Finite Group Databasebeta

← Group #423846

Character table — Group #423846

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222224444444488882244444444444444888888222444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111111-11-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111111111111-1-1-11-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-11111-1-111
χ51111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-11-11-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1111-111111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ10111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-1-1-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1111-1-1-1-11111-1-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-11111-1-11111
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111-11-1-1-111-1-111-1-111
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-11111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-11-111-1-1-1-1111111
χ17222222-2-2-2-2222-22-2-2-20000002200-2-200002i2i−2i−2i00000000000000000000002i−2i
χ18222222-2-2-2-2222-22-2-2-20000002200-2-20000−2i−2i2i2i0000000000000000000000−2i2i
χ19222222-2-2-2-2222-22-2-2-2000000-2-2002200002i2i−2i−2i0000000000000000000000−2i2i
χ20222222-2-2-2-2222-22-2-2-2000000-2-200220000−2i−2i2i2i00000000000000000000002i−2i
χ21222222-2-2-2-2-2-2-22-222222-2-22200-2-2000000000000002-22000-20000000000000
χ22222222-2-2-2-2-2-2-22-222222-2-2-2-20022000000000000002-2-200020000000000000
χ23222222-2-2-2-2-2-2-22-2222-2-2222200-2-200000000000000-22-200020000000000000
χ24222222-2-2-2-2-2-2-22-2222-2-222-2-2002200000000000000-222000-20000000000000
χ252222-2-22-22-22-2-222-2-222222002-2002-2000000000000-2-2000000000000002-200
χ262222-2-22-22-22-2-222-2-22222200-2200-22000000000000-2-200000000000000-2200
χ272222-2-22-22-22-2-222-2-22-2-2-2-2002-2002-20000000000002200000000000000-2200
χ282222-2-22-22-22-2-222-2-22-2-2-2-200-2200-2200000000000022000000000000002-200
χ292222-2-2-22-222-2-2-2222-20000002-200-220000000022-2-20000020-2000000000000
χ302222-2-2-22-222-2-2-2222-20000002-200-2200000000-2-22200000-202000000000000
χ312222-2-2-22-222-2-2-2222-2000000-22002-20000000022-2-200000-202000000000000
χ322222-2-2-22-222-2-2-2222-2000000-22002-200000000-2-2220000020-2000000000000
χ332222-2-2-22-22-2222-2-2-2222-2-20000000022-2-200000000-2202-2000000000000000
χ342222-2-2-22-22-2222-2-2-2222-2-200000000-2-22200000000-220-22000000000000000
χ352222-2-2-22-22-2222-2-2-22-2-2220000000022-2-2000000002-20-22000000000000000
χ362222-2-2-22-22-2222-2-2-22-2-22200000000-2-222000000002-202-2000000000000000
χ372-22-22-222-2-222-2-2-22-2200002-2002-20000002i−2i2i−2i0000000000002i−2i0000000000
χ382-22-22-222-2-222-2-2-22-2200002-2002-2000000−2i2i−2i2i000000000000−2i2i0000000000
χ392-22-22-222-2-222-2-2-22-220000-2200-220000002i−2i2i−2i000000000000−2i2i0000000000
χ402-22-22-222-2-222-2-2-22-220000-2200-22000000−2i2i−2i2i0000000000002i−2i0000000000
χ412-22-22-2-2-22222-22-2-22-20000000000002i−2i2i−2i2-2-2200000000000000002i−2i000000
χ422-22-22-2-2-22222-22-2-22-20000000000002i−2i2i−2i-222-20000000000000000−2i2i000000
χ432-22-22-2-2-22222-22-2-22-2000000000000−2i2i−2i2i2-2-220000000000000000−2i2i000000
χ442-22-22-2-2-22222-22-2-22-2000000000000−2i2i−2i2i-222-200000000000000002i−2i000000
χ452-22-22-2-2-222-2-22-222-2200002-200-2200000000002-22-200000000002-200000000
χ462-22-22-2-2-222-2-22-222-2200002-200-220000000000-22-220000000000-2200000000
χ472-22-22-2-2-222-2-22-222-220000-22002-200000000002-22-20000000000-2200000000
χ482-22-22-2-2-222-2-22-222-220000-22002-20000000000-22-2200000000002-200000000
χ492-22-2-222-2-22-22-2222-2-20000000000002i−2i−2i2i00002-2-22000000000000002i−2i0000
χ502-22-2-222-2-22-22-2222-2-20000000000002i−2i−2i2i0000-222-200000000000000−2i2i0000
χ512-22-2-222-2-22-22-2222-2-2000000000000−2i2i2i−2i00002-2-2200000000000000−2i2i0000
χ522-22-2-222-2-22-22-2222-2-2000000000000−2i2i2i−2i0000-222-2000000000000002i−2i0000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-4-44-44-4-444-4-444-400000000000000000000000000000000000000000000
χ554-44-44-444-4-4-4-4444-44-400000000000000000000000000000000000000000000
χ564-44-4-444-4-444-44-4-4-44400000000000000000000000000000000000000000000
χ574-44-4-44-444-44-444-44-4-400000000000000000000000000000000000000000000
χ584-44-4-44-444-4-44-4-44-44400000000000000000000000000000000000000000000
χ5988-8-800000000000000004i2−4i20000000000000000000000000000000000000000
χ6088-8-80000000000000000−4i24i20000000000000000000000000000000000000000
χ618-8-880000000000000042−42000000000000000000000000000000000000000000
χ628-8-8800000000000000−4242000000000000000000000000000000000000000000

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