Finite Group Databasebeta

← Group #325010

Character table — Group #325010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444444444888844448888888888888888888888888844884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11-1-11
χ17222222222-2-222-2-22-2-22222-2-2-2-2000022-2-200000000000000000000000000-22000000
χ18222222222-2-222-2-22-2-22222-2-2-2-20000-2-222000000000000000000000000002-2000000
χ19222222222-2-222-2-22-2-2-2-2-2-22222000022-2-2000000000000000000000000002-2000000
χ20222222222-2-222-2-22-2-2-2-2-2-222220000-2-22200000000000000000000000000-22000000
χ2122222222-222-2-222-2-2-222-2-222-2-222220000-2-20000000022-2-200000000000000000000
χ2222222222-222-2-222-2-2-222-2-222-2-2-2-2-2-200002200000000-2-22200000000000000000000
χ2322222222-222-2-222-2-2-2-2-222-2-22222220000-2-200000000-2-22200000000000000000000
χ2422222222-222-2-222-2-2-2-2-222-2-222-2-2-2-20000220000000022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000002i2i−2i−2i00000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000000000−2i−2i2i2i0000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-22222-2-200000000000000000000002i2i−2i−2i0000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-22222-2-20000000000000000000000−2i−2i2i2i00000000002i−2i0000
χ2922-2-222-2-22-2-2-2-22222-2000000002i2i−2i−2i00002i−2i2i2i−2i−2i000000000000000022-2-200000000
χ3022-2-222-2-22-2-2-2-22222-2000000002i2i−2i−2i00002i−2i−2i−2i2i2i0000000000000000-2-22200000000
χ3122-2-222-2-22-2-2-2-22222-200000000−2i−2i2i2i0000−2i2i2i2i−2i−2i0000000000000000-2-22200000000
χ3222-2-222-2-22-2-2-2-22222-200000000−2i−2i2i2i0000−2i2i−2i−2i2i2i000000000000000022-2-200000000
χ3322-2-222-2-2-2-2-22222-2-22000000002i2i−2i−2i0000−2i2i000022-2-2000000002i2i−2i−2i000000000000
χ3422-2-222-2-2-2-2-22222-2-22000000002i2i−2i−2i0000−2i2i0000-2-22200000000−2i−2i2i2i000000000000
χ3522-2-222-2-2-2-2-22222-2-2200000000−2i−2i2i2i00002i−2i000022-2-200000000−2i−2i2i2i000000000000
χ3622-2-222-2-2-2-2-22222-2-2200000000−2i−2i2i2i00002i−2i0000-2-222000000002i2i−2i−2i000000000000
χ372-22-22-22-202-2002-2000002i−2i002i−2i2-22-20000002−22−2i2−i2i2−i2002i−2i0000i2−i2i2−i22−22−200000000
χ382-22-22-22-202-2002-2000002i−2i002i−2i2-22-2000000−22−22−i2i2−i2i2002i−2i0000−i2i2−i2i2−22−2200000000
χ392-22-22-22-202-2002-2000002i−2i002i−2i-22-220000002−22−2−i2i2−i2i200−2i2i0000i2−i2i2−i2−22−2200000000
χ402-22-22-22-202-2002-2000002i−2i002i−2i-22-22000000−22−22i2−i2i2−i200−2i2i0000−i2i2−i2i22−22−200000000
χ412-22-22-22-202-2002-200000−2i2i00−2i2i2-22-20000002−22−2−i2i2−i2i200−2i2i0000−i2i2−i2i22−22−200000000
χ422-22-22-22-202-2002-200000−2i2i00−2i2i2-22-2000000−22−22i2−i2i2−i200−2i2i0000i2−i2i2−i2−22−2200000000
χ432-22-22-22-202-2002-200000−2i2i00−2i2i-22-220000002−22−2i2−i2i2−i2002i−2i0000−i2i2−i2i2−22−2200000000
χ442-22-22-22-202-2002-200000−2i2i00−2i2i-22-22000000−22−22−i2i2−i2i2002i−2i0000i2−i2i2−i22−22−200000000
χ452-2-222-2-220-22002-20002i−2i002i−2i002i−2i−2i2i000000i2−i2−i2i2i2−i2−i2i22-2000000−222−22−2−2200000000
χ462-2-222-2-220-22002-20002i−2i002i−2i002i−2i−2i2i000000−i2i2i2−i2−i2i2i2−i22-20000002−2−22−222−200000000
χ472-2-222-2-220-22002-20002i−2i002i−2i00−2i2i2i−2i000000i2−i2−i2i2−i2i2i2−i2-22000000−222−2−222−200000000
χ482-2-222-2-220-22002-20002i−2i002i−2i00−2i2i2i−2i000000−i2i2i2−i2i2−i2−i2i2-220000002−2−222−2−2200000000
χ492-2-222-2-220-22002-2000−2i2i00−2i2i002i−2i−2i2i000000i2−i2−i2i2−i2i2i2−i2-220000002−2−222−2−2200000000
χ502-2-222-2-220-22002-2000−2i2i00−2i2i002i−2i−2i2i000000−i2i2i2−i2i2−i2−i2i2-22000000−222−2−222−200000000
χ512-2-222-2-220-22002-2000−2i2i00−2i2i00−2i2i2i−2i000000i2−i2−i2i2i2−i2−i2i22-20000002−2−22−222−200000000
χ522-2-222-2-220-22002-2000−2i2i00−2i2i00−2i2i2i−2i000000−i2i2i2−i2−i2i2i2−i22-2000000−222−22−2−2200000000
χ5344-4-444-4-4444-4-4-4-44-4400000000000000000000000000000000000000000000000000
χ5444-4-444-4-4-44444-4-4-44-400000000000000000000000000000000000000000000000000
χ554-444-44-4-44004-400-40000000000000000000000000000000022−2222−220000000000000000
χ564-444-44-4-44004-400-400000000000000000000000000000000−2222−22220000000000000000
χ574-444-44-4-4-400-44004000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-444-44-4-4-400-4400400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-44-44-44-40-4400-44000004i−4i00−4i4i000000000000000000000000000000000000000000
χ604-44-44-44-40-4400-4400000−4i4i004i−4i000000000000000000000000000000000000000000
χ614-4-444-4-4404-400-440004i−4i00−4i4i00000000000000000000000000000000000000000000
χ624-4-444-4-4404-400-44000−4i4i004i−4i00000000000000000000000000000000000000000000
χ634-4-4-4-4444400-4400-4000000000000004i−4i000000000000000000000000000000000000
χ644-4-4-4-4444400-4400-400000000000000−4i4i000000000000000000000000000000000000
χ654-4-4-4-4444-4004-400400000000000000004-40000000000000000000000000000000000
χ664-4-4-4-4444-4004-40040000000000000000-440000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ6888-88-8-88-8000000000000000000000000000000000000000000000000000000000000

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