2222−2200022−2200000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000
χ604-4-444-400000022−2222−2200022−220000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000
χ614-4-444-4000000−2222−2222000−222200000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000
χ624-4-444-4000000−2222−2222000−22220000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000
χ634-4-44-4400000022−2222−22000−222200000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000
χ644-4-44-4400000022−2222−22000−22220000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000
χ654-4-44-44000000−2222−222200022−2200000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000
χ664-4-44-44000000−2222−222200022−220000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000
χ678-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000000
χ688-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.