Finite Group Databasebeta

← Group #118340

Character table — Group #118340

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ202222222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ21222222-2-2-2-22222222-22-2-2-2-2-22-22-20000000000000000000000000000000000002i−2i2i−2i
χ22222222-2-2-2-22222222-22-2-2-2-2-22-22-2000000000000000000000000000000000000−2i2i−2i2i
χ23222222-2-2-2-22222-2-2-22-2222-2-2-22-22000000000000000000000000000000002-22-20000
χ24222222-2-2-2-22222-2-2-22-2222-2-2-22-2200000000000000000000000000000000-22-220000
χ25222222-2-2-2-2-2-2-2-2222-22-2-2-222-22-22000000000000000000000000000000002i−2i−2i2i0000
χ26222222-2-2-2-2-2-2-2-2222-22-2-2-222-22-2200000000000000000000000000000000−2i2i2i−2i0000
χ27222222-2-2-2-2-2-2-2-2-2-2-22-2222222-22-20000000000000000000000000000000000002-2-22
χ28222222-2-2-2-2-2-2-2-2-2-2-22-2222222-22-2000000000000000000000000000000000000-222-2
χ292222-2-222-2-222-2-222-22-22-2-22-22-2-2200000000000000000000000000002i−2i2i−2i00000000
χ302222-2-222-2-222-2-222-22-22-2-22-22-2-220000000000000000000000000000−2i2i−2i2i00000000
χ312222-2-222-2-222-2-2-2-22-22-2222-2-222-20000000000000000000000002-22-2000000000000
χ322222-2-222-2-222-2-2-2-22-22-2222-2-222-2000000000000000000000000-22-22000000000000
χ332222-2-222-2-2-2-22222-22-22-2-2-22-222-20000000000000000000000002i−2i−2i2i000000000000
χ342222-2-222-2-2-2-22222-22-22-2-2-22-222-2000000000000000000000000−2i2i2i−2i000000000000
χ352222-2-222-2-2-2-222-2-22-22-222-222-2-2200000000000000000000000000002-2-2200000000
χ362222-2-222-2-2-2-222-2-22-22-222-222-2-220000000000000000000000000000-222-200000000
χ372222-2-2-2-22222-2-222-2-2-2-222-2222-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382222-2-2-2-22222-2-222-2-2-2-222-2222-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392222-2-2-2-22222-2-2-2-22222-2-2-22-2-222000000000000000022-2-222-2-20000000000000000
χ402222-2-2-2-22222-2-2-2-22222-2-2-22-2-2220000000000000000-2-222-2-2220000000000000000
χ412222-2-2-2-222-2-22222-2-2-2-2222-2-2-222000000000000000022-2-2-2-2220000000000000000
χ422222-2-2-2-222-2-22222-2-2-2-2222-2-2-2220000000000000000-2-22222-2-20000000000000000
χ432222-2-2-2-222-2-222-2-22222-2-22-222-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ442222-2-2-2-222-2-222-2-22222-2-22-222-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ452-22-22-22-22-200002-22-2-222-2000000002i−2i2i−2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ462-22-22-22-22-200002-22-2-222-2000000002i−2i2i−2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ472-22-22-22-22-200002-22-2-222-200000000−2i2i−2i2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-22-22-22-22-200002-22-2-222-200000000−2i2i−2i2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ492-22-22-22-22-20000-22-222-2-22000000002i−2i−2i2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ502-22-22-22-22-20000-22-222-2-22000000002i−2i−2i2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ512-22-22-22-22-20000-22-222-2-2200000000−2i2i2i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ522-22-22-22-22-20000-22-222-2-2200000000−2i2i2i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ532-22-2-22-222-200002-2-222-22-20000002-200002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ542-22-2-22-222-200002-2-222-22-20000002-200002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ552-22-2-22-222-200002-2-222-22-2000000-220000-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ562-22-2-22-222-200002-2-222-22-2000000-220000-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ572-22-2-22-222-20000-222-2-22-220000002-20000-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ582-22-2-22-222-20000-222-2-22-220000002-20000-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ592-22-2-22-222-20000-222-2-22-22000000-2200002-2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ602-22-2-22-222-20000-222-2-22-22000000-2200002-2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ614-44-44-4-44-4400004-444-4-4-440000000000000000000000000000000000000000000000
χ624-44-44-4-44-440000-44-4-4444-40000000000000000000000000000000000000000000000
χ634-44-4-444-4-4400004-4-4-444-440000000000000000000000000000000000000000000000
χ644-44-4-444-4-440000-4444-4-44-40000000000000000000000000000000000000000000000
χ6588-8-80000008-800000000000000000000000000000000000000000000000000000000
χ6688-8-8000000-8800000000000000000000000000000000000000000000000000000000
χ678-8-88000000008i−8i000000000000000000000000000000000000000000000000000000
χ688-8-8800000000−8i8i000000000000000000000000000000000000000000000000000000

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