Finite Group Databasebeta

← Group #511997

Character table — Group #511997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488882244444444488882244444444444444888881616161616161616161616164488
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
χ51111111111111111-1-11-1-1-1-111-1-11111111111-1-1-1-111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111
χ61111111111111111-1-11-1-1-1-111-1-11111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111-1-11-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111-1-11-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111111-1-1111111111-111-1-1-1-1-1-11-1-111111-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ101111111-1-1111111111-111-1-1-1-1-1-11-1-111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-11-11
χ111111111-1-1111111111-111-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-111-1-11111-1-1-1-111-1-1-11-11
χ121111111-1-1111111111-111-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1111-11-1
χ131111111-1-11111111-1-1-1-1-111-1-1111-1-111111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-111-111-1
χ141111111-1-11111111-1-1-1-1-111-1-1111-1-111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-1-11-1-11
χ151111111-1-11111111-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ161111111-1-11111111-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1
χ17222222222222-2-2-2-222222222222-2-2-2-20000000000000000-2-2-2-2-20000000000000000
χ18222222222222-2-2-2-2-2-22-2-2-2-222-2-2-2-2-2-20000000000000000-222220000000000000000
χ192222222-2-2222-2-2-2-222-222-2-2-2-2-2-2-222-200000000000000002-2-2220000000000000000
χ202222222-2-2222-2-2-2-2-2-2-2-2-222-2-222-222-20000000000000000222-2-20000000000000000
χ212222-2-2222-2-22000022-2-2-2222-2-2-2000000000000000000000000022−2−222−2−22−22−20000
χ222222-2-2222-2-22000022-2-2-2222-2-2-20000000000000000000000000−2−222−2−222−22−220000
χ232222-2-2222-2-220000-2-2-222-2-22-222000000000000000000000000022−2−222−2−2−22−220000
χ242222-2-2222-2-220000-2-2-222-2-22-2220000000000000000000000000−2−222−2−2222−22−20000
χ252222-2-22-2-2-2-220000222-2-2-2-2-2222000000000000000000000000022−2−2−2−2222−2−220000
χ262222-2-22-2-2-2-220000222-2-2-2-2-22220000000000000000000000000−2−22222−2−2−222−20000
χ272222-2-22-2-2-2-220000-2-222222-22-2-2000000000000000000000000022−2−2−2−222−222−20000
χ282222-2-22-2-2-2-220000-2-222222-22-2-20000000000000000000000000−2−22222−2−22−2−220000
χ292222-2-2-22222-2222200-20000-2200-222-222-2-2220000-2-20000-200000000000000000000
χ302222-2-2-22222-2222200-20000-2200-222-2-2-222-2-20000220000-200000000000000000000
χ312222-2-2-22222-2-2-2-2-200-20000-22002-2-2200000022-2-20022-2-2200000000000000000000
χ322222-2-2-22222-2-2-2-2-200-20000-22002-2-22000000-2-22200-2-222200000000000000000000
χ332222-2-2-2-2-222-2222200200002-200-2-2-2-222-2-2-2-20000220000200000000000000000000
χ342222-2-2-2-2-222-2222200200002-200-2-2-2-2-2-222220000-2-20000200000000000000000000
χ352222-2-2-2-2-222-2-2-2-2-200200002-200222200000022-2-200-2-222-200000000000000000000
χ362222-2-2-2-2-222-2-2-2-2-200200002-2002222000000-2-2220022-2-2-200000000000000000000
χ3722-2-22-22002-2-222-2-22-202-2000000200-22-22-2002-22-200000002-2000000000000000000
χ3822-2-22-22002-2-222-2-22-202-2000000200-2-22-2200-22-2200000002-2000000000000000000
χ3922-2-22-22002-2-222-2-2-220-22000000200-22-22-200-22-220000000-22000000000000000000
χ4022-2-22-22002-2-222-2-2-220-22000000200-2-22-22002-22-20000000-22000000000000000000
χ4122-2-22-22002-2-2-2-2222-202-2000000-200200002i−2i00002i−2i2i−2i2i−2i0-22000000000000000000
χ4222-2-22-22002-2-2-2-2222-202-2000000-20020000−2i2i0000−2i2i−2i2i−2i2i0-22000000000000000000
χ4322-2-22-22002-2-2-2-222-220-22000000-200200002i−2i00002i−2i−2i2i−2i2i02-2000000000000000000
χ4422-2-22-22002-2-2-2-222-220-22000000-20020000−2i2i0000−2i2i2i−2i2i−2i02-2000000000000000000
χ4522-2-2-22-2002-2222-2-2000002i−2i002i−2i-20022-2-22000000002i−2i−2i2i0002i−2i0000000000000000
χ4622-2-2-22-2002-2222-2-2000002i−2i002i−2i-2002-222-200000000−2i2i2i−2i0002i−2i0000000000000000
χ4722-2-2-22-2002-2222-2-200000−2i2i00−2i2i-20022-2-2200000000−2i2i2i−2i000−2i2i0000000000000000
χ4822-2-2-22-2002-2222-2-200000−2i2i00−2i2i-2002-222-2000000002i−2i−2i2i000−2i2i0000000000000000
χ4922-2-2-22-2002-22-2-222000002i−2i002i−2i200-200002i−2i2-2-22−2i2i0000000−2i2i0000000000000000
χ5022-2-2-22-2002-22-2-222000002i−2i002i−2i200-20000−2i2i-222-22i−2i0000000−2i2i0000000000000000
χ5122-2-2-22-2002-22-2-22200000−2i2i00−2i2i200-200002i−2i-222-2−2i2i00000002i−2i0000000000000000
χ5222-2-2-22-2002-22-2-22200000−2i2i00−2i2i200-20000−2i2i2-2-222i−2i00000002i−2i0000000000000000
χ53444444-444-4-4-400000040000-4-40000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-4000000-40000440000000000000000000000000000000000000000000
χ5544-4-44-4-400-4440000000004i−4i00−4i4i00000000000000000000000000000000000000000
χ5644-4-44-4-400-444000000000−4i4i004i−4i00000000000000000000000000000000000000000
χ5744-4-4-44400-44-400004-40-4400000000000000000000000000000000000000000000000
χ5844-4-4-44400-44-40000-4404-400000000000000000000000000000000000000000000000
χ594-4-440004i−4i00022−2222−220000000000002i2−2i20000000000000000000000ζ+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
χ604-4-440004i−4i00022−2222−220000000000002i2−2i20000000000000000000000−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
χ614-4-440004i−4i000−2222−2222000000000000−2i22i20000000000000000000000ζ−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
χ624-4-440004i−4i000−2222−2222000000000000−2i22i20000000000000000000000−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
χ634-4-44000−4i4i00022−2222−22000000000000−2i22i20000000000000000000000ζ+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
χ644-4-44000−4i4i00022−2222−22000000000000−2i22i20000000000000000000000−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
χ654-4-44000−4i4i000−2222−22220000000000002i2−2i20000000000000000000000ζ−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
χ664-4-44000−4i4i000−2222−22220000000000002i2−2i20000000000000000000000−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
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.