Finite Group Databasebeta

← Group #419238

Character table — Group #419238

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222224444444444442222224444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ9111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111
χ13111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-111-1-1-1-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1
χ1722222-2-22-2-222-2-2-2-222000000220000-2-20000000022-2-2000000000000002-200
χ1822222-2-22-2-222-2-2-2-222000000220000-2-200000000-2-22200000000000000-2200
χ1922222-2-22-2-222-2-2-2-222000000-2-20000220000000022-2-200000000000000-2200
χ2022222-2-22-2-222-2-2-2-222000000-2-200002200000000-2-222000000000000002-200
χ212222-22-2-22-22-2-2-2222-200000000220000-2-20022-2-2000000000000000000002-2
χ222222-22-2-22-22-2-2-2222-200000000220000-2-200-2-22200000000000000000000-22
χ232222-22-2-22-22-2-2-2222-200000000-2-20000220022-2-200000000000000000000-22
χ242222-22-2-22-22-2-2-2222-200000000-2-200002200-2-222000000000000000000002-2
χ252222-2-22-2-22-22-2-222-222222220000-2-20000-2-2000000002-20000000000000000
χ262222-2-22-2-22-22-2-222-222222-2-20000220000-2-200000000-220000000000000000
χ272222-2-22-2-22-22-2-222-22-2-2-2-2220000-2-200002200000000-220000000000000000
χ282222-2-22-2-22-22-2-222-22-2-2-2-2-2-2000022000022000000002-20000000000000000
χ292-2-22222-2-2-22-22-22-2-2200002-200002-20000002i−2i2i−2i0000002i−2i00000000000000
χ302-2-22222-2-2-22-22-22-2-2200002-200002-2000000−2i2i−2i2i000000−2i2i00000000000000
χ312-2-22222-2-2-22-22-22-2-220000-220000-220000002i−2i2i−2i000000−2i2i00000000000000
χ322-2-22222-2-2-22-22-22-2-220000-220000-22000000−2i2i−2i2i0000002i−2i00000000000000
χ332-2-22222-2-2-2-22-22-222-22i2i−2i−2i00002-200002-22i−2i000000000000000000002i−2i0000
χ342-2-22222-2-2-2-22-22-222-22i2i−2i−2i0000-220000-222i−2i00000000000000000000−2i2i0000
χ352-2-22222-2-2-2-22-22-222-2−2i−2i2i2i00002-200002-2−2i2i00000000000000000000−2i2i0000
χ362-2-22222-2-2-2-22-22-222-2−2i−2i2i2i0000-220000-22−2i2i000000000000000000002i−2i0000
χ372-2-22-22-22-2222-222-2-2-20000002-200002-200002i−2i−2i2i00000000002i−2i0000000000
χ382-2-22-22-22-2222-222-2-2-20000002-200002-20000−2i2i2i−2i0000000000−2i2i0000000000
χ392-2-22-22-22-2222-222-2-2-2000000-220000-2200002i−2i−2i2i0000000000−2i2i0000000000
χ402-2-22-22-22-2222-222-2-2-2000000-220000-220000−2i2i2i−2i00000000002i−2i0000000000
χ412-2-22-22-22-22-2-22-2-2222000000002-20000-220000002-22-2000000002-200000000
χ422-2-22-22-22-22-2-22-2-2222000000002-20000-22000000-22-2200000000-2200000000
χ432-2-22-22-22-22-2-22-2-222200000000-2200002-20000002-22-200000000-2200000000
χ442-2-22-22-22-22-2-22-2-222200000000-2200002-2000000-22-22000000002-200000000
χ452-2-22-2-2222-2222-2-22-2-22i2i−2i−2i002-20000-2200−2i2i0000000000000000002i−2i000000
χ462-2-22-2-2222-2222-2-22-2-22i2i−2i−2i00-2200002-200−2i2i000000000000000000−2i2i000000
χ472-2-22-2-2222-2222-2-22-2-2−2i−2i2i2i002-20000-22002i−2i000000000000000000−2i2i000000
χ482-2-22-2-2222-2222-2-22-2-2−2i−2i2i2i00-2200002-2002i−2i0000000000000000002i−2i000000
χ492-2-22-2-2222-2-2-2-222-22200002-20000-2200000000002-2-2200002-2000000000000
χ502-2-22-2-2222-2-2-2-222-22200002-20000-220000000000-222-20000-22000000000000
χ512-2-22-2-2222-2-2-2-222-2220000-2200002-200000000002-2-220000-22000000000000
χ522-2-22-2-2222-2-2-2-222-2220000-2200002-20000000000-222-200002-2000000000000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ5444444-4-44-4-4-4-44444-4-400000000000000000000000000000000000000000000
χ554444-44-4-44-4-4444-4-4-4400000000000000000000000000000000000000000000
χ564444-4-44-4-444-444-4-44-400000000000000000000000000000000000000000000
χ574-4-444-4-4-4444-4-44-44-4400000000000000000000000000000000000000000000
χ584-4-444-4-4-444-444-44-44-400000000000000000000000000000000000000000000
χ5988-8-8000000000000004-44-40000000000000000000000000000000000000000
χ6088-8-800000000000000-44-440000000000000000000000000000000000000000
χ618-88-8000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ628-88-800000000000000−4i4i4i−4i0000000000000000000000000000000000000000

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