Finite Group Databasebeta

← Group #138290

Character table — Group #138290

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222222444488882444444444488884444444444444444888881616161616161616161616162488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111
χ61111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ9111111-1-11111-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i111-1-1iiii−i−i−i−iii−i−i1-11-1
χ10111111-1-11111-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i111-1-1−i−i−i−iiiii−i−iii-11-11
χ11111111-1-11111-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiii111-1-1iiii−i−i−i−iii−i−i-11-11
χ12111111-1-11111-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiii111-1-1−i−i−i−iiiii−i−iii1-11-1
χ13111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1-111iiii−i−i−i−i−i−iii-111-1
χ14111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1-111−i−i−i−iiiiiii−i−i1-1-11
χ15111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1-111iiii−i−i−i−i−i−iii1-1-11
χ16111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1-111−i−i−i−iiiiiii−i−i-111-1
χ17222222222222-2-2-2-222222222222-2-2-2-20000000000000000-2-2-2-2-20000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-222220000000000000000
χ19222222-2-222222222-2-2-222-2-222-2-2-2-2220000000000000000-2-2-2220000000000000000
χ20222222-2-222222222-2-2-2-2-222-2-222-2-2220000000000000000-222-2-20000000000000000
χ212222-2-22222-2-20000-22-22222-2-2-2-2000000000000000000000000022−2−222−2−22−22−20000
χ222222-2-22222-2-20000-22-22222-2-2-2-20000000000000000000000000−2−222−2−222−22−220000
χ232222-2-22222-2-20000-22-2-2-2-2-22222000000000000000000000000022−2−222−2−2−22−220000
χ242222-2-22222-2-20000-22-2-2-2-2-222220000000000000000000000000−2−222−2−2222−22−20000
χ252222-2-222-2-2222222-2-220000000022-2-22222-2-2-2-200000000-200000000000000000000
χ262222-2-222-2-2222222-2-220000000022-2-2-2-2-2-2222200000000-200000000000000000000
χ272222-2-222-2-222-2-2-2-2-2-2200000000-2-2220000000022-2-222-2-2200000000000000000000
χ282222-2-222-2-222-2-2-2-2-2-2200000000-2-22200000000-2-222-2-222200000000000000000000
χ292222-2-2-2-222-2-200002-2222-2-2-2-2220000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i20000
χ302222-2-2-2-222-2-200002-2222-2-2-2-2220000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i20000
χ312222-2-2-2-222-2-200002-22-2-22222-2-20000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i20000
χ322222-2-2-2-222-2-200002-22-2-22222-2-20000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i20000
χ332222-2-2-2-2-2-222222222-200000000-2-2-2-2000000002i2i−2i−2i−2i−2i2i2i200000000000000000000
χ342222-2-2-2-2-2-222222222-200000000-2-2-2-200000000−2i−2i2i2i2i2i−2i−2i200000000000000000000
χ352222-2-2-2-2-2-222-2-2-2-222-20000000022222i2i−2i−2i−2i−2i2i2i00000000-200000000000000000000
χ362222-2-2-2-2-2-222-2-2-2-222-2000000002222−2i−2i2i2i2i2i−2i−2i00000000-200000000000000000000
χ3722-2-22-2002-22-22i2i−2i−2i000002i−2i002i−2i002i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i02-2000000000000000000
χ3822-2-22-2002-22-22i2i−2i−2i000002i−2i002i−2i002i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i02-2000000000000000000
χ3922-2-22-2002-22-22i2i−2i−2i00000−2i2i00−2i2i002i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0-22000000000000000000
χ4022-2-22-2002-22-22i2i−2i−2i00000−2i2i00−2i2i002i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0-22000000000000000000
χ4122-2-22-2002-22-2−2i−2i2i2i000002i−2i002i−2i00−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0-22000000000000000000
χ4222-2-22-2002-22-2−2i−2i2i2i000002i−2i002i−2i00−2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0-22000000000000000000
χ4322-2-22-2002-22-2−2i−2i2i2i00000−2i2i00−2i2i00−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i02-2000000000000000000
χ4422-2-22-2002-22-2−2i−2i2i2i00000−2i2i00−2i2i00−2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i02-2000000000000000000
χ4522-2-2-2200-222-22i2i−2i−2i0002i−2i002i−2i0000−2i2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0002-20000000000000000
χ4622-2-2-2200-222-22i2i−2i−2i0002i−2i002i−2i0000−2i2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0002-20000000000000000
χ4722-2-2-2200-222-22i2i−2i−2i000−2i2i00−2i2i0000−2i2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000-220000000000000000
χ4822-2-2-2200-222-22i2i−2i−2i000−2i2i00−2i2i0000−2i2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000-220000000000000000
χ4922-2-2-2200-222-2−2i−2i2i2i0002i−2i002i−2i00002i−2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000-220000000000000000
χ5022-2-2-2200-222-2−2i−2i2i2i0002i−2i002i−2i00002i−2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000-220000000000000000
χ5122-2-2-2200-222-2−2i−2i2i2i000−2i2i00−2i2i00002i−2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0002-20000000000000000
χ5222-2-2-2200-222-2−2i−2i2i2i000−2i2i00−2i2i00002i−2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0002-20000000000000000
χ5344444444-4-4-4-400004-4-40000000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000000000000
χ5544-4-44-400-44-4400000004i−4i00−4i4i0000000000000000000000000000000000000000000
χ5644-4-44-400-44-440000000−4i4i004i−4i0000000000000000000000000000000000000000000
χ5744-4-4-44004-4-440000000004i−4i00−4i4i00000000000000000000000000000000000000000
χ5844-4-4-44004-4-44000000000−4i4i004i−4i00000000000000000000000000000000000000000
χ594-4-44004-4000022−2222−220000000000022−2200000000000000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000
χ604-4-44004-4000022−2222−220000000000022−2200000000000000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000
χ614-4-44004-40000−2222−222200000000000−222200000000000000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000
χ624-4-44004-40000−2222−222200000000000−222200000000000000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000
χ634-4-4400-44000022−2222−2200000000000−222200000000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000
χ644-4-4400-44000022−2222−2200000000000−222200000000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000
χ654-4-4400-440000−2222−22220000000000022−2200000000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000
χ664-4-4400-440000−2222−22220000000000022−2200000000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000
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.