Finite Group Databasebeta

← Group #419813

Character table — Group #419813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222222222222244442244444444444444444444224444444444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-1111111-1-1
χ51111111111111111111111-1-111-1-1111111111111-1-1-1-1-11-1-1-1111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1
χ71111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1111-111-1-1-1-111-1-111
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111
χ9111111111111111111-1-1-1-111-1-1111111-1-1-1-1111111111-1-1-11-1-1-1-1-11111-1-1-1-1
χ10111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1111111111111-1111-11-1-1-1-1-1-1-1-1-1-111
χ12111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1111-1-1-1-1111111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-111-1-111-1-111-1-1
χ1722222222-2-2-222-2-2-2-2-2000000000000002i2i−2i−2i00002i2i−2i−2i002-200000000000000
χ1822222222-2-2-222-2-2-2-2-2000000000000002i2i−2i−2i0000−2i−2i2i2i00-2200000000000000
χ1922222222-2-2-222-2-2-2-2-200000000000000−2i−2i2i2i00002i2i−2i−2i00-2200000000000000
χ2022222222-2-2-222-2-2-2-2-200000000000000−2i−2i2i2i0000−2i−2i2i2i002-200000000000000
χ21222222-2-222-2-2-222-2-2-2000000000000002i−2i2i−2i2i2i−2i−2i000002000-2000000000000
χ22222222-2-222-2-2-222-2-2-2000000000000002i−2i2i−2i−2i−2i2i2i00000-20002000000000000
χ23222222-2-222-2-2-222-2-2-200000000000000−2i2i−2i2i2i2i−2i−2i00000-20002000000000000
χ24222222-2-222-2-2-222-2-2-200000000000000−2i2i−2i2i−2i−2i2i2i000002000-2000000000000
χ25222222-2-2-2-22-2-2-2-222200002200-2-200002-2-220000000000000000000000002-2
χ26222222-2-2-2-22-2-2-2-222200002200-2-20000-222-2000000000000000000000000-22
χ27222222-2-2-2-22-2-2-2-22220000-2-2002200002-2-22000000000000000000000000-22
χ28222222-2-2-2-22-2-2-2-22220000-2-200220000-222-20000000000000000000000002-2
χ292222-2-22-22-2-22-22-222-200002-2002-222-2-20000000000002000-20000000000000
χ302222-2-22-22-2-22-22-222-200002-2002-2-2-222000000000000-200020000000000000
χ312222-2-22-22-2-22-22-222-20000-2200-2222-2-2000000000000-200020000000000000
χ322222-2-22-22-2-22-22-222-20000-2200-22-2-2220000000000002000-20000000000000
χ332222-2-2-22-22-2-22-2222-222222-2-2-2-220000000000000000000000000000002-200
χ342222-2-2-22-22-2-22-2222-22222-22-2-22-2000000000000000000000000000000-2200
χ352222-2-2-22-22-2-22-2222-2-2-2-2-22-222-22000000000000000000000000000000-2200
χ362222-2-2-22-22-2-22-2222-2-2-2-2-2-22222-20000000000000000000000000000002-200
χ372-2-222-2222-22-2-2-222-2-222-2-2002-200000000002i−2i2i−2i00000000002i−2i0000000000
χ382-2-222-2222-22-2-2-222-2-222-2-2002-20000000000−2i2i−2i2i0000000000−2i2i0000000000
χ392-2-222-2222-22-2-2-222-2-2-2-22200-2200000000002i−2i2i−2i0000000000−2i2i0000000000
χ402-2-222-2222-22-2-2-222-2-2-2-22200-220000000000−2i2i−2i2i00000000002i−2i0000000000
χ412-2-222-2-2-22-2-222-22-22200000000002-22-200002-2-22000000000000002-2000000
χ422-2-222-2-2-22-2-222-22-22200000000002-22-20000-222-200000000000000-22000000
χ432-2-222-2-2-22-2-222-22-2220000000000-22-2200002-2-2200000000000000-22000000
χ442-2-222-2-2-22-2-222-22-2220000000000-22-220000-222-2000000000000002-2000000
χ452-2-22-22-222222-2-2-2-22-200000000002-2-22000000002i−2i2i−2i0000000000002i−2i0000
χ462-2-22-22-222222-2-2-2-22-200000000002-2-2200000000−2i2i−2i2i000000000000−2i2i0000
χ472-2-22-22-222222-2-2-2-22-20000000000-222-2000000002i−2i2i−2i000000000000−2i2i0000
χ482-2-22-22-222222-2-2-2-22-20000000000-222-200000000−2i2i−2i2i0000000000002i−2i0000
χ492-2-22-22-22-2-2-22-2222-2222-2-200-22000000000000002-2-22000000002-200000000
χ502-2-22-22-22-2-2-22-2222-2222-2-200-2200000000000000-222-200000000-2200000000
χ512-2-22-22-22-2-2-22-2222-22-2-222002-2000000000000002-2-2200000000-2200000000
χ522-2-22-22-22-2-2-22-2222-22-2-222002-200000000000000-222-2000000002-200000000
χ534444-4-44-4-4444-4-44-4-4400000000000000000000000000000000000000000000
χ544444-4-4-444-44-444-4-4-4400000000000000000000000000000000000000000000
χ554-4-444-444-44-4-4-44-4-44400000000000000000000000000000000000000000000
χ564-4-444-4-4-4-444444-44-4-400000000000000000000000000000000000000000000
χ574-4-44-444-444-4-44-4-44-4400000000000000000000000000000000000000000000
χ584-4-44-444-4-4-44-4444-44-400000000000000000000000000000000000000000000
χ5988-8-8000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ6088-8-800000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ618-88-8000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ628-88-800000000000000−4i4i4i−4i0000000000000000000000000000000000000000

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