Finite Group Databasebeta

← Group #419209

Character table — Group #419209

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222224444444488882222444444444444888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1111-111-11-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111111111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111
χ51111111111111111111111-1-111-1-111-1-1-1-11111111111-11-1-11-1-1-1-1-111-1-1-1-111
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
χ71111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11111-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ10111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-11-1-11-1-1-111-1-1-1-111-1-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-111-1-111-1-111-1-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-111-11-1-111-1-1-1-11111
χ14111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-1-1111-1-111-1-11111
χ17222222-2-2-2-22222-2-2-2-20000002200-2-200002i2i−2i−2i00000000000000000000002i−2i
χ18222222-2-2-2-22222-2-2-2-20000002200-2-20000−2i−2i2i2i0000000000000000000000−2i2i
χ19222222-2-2-2-22222-2-2-2-2000000-2-2002200002i2i−2i−2i0000000000000000000000−2i2i
χ20222222-2-2-2-22222-2-2-2-2000000-2-200220000−2i−2i2i2i00000000000000000000002i−2i
χ21222222-2-2-2-2-2-2-2-2222222-2-22200-2-2000000000000002-220000-2000000000000
χ22222222-2-2-2-2-2-2-2-2222222-2-2-2-20022000000000000002-2-200002000000000000
χ23222222-2-2-2-2-2-2-2-22222-2-2222200-2-200000000000000-22-200002000000000000
χ24222222-2-2-2-2-2-2-2-22222-2-222-2-2002200000000000000-2220000-2000000000000
χ252222-2-22-22-22-2-222-2-222222002-2002-2000000000000-2-200000000002-2000000
χ262222-2-22-22-22-2-222-2-22222200-2200-22000000000000-2-20000000000-22000000
χ272222-2-22-22-22-2-222-2-22-2-2-2-2002-2002-2000000000000220000000000-22000000
χ282222-2-22-22-22-2-222-2-22-2-2-2-200-2200-220000000000002200000000002-2000000
χ292222-2-2-22-222-2-22-222-20000002-200-220000000022-2-2000200-20000000000000
χ302222-2-2-22-222-2-22-222-20000002-200-2200000000-2-222000-20020000000000000
χ312222-2-2-22-222-2-22-222-2000000-22002-20000000022-2-2000-20020000000000000
χ322222-2-2-22-222-2-22-222-2000000-22002-200000000-2-222000200-20000000000000
χ332222-2-2-22-22-222-22-2-2222-2-20000000022-2-200000000-22002-200000000000000
χ342222-2-2-22-22-222-22-2-2222-2-200000000-2-22200000000-2200-2200000000000000
χ352222-2-2-22-22-222-22-2-22-2-2220000000022-2-2000000002-200-2200000000000000
χ362222-2-2-22-22-222-22-2-22-2-22200000000-2-222000000002-2002-200000000000000
χ372-2-222-222-2-222-2-2-22-2200002-2002-200000000002i−2i2i−2i00000000002i−2i00000000
χ382-2-222-222-2-222-2-2-22-2200002-2002-20000000000−2i2i−2i2i0000000000−2i2i00000000
χ392-2-222-222-2-222-2-2-22-220000-2200-2200000000002i−2i2i−2i0000000000−2i2i00000000
χ402-2-222-222-2-222-2-2-22-220000-2200-220000000000−2i2i−2i2i00000000002i−2i00000000
χ412-2-222-222-2-2-2-2222-22-20000000000002-22-22i−2i2i−2i0000000000000000002i−2i0000
χ422-2-222-222-2-2-2-2222-22-20000000000002-22-2−2i2i−2i2i000000000000000000−2i2i0000
χ432-2-222-222-2-2-2-2222-22-2000000000000-22-222i−2i2i−2i000000000000000000−2i2i0000
χ442-2-222-222-2-2-2-2222-22-2000000000000-22-22−2i2i−2i2i0000000000000000002i−2i0000
χ452-2-222-2-2-222-2-222-22-2200002-200-220000002-2-220000000000002-20000000000
χ462-2-222-2-2-222-2-222-22-2200002-200-22000000-222-2000000000000-220000000000
χ472-2-222-2-2-222-2-222-22-220000-22002-20000002-2-22000000000000-220000000000
χ482-2-222-2-2-222-2-222-22-220000-22002-2000000-222-20000000000002-20000000000
χ492-2-22-22-222-22-22-222-2-20000000000002-2-2200002i−2i−2i2i00000000000000002i−2i00
χ502-2-22-22-222-22-22-222-2-20000000000002-2-220000−2i2i2i−2i0000000000000000−2i2i00
χ512-2-22-22-222-22-22-222-2-2000000000000-222-200002i−2i−2i2i0000000000000000−2i2i00
χ522-2-22-22-222-22-22-222-2-2000000000000-222-20000−2i2i2i−2i00000000000000002i−2i00
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-4-44-44-4-444-4-444-400000000000000000000000000000000000000000000
χ554-4-444-4-4-44444-4-44-44-400000000000000000000000000000000000000000000
χ564-4-44-444-4-444-44-4-4-44400000000000000000000000000000000000000000000
χ574-4-44-444-4-44-44-4444-4-400000000000000000000000000000000000000000000
χ584-4-44-44-444-4-44-44-4-44400000000000000000000000000000000000000000000
χ5988-8-80000000000000042−42000000000000000000000000000000000000000000
χ6088-8-800000000000000−4242000000000000000000000000000000000000000000
χ618-88-800000000000000004i2−4i20000000000000000000000000000000000000000
χ628-88-80000000000000000−4i24i20000000000000000000000000000000000000000

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