Finite Group Databasebeta

← Group #138708

Character table — Group #138708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order12222244444488884448888888888888161616161616161622448888161616162288
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-111-1-1-1-1-1-1-111-11111-1ii−i−iii−i−i1111-1-1-1-11-11-1ii−i−iii−i−i1-1i−i
χ101111-1-1-111-1-1-1-1-1-1-111-11111-1ii−i−iii−i−i1111-1-1-1-1-11-11−i−iiiii−i−i-11−ii
χ111111-1-1-111-1-1-1-1-1-1-111-11111-1ii−i−iii−i−i-1-1-1-111111-11-1ii−i−i−i−iii-11−ii
χ121111-1-1-111-1-1-1-1-1-1-111-11111-1ii−i−iii−i−i-1-1-1-11111-11-11−i−iii−i−iii1-1i−i
χ131111-1-1-111-1-1-1-1-1-1-111-11111-1−i−iii−i−iii1111-1-1-1-11-11-1−i−iii−i−iii1-1−ii
χ141111-1-1-111-1-1-1-1-1-1-111-11111-1−i−iii−i−iii1111-1-1-1-1-11-11ii−i−i−i−iii-11i−i
χ151111-1-1-111-1-1-1-1-1-1-111-11111-1−i−iii−i−iii-1-1-1-111111-11-1−i−iiiii−i−i-11i−i
χ161111-1-1-111-1-1-1-1-1-1-111-11111-1−i−iii−i−iii-1-1-1-11111-11-11ii−i−iii−i−i1-1−ii
χ17222222222222-2-2-2-2222-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222-2-222222-2-2-22-2-22-2000000000000000022-2-2000000000000
χ20222222222-2-222222-2-2-22-2-22-20000000000000000-2-222000000000000
χ21222222222-2-22-2-2-2-2-2-2-2-222-22000000000000000000002i−2i2i−2i00000000
χ22222222222-2-22-2-2-2-2-2-2-2-222-2200000000000000000000−2i2i−2i2i00000000
χ23222222-2-2-2-2-2-200002-22000002i−2i2i−2i000022−2−222−2−200000000i2−i2i2−i20000
χ24222222-2-2-2-2-2-200002-22000002i−2i2i−2i0000−2−222−2−22200000000−i2i2−i2i20000
χ25222222-2-2-2-2-2-200002-2200000−2i2i−2i2i000022−2−222−2−200000000−i2i2−i2i20000
χ26222222-2-2-2-2-2-200002-2200000−2i2i−2i2i0000−2−222−2−22200000000i2−i2i2−i20000
χ272222-2-22-2-222200002-2-2000002-2-22000022−2−2−2−222000000002−2−220000
χ282222-2-22-2-222200002-2-2000002-2-220000−2−22222−2−200000000−222−20000
χ292222-2-22-2-222200002-2-200000-222-2000022−2−2−2−22200000000−222−20000
χ302222-2-22-2-222200002-2-200000-222-20000−2−22222−2−2000000002−2−220000
χ312222-2-2-22222-22222-2-22-222-2-2000000000000000000002-2-2200000000
χ322222-2-2-22222-22222-2-22-222-2-200000000000000000000-222-200000000
χ332222-2-2-22222-2-2-2-2-2-2-222-2-22200000000000000002-2-22000000000000
χ342222-2-2-22222-2-2-2-2-2-2-222-2-2220000000000000000-222-2000000000000
χ352222-2-2-222-2-2-2222222-2-2-2-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-222-2-2-2222222-2-2-2-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ37444444-4-4-444-40000-44-40000000000000000000000000000000000000
χ384444-4-44-4-4-4-440000-4440000000000000000000000000000000000000
χ3944-4-44-444-400-400000000000000002i2−2i22i2−2i2000000000000000000000000
χ4044-4-44-444-400-40000000000000000−2i22i2−2i22i2000000000000000000000000
χ4144-4-44-4-4-4400444-4-4000-4004000000000000000000000000000000000
χ4244-4-44-4-4-44004-4-444000400-4000000000000000000000000000000000
χ4344-4-4-444-4400-444-4-4000400-4000000000000000000000000000000000
χ4444-4-4-444-4400-4-4-444000-4004000000000000000000000000000000000
χ4544-4-4-44-44-4004000000000000000022−22−2222000000000000000000000000
χ4644-4-4-44-44-40040000000000000000−222222−22000000000000000000000000
χ474-4-44000004-4022−2222−22000022−220000000000ζ+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+ζ70000000000000000
χ484-4-44000004-4022−2222−22000022−220000000000−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−ζ70000000000000000
χ494-4-44000004-40−2222−22220000−22220000000000ζ−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+ζ70000000000000000
χ504-4-44000004-40−2222−22220000−22220000000000−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−ζ70000000000000000
χ514-4-4400000-44022−2222−220000−22220000000000ζ−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−ζ70000000000000000
χ524-4-4400000-44022−2222−220000−22220000000000−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+ζ70000000000000000
χ534-4-4400000-440−2222−2222000022−220000000000ζ+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−ζ70000000000000000
χ544-4-4400000-440−2222−2222000022−220000000000−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+ζ70000000000000000
χ558-88-80000000042−42−42420000000000000000000000000000000000000000
χ568-88-800000000−424242−420000000000000000000000000000000000000000

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