Finite Group Databasebeta

← Group #437796

Character table — Group #437796

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222224444444488882244444444444444888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ51111111111111111111111-1-11111-1-1-1-1-1-11111111111-111-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-11-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-11111-1-11111111111-1-1-111-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-11111111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ10111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111-1-1-1-11-1-111-1-111-1-1-1-1
χ11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-111-1-111-1-111
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11111-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-11-1-11111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-1-1111111
χ17222222-2-2-2-22222-2-2-2-200002200000000-2-22i2i−2i−2i00000000000000000000002i−2i
χ18222222-2-2-2-22222-2-2-2-200002200000000-2-2−2i−2i2i2i0000000000000000000000−2i2i
χ19222222-2-2-2-22222-2-2-2-20000-2-200000000222i2i−2i−2i0000000000000000000000−2i2i
χ20222222-2-2-2-22222-2-2-2-20000-2-20000000022−2i−2i2i2i00000000000000000000002i−2i
χ21222222-2-2-2-2-2-2-2-2222222-2-20022-2-200000000002-2000002-2000000000000000
χ22222222-2-2-2-2-2-2-2-2222222-2-200-2-22200000000002-200000-22000000000000000
χ23222222-2-2-2-2-2-2-2-22222-2-2220022-2-20000000000-2200000-22000000000000000
χ24222222-2-2-2-2-2-2-2-22222-2-22200-2-2220000000000-22000002-2000000000000000
χ252222-2-22-22-22-2-222-2-2222222-2000000002-20000-2-20000000000000000002-200
χ262222-2-22-22-22-2-222-2-222222-2200000000-220000-2-2000000000000000000-2200
χ272222-2-22-22-22-2-222-2-22-2-2-2-22-2000000002-2000022000000000000000000-2200
χ282222-2-22-22-22-2-222-2-22-2-2-2-2-2200000000-220000220000000000000000002-200
χ292222-2-2-22-222-2-22-222-200002-200000000-2200000022-2-220000-2000000000000
χ302222-2-2-22-222-2-22-222-200002-200000000-22000000-2-222-200002000000000000
χ312222-2-2-22-222-2-22-222-20000-22000000002-200000022-2-2-200002000000000000
χ322222-2-2-22-222-2-22-222-20000-22000000002-2000000-2-22220000-2000000000000
χ332222-2-2-22-22-222-22-2-2222-2-200000022-2-2000000-2200000002-20000000000000
χ342222-2-2-22-22-222-22-2-2222-2-2000000-2-222000000-220000000-220000000000000
χ352222-2-2-22-22-222-22-2-22-2-22200000022-2-20000002-20000000-220000000000000
χ362222-2-2-22-22-222-22-2-22-2-222000000-2-2220000002-200000002-20000000000000
χ372-2-222-222-2-2-22-22-22-2200000000002i−2i2i−2i000000002-22-20000000000002i−2i0000
χ382-2-222-222-2-2-22-22-22-2200000000002i−2i2i−2i00000000-22-22000000000000−2i2i0000
χ392-2-222-222-2-2-22-22-22-220000000000−2i2i−2i2i000000002-22-2000000000000−2i2i0000
χ402-2-222-222-2-2-22-22-22-220000000000−2i2i−2i2i00000000-22-220000000000002i−2i0000
χ412-2-22-222-2-2222-2-222-2-20000002i−2i2i−2i0000002i−2i2i−2i0000000000002-20000000000
χ422-2-22-222-2-2222-2-222-2-20000002i−2i2i−2i000000−2i2i−2i2i000000000000-220000000000
χ432-2-22-222-2-2222-2-222-2-2000000−2i2i−2i2i0000002i−2i2i−2i000000000000-220000000000
χ442-2-22-222-2-2222-2-222-2-2000000−2i2i−2i2i000000−2i2i−2i2i0000000000002-20000000000
χ452-2-22-22-222-222-2-2-2-22200000000002i−2i−2i2i002-2-2200000000000000002i−2i000000
χ462-2-22-22-222-222-2-2-2-22200000000002i−2i−2i2i00-222-20000000000000000−2i2i000000
χ472-2-22-22-222-222-2-2-2-2220000000000−2i2i2i−2i002-2-220000000000000000−2i2i000000
χ482-2-22-22-222-222-2-2-2-2220000000000−2i2i2i−2i00-222-200000000000000002i−2i000000
χ492-2-22-22-222-2-2-22222-2-20000002i−2i−2i2i0000000000002-2-22000000002i−2i00000000
χ502-2-22-22-222-2-2-22222-2-20000002i−2i−2i2i000000000000-222-200000000−2i2i00000000
χ512-2-22-22-222-2-2-22222-2-2000000−2i2i2i−2i0000000000002-2-2200000000−2i2i00000000
χ522-2-22-22-222-2-2-22222-2-2000000−2i2i2i−2i000000000000-222-2000000002i−2i00000000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-4-44-44-4-444-4-444-400000000000000000000000000000000000000000000
χ554-4-444-444-4-44-44-44-44-400000000000000000000000000000000000000000000
χ564-4-444-4-4-4444-44-4-44-4400000000000000000000000000000000000000000000
χ574-4-444-4-4-444-44-444-44-400000000000000000000000000000000000000000000
χ584-4-44-444-4-44-4-444-4-44400000000000000000000000000000000000000000000
χ5988-8-80000000000000042−42000000000000000000000000000000000000000000
χ6088-8-800000000000000−4242000000000000000000000000000000000000000000
χ618-88-800000000000000004i2−4i20000000000000000000000000000000000000000
χ628-88-80000000000000000−4i24i20000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).