Finite Group Databasebeta

← Group #138613

Character table — Group #138613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488884448888888888884444444488888888888881616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-1-111-1-1-1-1-1-1-111-1111iiii−i−i−i−i11111-1-1-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1ii−i−i1-1i−i
χ101111-1-1-111-1-1-1-1-1-1-111-1111iiii−i−i−i−i11111-1-1-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−iii-11−ii
χ111111-1-1-111-1-1-1-1-1-1-111-1111iiii−i−i−i−i1-1-1-1-11111-1−i−i−i−iiiiiii−i−i1111-1-1-1-1ii−i−i-11−ii
χ121111-1-1-111-1-1-1-1-1-1-111-1111iiii−i−i−i−i1-1-1-1-11111-1−i−i−i−iiiiiii−i−i-1-1-1-11111−i−iii1-1i−i
χ131111-1-1-111-1-1-1-1-1-1-111-1111−i−i−i−iiiii11111-1-1-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−iii1-1−ii
χ141111-1-1-111-1-1-1-1-1-1-111-1111−i−i−i−iiiii11111-1-1-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111ii−i−i-11i−i
χ151111-1-1-111-1-1-1-1-1-1-111-1111−i−i−i−iiiii1-1-1-1-11111-1iiii−i−i−i−i−i−iii1111-1-1-1-1−i−iii-11i−i
χ161111-1-1-111-1-1-1-1-1-1-111-1111−i−i−i−iiiii1-1-1-1-11111-1iiii−i−i−i−i−i−iii-1-1-1-11111ii−i−i1-1−ii
χ17222222222222-2-2-2-2222-2-2-222222222-200000000-200000000-2-2-2-20000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-200000000-20000000022220000000000000000
χ19222222222-2-222222-2-2-22-2-200000000222-2-222-2-2-20000000000000000000000000000
χ20222222222-2-222222-2-2-22-2-2000000002-2-222-2-222-20000000000000000000000000000
χ21222222222-2-22-2-2-2-2-2-2-2-22200000000-20000000022i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222-2-22-2-2-2-2-2-2-2-22200000000-2000000002−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ23222222-2-2-2-2-2-200002-220002i2i−2i−2i2i2i−2i−2i000000000000000000000022−2−222−2−2i2−i2i2−i20000
χ24222222-2-2-2-2-2-200002-220002i2i−2i−2i2i2i−2i−2i0000000000000000000000−2−222−2−222−i2i2−i2i20000
χ25222222-2-2-2-2-2-200002-22000−2i−2i2i2i−2i−2i2i2i000000000000000000000022−2−222−2−2−i2i2−i2i20000
χ26222222-2-2-2-2-2-200002-22000−2i−2i2i2i−2i−2i2i2i0000000000000000000000−2−222−2−222i2−i2i2−i20000
χ272222-2-22-2-222200002-2-200022-2-2-2-222000000000000000000000022−2−2−2−2222−2−220000
χ282222-2-22-2-222200002-2-200022-2-2-2-2220000000000000000000000−2−22222−2−2−222−20000
χ292222-2-22-2-222200002-2-2000-2-22222-2-2000000000000000000000022−2−2−2−222−222−20000
χ302222-2-22-2-222200002-2-2000-2-22222-2-20000000000000000000000−2−22222−2−22−2−220000
χ312222-2-2-22222-22222-2-22-22200000000-200000000-222-2-2-2-22200000000000000000000
χ322222-2-2-22222-22222-2-22-22200000000-200000000-2-2-22222-2-200000000000000000000
χ332222-2-2-22222-2-2-2-2-2-2-222-2-200000000222-2-2-2-22220000000000000000000000000000
χ342222-2-2-22222-2-2-2-2-2-2-222-2-2000000002-2-22222-2-220000000000000000000000000000
χ352222-2-2-222-2-2-2222222-2-2-2-22i2i2i2i−2i−2i−2i−2i-200000000200000000−2i−2i2i2i0000000000000000
χ362222-2-2-222-2-2-2222222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2000000002000000002i2i−2i−2i0000000000000000
χ3722-2-22-222-200-222-2-20002002−22−22−22−2-2002-2002-202−22−22−22−22−22−20000000000000000
χ3822-2-22-222-200-222-2-20002002−22−22−22−2-200-2200-220−22−22−22−222−22−20000000000000000
