Finite Group Databasebeta

← Group #424643

Character table — Group #424643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222224444444488882222444444444444888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ51111111111111111111111-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-111-1-1-1-111-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ11111111111111111111-1-1-1-111-1-11111-1-1111111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111
χ13111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-11111
χ17222222-2-2-2-2222-22-2-2-200000000220000-2-20000002i2i−2i−2i00002i−2i000000000000
χ18222222-2-2-2-2222-22-2-2-200000000220000-2-2000000−2i−2i2i2i0000−2i2i000000000000
χ19222222-2-2-2-2222-22-2-2-200000000-2-20000220000002i2i−2i−2i0000−2i2i000000000000
χ20222222-2-2-2-2222-22-2-2-200000000-2-2000022000000−2i−2i2i2i00002i−2i000000000000
χ21222222-2-2-2-2-2-2-22-222222-2-2220000-2-2000000002-200002-20000000000000000
χ22222222-2-2-2-2-2-2-22-222222-2-2-2-2000022000000002-20000-220000000000000000
χ23222222-2-2-2-2-2-2-22-2222-2-222220000-2-200000000-220000-220000000000000000
χ24222222-2-2-2-2-2-2-22-2222-2-222-2-200002200000000-2200002-20000000000000000
χ252222-2-22-22-22-2-222-2-2222-2-200002-200002-20000-22000000000000000000002-2
χ262222-2-22-22-22-2-222-2-2222-2-20000-220000-220000-2200000000000000000000-22
χ272222-2-22-22-22-2-222-2-22-2-22200002-200002-200002-200000000000000000000-22
χ282222-2-22-22-22-2-222-2-22-2-2220000-220000-2200002-2000000000000000000002-2
χ292222-2-2-22-222-2-2-2222-2000000222-200-2-2-220000000000000000000000002-200
χ302222-2-2-22-222-2-2-2222-200000022-2200-2-22-2000000000000000000000000-2200
χ312222-2-2-22-222-2-2-2222-2000000-2-22-20022-22000000000000000000000000-2200
χ322222-2-2-22-222-2-2-2222-2000000-2-2-2200222-20000000000000000000000002-200
χ332222-2-2-22-22-2222-2-2-22222200000000000022-2-2-2-20000002-200000000000000
χ342222-2-2-22-22-2222-2-2-222222000000000000-2-222-2-2000000-2200000000000000
χ352222-2-2-22-22-2222-2-2-22-2-2-2-200000000000022-2-222000000-2200000000000000
χ362222-2-2-22-22-2222-2-2-22-2-2-2-2000000000000-2-222220000002-200000000000000
χ372-22-22-222-2-222-22-22-2-200002-22-2002-22-200000000000000000000002-2000000
χ382-22-22-222-2-222-22-22-2-200002-2-22002-2-220000000000000000000000-22000000
χ392-22-22-222-2-222-22-22-2-20000-222-200-222-20000000000000000000000-22000000
χ402-22-22-222-2-222-22-22-2-20000-22-2200-22-2200000000000000000000002-2000000
χ412-22-22-222-2-2-2-22-22-22200000000000000002i−2i2i−2i002-22-2000000002i−2i00000000
χ422-22-22-222-2-2-2-22-22-22200000000000000002i−2i2i−2i00-22-2200000000−2i2i00000000
χ432-22-22-222-2-2-2-22-22-2220000000000000000−2i2i−2i2i002-22-200000000−2i2i00000000
χ442-22-22-222-2-2-2-22-22-2220000000000000000−2i2i−2i2i00-22-22000000002i−2i00000000
χ452-22-22-2-2-222-2-22222-2-200002-20000-2200000000002i−2i−2i2i0000000000002i−2i0000
χ462-22-22-2-2-222-2-22222-2-200002-20000-220000000000−2i2i2i−2i000000000000−2i2i0000
χ472-22-22-2-2-222-2-22222-2-20000-2200002-200000000002i−2i−2i2i000000000000−2i2i0000
χ482-22-22-2-2-222-2-22222-2-20000-2200002-20000000000−2i2i2i−2i0000000000002i−2i0000
χ492-22-2-22-222-22-22-2-22-220000002-20000-22002i−2i−2i2i0000000000002i−2i0000000000
χ502-22-2-22-222-22-22-2-22-220000002-20000-2200−2i2i2i−2i000000000000−2i2i0000000000
χ512-22-2-22-222-22-22-2-22-22000000-2200002-2002i−2i−2i2i000000000000−2i2i0000000000
χ522-22-2-22-222-22-22-2-22-22000000-2200002-200−2i2i2i−2i0000000000002i−2i0000000000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-4-44-44-4-444-4-444-400000000000000000000000000000000000000000000
χ554-44-44-4-4-44444-4-4-4-44400000000000000000000000000000000000000000000
χ564-44-4-444-4-444-444-4-44-400000000000000000000000000000000000000000000
χ574-44-4-444-4-44-44-4-444-4400000000000000000000000000000000000000000000
χ584-44-4-44-444-4-44-444-44-400000000000000000000000000000000000000000000
χ5988-8-80000000000000042−42000000000000000000000000000000000000000000
χ6088-8-800000000000000−4242000000000000000000000000000000000000000000
χ618-8-88000000000000000042−420000000000000000000000000000000000000000
χ628-8-880000000000000000−42420000000000000000000000000000000000000000

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