Finite Group Databasebeta

← Group #131649

Character table — Group #131649

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122244444444888824444448888882488881616161616161616161616161616161622244444888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-11111-1-1
χ61111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111
χ71111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-111
χ81111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-111111-1-1
χ9111111-1-111-1-1-1-1-1-1-11-111-1-11111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−ii−i
χ10111111-1-111-1-1-1-1-1-1-11-111-1-11111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−ii
χ11111111-1-111-1-1-1-1-1-1-11-111-1-11111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−ii
χ12111111-1-111-1-1-1-1-1-1-11-111-1-11111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−ii−i
χ13111111-1-111-1-1-1-1-1-1-11-1-1-1111111-1-11-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-11-1-11ii−i−i−ii
χ14111111-1-111-1-1-1-1-1-1-11-1-1-1111111-1-11-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-111-1−i−iiii−i
χ15111111-1-111-1-1-1-1-1-1-11-1-1-1111111-1-11-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-11−i−iiii−i
χ16111111-1-111-1-1-1-1-1-1-11-1-1-1111111-1-11-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-111-1ii−i−i−ii
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ1922222222-2-2220000-2-2-22222000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ2022222222-2-2220000-2-2-22222000000-2-20000−2−222−2−222−2−222−2−22200000000000000
χ2122222222-2-2220000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−22200000000000000
χ2222222222-2-2220000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−200000000000000
χ23222222-2-222-2-22222-22-222-2-2-2-2-2-222-22-2-222000000000000000000000000000000
χ24222222-2-222-2-22222-22-2-2-222-2-2-2-2222-222-2-2000000000000000000000000000000
χ25222222-2-2-2-2-2-200002-2222-2-20000002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ26222222-2-2-2-2-2-200002-2222-2-20000002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ27222222-2-2-2-2-2-200002-22-2-222000000-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ28222222-2-2-2-2-2-200002-22-2-222000000-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ292222-2-22222-2-22222-2-22000022-2-2-2-20000000000000000000000002-2-2002000000
χ302222-2-22222-2-22222-2-22000022-2-2-2-2000000000000000000000000-22200-2000000
χ312222-2-22222-2-2-2-2-2-2-2-220000-2-2222200000000000000000000002-20002-20000000
χ322222-2-22222-2-2-2-2-2-2-2-220000-2-222220000000000000000000000-22000-220000000
χ332222-2-2-2-2222222222-2-20000-2-222-2-200000000000000000000002-2000-220000000
χ342222-2-2-2-2222222222-2-20000-2-222-2-20000000000000000000000-220002-20000000
χ352222-2-2-2-22222-2-2-2-22-2-2000022-2-2220000000000000000000000002-2200-2000000
χ362222-2-2-2-22222-2-2-2-22-2-2000022-2-222000000000000000000000000-22-2002000000
χ3722-2-22-22i−2i002i−2ii2−i2i2−i20002-22i−2i2−22−2i2−i2002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ300000000000000
χ3822-2-22-22i−2i002i−2ii2−i2i2−i20002-22i−2i2−22−2i2−i2002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ300000000000000
χ3922-2-22-22i−2i002i−2ii2−i2i2−i2000-22−2i2i2−22−2i2−i200−22−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ300000000000000
χ4022-2-22-22i−2i002i−2ii2−i2i2−i2000-22−2i2i2−22−2i2−i200−22−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ300000000000000
χ4122-2-22-22i−2i002i−2i−i2i2−i2i20002-22i−2i−22−22−i2i200−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ700000000000000
χ4222-2-22-22i−2i002i−2i−i2i2−i2i20002-22i−2i−22−22−i2i200−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ700000000000000
χ4322-2-22-22i−2i002i−2i−i2i2−i2i2000-22−2i2i−22−22−i2i2002−2i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ700000000000000
χ4422-2-22-22i−2i002i−2i−i2i2−i2i2000-22−2i2i−22−22−i2i2002−2i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ700000000000000
χ4522-2-22-2−2i2i00−2i2ii2−i2i2−i20002-2−2i2i−22−22i2−i200−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ300000000000000
χ4622-2-22-2−2i2i00−2i2ii2−i2i2−i20002-2−2i2i−22−22i2−i200−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ300000000000000
χ4722-2-22-2−2i2i00−2i2ii2−i2i2−i2000-222i−2i−22−22i2−i2002−2−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ300000000000000
χ4822-2-22-2−2i2i00−2i2ii2−i2i2−i2000-222i−2i−22−22i2−i2002−2−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ300000000000000
χ4922-2-22-2−2i2i00−2i2i−i2i2−i2i20002-2−2i2i2−22−2−i2i2002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ700000000000000
χ5022-2-22-2−2i2i00−2i2i−i2i2−i2i20002-2−2i2i2−22−2−i2i2002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ700000000000000
χ5122-2-22-2−2i2i00−2i2i−i2i2−i2i2000-222i−2i2−22−2−i2i200−22i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ700000000000000
χ5222-2-22-2−2i2i00−2i2i−i2i2−i2i2000-222i−2i2−22−2−i2i200−22i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ700000000000000
χ534444-4-444-4-4-4-4000044-40000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4440000-4440000000000000000000000000000000000000000000000
χ5544-4-4-444i−4i00−4i4i2i2−2i22i2−2i2000000022−22−2222−2i22i2000000000000000000000000000000000000
χ5644-4-4-444i−4i00−4i4i−2i22i2−2i22i20000000−222222−222i2−2i2000000000000000000000000000000000000
χ5744-4-4-44−4i4i004i−4i2i2−2i22i2−2i20000000−222222−22−2i22i2000000000000000000000000000000000000
χ5844-4-4-44−4i4i004i−4i−2i22i2−2i22i2000000022−22−22222i2−2i2000000000000000000000000000000000000
χ594-4-4400004-40044-4-400000000000000000000000000000000000000000002i−2i2i−2i00
χ604-4-4400004-40044-4-40000000000000000000000000000000000000000000−2i2i−2i2i00
χ614-4-4400004-400-4-44400000000000000000000000000000000000000000002-2-2200
χ624-4-4400004-400-4-4440000000000000000000000000000000000000000000-222-200
χ638-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000
χ648-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000
χ658-8-880000-880000000000000000000000000000000000000000000000000000000

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