χ3922-2-22-222-200-222-2-2000200−22−22−22−22-2002-2002-20−22−22−22−22−22−220000000000000000
χ4022-2-22-222-200-222-2-2000200−22−22−22−22-200-2200-2202−22−22−22−2−22−220000000000000000
χ4122-2-22-222-200-2-2-222000-2002−22−22−22−222i−2i002i−2i000i2−i2−i2i2i2−i2−i2i2−22−220000000000000000
χ4222-2-22-222-200-2-2-222000-2002−22−22−22−22−2i2i00−2i2i000−i2i2i2−i2−i2i2i2−i2−22−220000000000000000
χ4322-2-22-222-200-2-2-222000-200−22−22−22−2222i−2i002i−2i000−i2i2i2−i2−i2i2i2−i22−22−20000000000000000
χ4422-2-22-222-200-2-2-222000-200−22−22−22−222−2i2i00−2i2i000i2−i2−i2i2i2−i2−i2i22−22−20000000000000000
χ4522-2-2-22-22-200222-2-2000-200i2−i2i2−i2−i2i2−i2i222i−2i00−2i2i000−222−22−2−22−i2i2i2−i20000000000000000
χ4622-2-2-22-22-200222-2-2000-200i2−i2i2−i2−i2i2−i2i22−2i2i002i−2i0002−2−22−222−2−i2i2i2−i20000000000000000
χ4722-2-2-22-22-200222-2-2000-200−i2i2−i2i2i2−i2i2−i222i−2i00−2i2i0002−2−22−222−2i2−i2−i2i20000000000000000
χ4822-2-2-22-22-200222-2-2000-200−i2i2−i2i2i2−i2i2−i22−2i2i002i−2i000−222−22−2−22i2−i2−i2i20000000000000000
χ4922-2-2-22-22-2002-2-222000200i2−i2i2−i2−i2i2−i2i2-2002-200-220i2−i2i2−i2−i2i2−i2i2i2−i2−i2i20000000000000000
χ5022-2-2-22-22-2002-2-222000200i2−i2i2−i2−i2i2−i2i2-200-22002-20−i2i2−i2i2i2−i2i2−i2i2−i2−i2i20000000000000000
χ5122-2-2-22-22-2002-2-222000200−i2i2−i2i2i2−i2i2−i2-2002-200-220−i2i2−i2i2i2−i2i2−i2−i2i2i2−i20000000000000000
χ5222-2-2-22-22-2002-2-222000200−i2i2−i2i2i2−i2i2−i2-200-22002-20i2−i2i2−i2−i2i2−i2i2−i2i2i2−i20000000000000000
χ53444444-4-4-444-40000-44-40000000000000000000000000000000000000000000000000
χ544444-4-44-4-4-4-440000-4440000000000000000000000000000000000000000000000000
χ5544-4-44-4-4-4400400000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5644-4-44-4-4-440040000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5744-4-4-444-4400-4000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-4-444-4400-40000000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-4-44000004-4022−2222−22000022−22000000000000000000000000000000ζ+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
χ604-4-44000004-4022−2222−22000022−22000000000000000000000000000000−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
χ614-4-44000004-40−2222−22220000−2222000000000000000000000000000000ζ−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
χ624-4-44000004-40−2222−22220000−2222000000000000000000000000000000−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
χ634-4-4400000-44022−2222−220000−2222000000000000000000000000000000ζ−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
χ644-4-4400000-44022−2222−220000−2222000000000000000000000000000000−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
χ654-4-4400000-440−2222−2222000022−22000000000000000000000000000000ζ+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
χ664-4-4400000-440−2222−2222000022−22000000000000000000000000000000−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
χ678-88-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-88-800000000−424242−420000000000000000000000000000000000000000000000000000

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