Finite Group Databasebeta

← Group #138134

Character table — Group #138134

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488888888888888888888888881616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-11-1-1-1-111-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ61111111111111111-1-11-1-1-1-111-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111-1-11-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ81111111111111111-1-11-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ9111111111-11-1-1-1-1-111-111-1-1-1-1-1-111-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i1-11-1
χ10111111111-11-1-1-1-1-111-111-1-1-1-1-1-111-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-11-11
χ11111111111-11-1-1-1-1-111-111-1-1-1-1-1-111-1-1111-1-1−i−iii−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11-11
χ12111111111-11-1-1-1-1-111-111-1-1-1-1-1-111-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii1-11-1
χ13111111111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1-111ii−i−iii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii-111-1
χ14111111111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1-111ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i1-1-11
χ15111111111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1-111−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii1-1-11
χ16111111111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1-111−i−iii−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i-111-1
χ17222222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222-2-2-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222-22-2222222-222-2-2-2-2-2-2-2-222-2-2-22200000000000000000000000000000000
χ20222222222-22-22222-2-2-2-2-222-2-222-2-222-222-2-200000000000000000000000000000000
χ212222-2-22-2-2222000022-2-2-2222-2-2-2000000000000000000000000022−2−222−2−22−22−20000
χ222222-2-22-2-2222000022-2-2-2222-2-2-20000000000000000000000000−2−222−2−222−22−220000
χ232222-2-22-2-22220000-2-2-222-2-22-222000000000000000000000000022−2−222−2−2−22−220000
χ242222-2-22-2-22220000-2-2-222-2-22-2220000000000000000000000000−2−222−2−2222−22−20000
χ252222-2-22-2-2-22-20000222-2-2-2-2-22220000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i20000
χ262222-2-22-2-2-22-20000222-2-2-2-2-22220000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i20000
χ272222-2-22-2-2-22-20000-2-222222-22-2-20000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i20000
χ282222-2-22-2-2-22-20000-2-222222-22-2-20000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i20000
χ292222-2-2-2222-22222200-20000-220022-2-2-200002222-2-2-2-2000000000000000000000000
χ302222-2-2-2222-22222200-20000-220022-2-2-20000-2-2-2-22222000000000000000000000000
χ312222-2-2-2222-22-2-2-2-200-20000-2200-2-222200000000000022-2-222-2-20000000000000000
χ322222-2-2-2222-22-2-2-2-200-20000-2200-2-2222000000000000-2-222-2-2220000000000000000
χ332222-2-2-222-2-2-2222200200002-200-2-2-2-220000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ342222-2-2-222-2-2-2222200200002-200-2-2-2-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ352222-2-2-222-2-2-2-2-2-2-200200002-2002222-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-222-2-2-2-2-2-2-200200002-2002222-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3722-2-22-222-20-2022-2-22-202-2000000002-20002-22−22−22−22−22−22−22−22−20000000000000000
χ3822-2-22-222-20-2022-2-22-202-2000000002-20002-2−22−22−22−22−22−22−22−220000000000000000
χ3922-2-22-222-20-2022-2-2-220-22000000002-2000-222−22−22−22−2−22−22−22−220000000000000000
χ4022-2-22-222-20-2022-2-2-220-22000000002-2000-22−22−22−22−222−22−22−22−20000000000000000
χ4122-2-22-222-20-20-2-2222-202-200000000-22000-22i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4222-2-22-222-20-20-2-2222-202-200000000-22000-22−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4322-2-22-222-20-20-2-222-220-2200000000-220002-2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4422-2-22-222-20-20-2-222-220-2200000000-220002-2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4522-2-2-22-22-202022-2-2000002i−2i002i−2i00-2202i−2i002−22−2−22−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ4622-2-2-22-22-202022-2-2000002i−2i002i−2i00-2202i−2i00−22−222−22−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4722-2-2-22-22-202022-2-200000−2i2i00−2i2i00-220−2i2i002−22−2−22−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ4822-2-2-22-22-202022-2-200000−2i2i00−2i2i00-220−2i2i00−22−222−22−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ4922-2-2-22-22-2020-2-222000002i−2i002i−2i002-20−2i2i00i2−i2−i2i2−i2i2i2−i22−2−222−2−220000000000000000
χ5022-2-2-22-22-2020-2-222000002i−2i002i−2i002-20−2i2i00−i2i2i2−i2i2−i2−i2i2−222−2−222−20000000000000000
χ5122-2-2-22-22-2020-2-22200000−2i2i00−2i2i002-202i−2i00i2−i2−i2i2−i2i2i2−i2−222−2−222−20000000000000000
χ5222-2-2-22-22-2020-2-22200000−2i2i00−2i2i002-202i−2i00−i2i2i2−i2i2−i2−i2i22−2−222−2−220000000000000000
χ53444444-4-4-44-4400000040000-4-40000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-4000000-40000440000000000000000000000000000000000000000000
χ5544-4-44-4-4-440400000000004i−4i00−4i4i00000000000000000000000000000000000000000
χ5644-4-44-4-4-44040000000000−4i4i004i−4i00000000000000000000000000000000000000000
χ5744-4-4-444-440-4000004-40-4400000000000000000000000000000000000000000000000
χ5844-4-4-444-440-400000-4404-400000000000000000000000000000000000000000000000
χ594-44-40000040-422−2222−220000000000022−2200000000000000000000000ζ+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
χ604-44-40000040-422−2222−220000000000022−2200000000000000000000000−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
χ614-44-40000040-4−2222−222200000000000−222200000000000000000000000ζ−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
χ624-44-40000040-4−2222−222200000000000−222200000000000000000000000−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
χ634-44-400000-40422−2222−2200000000000−222200000000000000000000000ζ−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
χ644-44-400000-40422−2222−2200000000000−222200000000000000000000000−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
χ654-44-400000-404−2222−22220000000000022−2200000000000000000000000ζ+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
χ664-44-400000-404−2222−22220000000000022−2200000000000000000000000−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
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

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