Finite Group Databasebeta

← Group #485000

Character table — Group #485000

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122244442244444444444488888888248888161616161616161616161616161616162244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1111-111-1-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-11-1-111-11-111-1-111-1-1
χ101111-1-1-1-111-1-1-1-1111-111-1-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-1-111-1-11-11-1-111-1-111
χ111111-1-1-1-111-1-1-1-1111-111-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-111111-1-111-11-1-1-111-1-111
χ121111-1-1-1-111-1-1-1-1111-111-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111-111-1-11-1111-1-111-1-1
χ131111-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-11111-11-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-111
χ141111-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-11111-11-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-1-11111-1-1
χ151111-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-111-1-11-1-11-1-11111-1-1
χ161111-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-11111-11-1-111-1-1-1-111111111-1-1-1-1-1-111-111-111-1-1-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2222200000000-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-2-2-2-2222200000000-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-22222-2-2000022-2-222-2-200000000000000000000002020-2-20000000000
χ2422222222-2-2-2-22222-2-2000022-2-222-2-20000000000000000000000-20-20220000000000
χ2522222222-2-2-2-22222-2-20000-2-222-2-2220000000000000000000000020200-2-200000000
χ2622222222-2-2-2-22222-2-20000-2-222-2-22200000000000000000000000-20-2002200000000
χ272222-2-2-2-222-2-222-2-2-2222-2-200000000-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ282222-2-2-2-222-2-222-2-2-2222-2-200000000-220000−2−22222−2−2−2−22222−2−20000000000000000
χ292222-2-2-2-222-2-222-2-2-22-2-222000000002-2000022−2−2−2−222−2−22222−2−20000000000000000
χ302222-2-2-2-222-2-222-2-2-22-2-222000000002-20000−2−22222−2−222−2−2−2−2220000000000000000
χ312222-2-2-2-222-2-2-2-2222-222-2-22222-2-2-2-22-2-2-22200000000000000000000000000000000
χ322222-2-2-2-222-2-2-2-2222-2-2-2222222-2-2-2-2-2222-2-200000000000000000000000000000000
χ332222-2-2-2-2-2-222-2-222-22000022-2-2-2-2220000000000000000000000020-2002-200000000
χ342222-2-2-2-2-2-222-2-222-22000022-2-2-2-22200000000000000000000000-20200-2200000000
χ352222-2-2-2-2-2-222-2-222-220000-2-22222-2-2000000000000000000000020-20-220000000000
χ362222-2-2-2-2-2-222-2-222-220000-2-22222-2-20000000000000000000000-20202-20000000000
χ372-22-22i2i−2i−2i2-22i−2i0000002i−2i2-2i2−i2i2−i22−22−200i2−i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ382-22-22i2i−2i−2i2-22i−2i0000002i−2i2-2i2−i2i2−i22−22−200i2−i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ392-22-22i2i−2i−2i2-22i−2i0000002i−2i2-2−i2i2−i2i2−22−2200−i2i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ402-22-22i2i−2i−2i2-22i−2i0000002i−2i2-2−i2i2−i2i2−22−2200−i2i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ412-22-22i2i−2i−2i2-22i−2i000000−2i2i-22i2−i2i2−i22−22−200−i2i2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ422-22-22i2i−2i−2i2-22i−2i000000−2i2i-22i2−i2i2−i22−22−200−i2i2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ432-22-22i2i−2i−2i2-22i−2i000000−2i2i-22−i2i2−i2i2−22−2200i2−i22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ442-22-22i2i−2i−2i2-22i−2i000000−2i2i-22−i2i2−i2i2−22−2200i2−i22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ452-22-2−2i−2i2i2i2-2−2i2i0000002i−2i-22i2−i2i2−i2−22−2200−i2i22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ462-22-2−2i−2i2i2i2-2−2i2i0000002i−2i-22i2−i2i2−i2−22−2200−i2i22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ472-22-2−2i−2i2i2i2-2−2i2i0000002i−2i-22−i2i2−i2i22−22−200i2−i2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ482-22-2−2i−2i2i2i2-2−2i2i0000002i−2i-22−i2i2−i2i22−22−200i2−i2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ492-22-2−2i−2i2i2i2-2−2i2i000000−2i2i2-2i2−i2i2−i2−22−2200i2−i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ502-22-2−2i−2i2i2i2-2−2i2i000000−2i2i2-2i2−i2i2−i2−22−2200i2−i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ512-22-2−2i−2i2i2i2-2−2i2i000000−2i2i2-2−i2i2−i2i22−22−200−i2i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ522-22-2−2i−2i2i2i2-2−2i2i000000−2i2i2-2−i2i2−i2i22−22−200−i2i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44444-4-44-400000000000000000000000000000000000000000000000000
χ554-44-44i4i−4i−4i-44−4i4i00000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000000
χ564-44-44i4i−4i−4i-44−4i4i0000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000000
χ574-44-4−4i−4i4i4i-444i−4i00000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000000
χ584-44-4−4i−4i4i4i-444i−4i0000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000000
χ594-4-444i−4i4i−4i00004i−4i4-40000000000000000000000000000000000000000000000002-22i−2i
χ604-4-444i−4i4i−4i00004i−4i4-4000000000000000000000000000000000000000000000000-22−2i2i
χ614-4-444i−4i4i−4i0000−4i4i-44000000000000000000000000000000000000000000002-22i−2i0000
χ624-4-444i−4i4i−4i0000−4i4i-4400000000000000000000000000000000000000000000-22−2i2i0000
χ634-4-44−4i4i−4i4i00004i−4i-44000000000000000000000000000000000000000000002-2−2i2i0000
χ644-4-44−4i4i−4i4i00004i−4i-4400000000000000000000000000000000000000000000-222i−2i0000
χ654-4-44−4i4i−4i4i0000−4i4i4-40000000000000000000000000000000000000000000000002-2−2i2i
χ664-4-44−4i4i−4i4i0000−4i4i4-4000000000000000000000000000000000000000000000000-222i−2i
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ6888-8-8-888-8000000000000000000000000000000000000000000000000000000000000

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