Finite Group Databasebeta

← Group #492499

Character table — Group #492499

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444444444444444444888816161616161616161616323232323232
order1222444488884888888888816161616161616161616161616161616444422448816161616244488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-1-1-11-1-111-1
χ611111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111-1-1-1-1-111-1-11
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-111-11-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111-1-11-11
χ91111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111111-111-1-111-1-1-1-1
χ101111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-11-111-1-1-1-11111
χ111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-111111-11-1-111-1-111-1-1
χ121111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1-11111-1-111
χ131111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-11-11-11-1-1-1111-11-1-11
χ141111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-11-111-1-1-111-11-111-1
χ151111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-111-11-1-1111-1-1-11-11-11
χ161111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-11-11-1111-1-11-11-11-1
χ1722222222-2-2-2-222222-2-2-2-2-2-2000000000000000022220000-2-20000000000
χ1822222222-2-2-2-222222-2-2-2-2-2-20000000000000000-2-2-2-20000220000000000
χ1922222222-2-2-2-22-2-2-2-22222-2-200000000000000002-22-20000-220000000000
χ2022222222-2-2-2-22-2-2-2-22222-2-20000000000000000-22-2200002-20000000000
χ2122222-22-22222-200000000-2-22222-2-2-2-200000000000022-2-2000000000000
χ2222222-22-22222-200000000-2-22222-2-2-2-2000000000000-2-222000000000000
χ2322222-22-22222-200000000-2-2-2-2-2-222220000000000002-2-22000000000000
χ2422222-22-22222-200000000-2-2-2-2-2-22222000000000000-222-2000000000000
χ252222-22-220000-222-2-200000022−2−222−2−22222−2−2−2−22-2-220000002−22−2000000
χ262222-22-220000-222-2-200000022−2−222−2−22222−2−2−2−2-222-2000000−22−22000000
χ272222-22-220000-222-2-2000000−2−222−2−222−2−2−2−222222-2-22000000−22−22000000
χ282222-22-220000-222-2-2000000−2−222−2−222−2−2−2−22222-222-20000002−22−2000000
χ292222-22-220000-2-2-22200000022−2−222−2−2−2−2−2−2222222-2-20000002−2−22000000
χ302222-22-220000-2-2-22200000022−2−222−2−2−2−2−2−22222-2-222000000−222−2000000
χ312222-22-220000-2-2-222000000−2−222−2−2222222−2−2−2−222-2-2000000−222−2000000
χ322222-22-220000-2-2-222000000−2−222−2−2222222−2−2−2−2-2-2220000002−2−22000000
χ3344444-44-4-4-4-4-4-40000000044000000000000000000000000000000000000
χ344444-4-4-4-40000400000000002222−22−22−22−2222220000000000000000000000000000
χ354444-4-4-4-4000040000000000−22−2222222222−22−220000000000000000000000000000
χ3644-4-440-4044-4-4000000000004-44-400000000000000000000000000000000
χ3744-4-440-4044-4-400000000000-44-4400000000000000000000000000000000
χ3844-4-440-40-4-44400000000000000000002i22i2−2i2−2i22i22i2−2i2−2i200000000000000000000
χ3944-4-440-40-4-4440000000000000000000−2i2−2i22i22i2−2i2−2i22i22i200000000000000000000
χ4044-4-4-40400000000002i22i2−2i2−2i20022−22−222200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4144-4-4-40400000000002i22i2−2i2−2i200−222222−220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4244-4-4-4040000000000−2i2−2i22i22i20022−22−22220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4344-4-4-4040000000000−2i2−2i22i22i200−222222−2200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ444-44-4000022−2222−2202i2−2i2002i−2i2i−2i0000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7ζ+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+ζ700000000000000000000
χ454-44-4000022−2222−2202i2−2i2002i−2i2i−2i000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−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−ζ700000000000000000000
χ464-44-4000022−2222−220−2i22i200−2i2i−2i2i0000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−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−ζ700000000000000000000
χ474-44-4000022−2222−220−2i22i200−2i2i−2i2i000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7ζ+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+ζ700000000000000000000
χ484-44-40000−2222−222202i2−2i200−2i2i−2i2i0000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5ζ−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−ζ700000000000000000000
χ494-44-40000−2222−222202i2−2i200−2i2i−2i2i000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−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+ζ700000000000000000000
χ504-44-40000−2222−22220−2i22i2002i−2i2i−2i0000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−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+ζ700000000000000000000
χ514-44-40000−2222−22220−2i22i2002i−2i2i−2i000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5ζ−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−ζ700000000000000000000
χ524-4-44040-422−22−222200000000022−22000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000
χ534-4-44040-422−22−222200000000022−2200000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000
χ544-4-44040-4−222222−22000000000−2222000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000
χ554-4-44040-4−222222−22000000000−222200000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000
χ564-4-440-40422−22−22220004-422−22−2222−2222000000000000000000000000000000000000
χ574-4-440-40422−22−2222000-44−222222−22−2222000000000000000000000000000000000000
χ584-4-440-404−222222−220004-4−222222−2222−22000000000000000000000000000000000000
χ594-4-440-404−222222−22000-4422−22−222222−22000000000000000000000000000000000000

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