Finite Group Databasebeta

← Group #352500

Character table — Group #352500

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442222444444444488888888444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ91111111111111111-1-1-1-111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-22-2-222222-2-2-2-2-2-222-2-200000000222-2-2-2000000000000000000000000
χ182222222222-2-22-2-222222-2-2-2-2-2-2-2-22200000000-2-2-2222000000000000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-2222222-2-200000000-2-22-222000000000000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-22222-2-2220000000022-22-2-2000000000000000000000000
χ2122222222-2-222-222-20000-2-2000022222222222200-2-200-2-2-2-200000000000000000000
χ2222222222-2-222-222-20000-2-200002222-2-2-2-2-2-2-2-200-2-200222200000000000000000000
χ2322222222-2-222-222-20000-2-20000-2-2-2-22222-2-2-2-2002200-2-22200000000000000000000
χ2422222222-2-222-222-20000-2-20000-2-2-2-2-2-2-2-2222200220022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022000022-2-20000000000-220000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000022000022-2-20000000000-22000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-20000220000-2-22200000000002-20000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-20000220000-2-22200000000002-2000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292222-2-2-2-2222-2-22-2-222-2-22-222-2-20000000022-2-2000000002-200002-22-2000000000000
χ302222-2-2-2-2222-2-22-2-222-2-22-222-2-200000000-2-22200000000-220000-22-22000000000000
χ312222-2-2-2-2222-2-22-2-2-2-2222-2-2-2220000000022-2-2000000002-20000-22-22000000000000
χ322222-2-2-2-2222-2-22-2-2-2-2222-2-2-22200000000-2-22200000000-2200002-22-2000000000000
χ332222-2-2-2-222-22-2-22-222-2-2-22-2-222000022-2-200000000002-2002-22-20000000000000000
χ342222-2-2-2-222-22-2-22-222-2-2-22-2-2220000-2-2220000000000-2200-22-220000000000000000
χ352222-2-2-2-222-22-2-22-2-2-222-2222-2-2000022-2-200000000002-200-22-220000000000000000
χ362222-2-2-2-222-22-2-22-2-2-222-2222-2-20000-2-2220000000000-22002-22-20000000000000000
χ372222-2-2-2-2-2-22-222-220000-2200000000000022-2-22i−2i002i−2i00-222i−2i−2i2i0000000000000000
χ382222-2-2-2-2-2-22-222-220000-2200000000000022-2-2−2i2i00−2i2i00-22−2i2i2i−2i0000000000000000
χ392222-2-2-2-2-2-22-222-220000-22000000000000-2-2222i−2i002i−2i002-2−2i2i2i−2i0000000000000000
χ402222-2-2-2-2-2-22-222-220000-22000000000000-2-222−2i2i00−2i2i002-22i−2i−2i2i0000000000000000
χ412222-2-2-2-2-2-2-222-22200002-20000000022-2-200002i−2i00−2i2i-22000000−2i2i2i−2i000000000000
χ422222-2-2-2-2-2-2-222-22200002-20000000022-2-20000−2i2i002i−2i-220000002i−2i−2i2i000000000000
χ432222-2-2-2-2-2-2-222-22200002-200000000-2-22200002i−2i00−2i2i2-20000002i−2i−2i2i000000000000
χ442222-2-2-2-2-2-2-222-22200002-200000000-2-2220000−2i2i002i−2i2-2000000−2i2i2i−2i000000000000
χ452-2-222-2-2200220-2-2000000000002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000i2−i2i2−i22−22−20000
χ462-2-222-2-2200220-2-2000000000002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000−i2i2−i2i2−22−220000
χ472-2-222-2-2200220-2-2000000000002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000i2−i2i2−i2−22−220000
χ482-2-222-2-2200220-2-2000000000002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000−i2i2−i2i22−22−20000
χ492-2-222-2-2200220-2-200000000000-22-222i−2i2i−2i−2i2i−2i2i000000000000000000i2−i2−i2i22−2−220000
χ502-2-222-2-2200220-2-200000000000-22-222i−2i2i−2i−2i2i−2i2i000000000000000000−i2i2i2−i2−222−20000
χ512-2-222-2-2200220-2-200000000000-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000i2−i2−i2i2−222−20000
χ522-2-222-2-2200220-2-200000000000-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000−i2i2i2−i22−2−220000
χ5344-4-444-4-44-400400-44-44-4000000000000000000000000000000000000000000000000
χ5444-4-444-4-44-400400-4-44-44000000000000000000000000000000000000000000000000
χ5544-4-444-4-4-4400-40040000004i−4i4i−4i000000000000000000000000000000000000000000
χ5644-4-444-4-4-4400-4004000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5744-4-4-4-4444-400-40044-4-44000000000000000000000000000000000000000000000000
χ5844-4-4-4-4444-400-4004-444-4000000000000000000000000000000000000000000000000
χ5944-4-4-4-444-4400400-40000004i−4i−4i4i000000000000000000000000000000000000000000
χ6044-4-4-4-444-4400400-4000000−4i4i4i−4i000000000000000000000000000000000000000000
χ614-4-444-4-4400-4-4044000000000004-4-4400000000000000000000000000000000000000
χ624-4-444-4-4400-4-404400000000000-444-400000000000000000000000000000000000000
χ634-4-44-444-4004-40-4400000000000000000004i−4i−4i4i000000000000000000000000000000
χ644-4-44-444-4004-40-440000000000000000000−4i4i4i−4i000000000000000000000000000000
χ654-4-44-444-400-4404-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ664-4-44-444-400-4404-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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