Finite Group Databasebeta

← Group #404103

Character table — Group #404103

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12222222224444444444444444888822444444888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ9111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ172222222222-2-2-2-2-2-2-2-20000000000002-200002-2002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ182222222222-2-2-2-2-2-2-2-20000000000002-200002-200−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ192222222222-2-2-2-2-2-2-2-2000000000000-220000-22002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ202222222222-2-2-2-2-2-2-2-2000000000000-220000-2200−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ21222222-2-2-2-2222-2-22-2-22222-2-2-2-20000000000000000002i2i−2i−2i2i−2i2i−2i0000000000000000
χ22222222-2-2-2-2222-2-22-2-22222-2-2-2-2000000000000000000−2i−2i2i2i−2i2i−2i2i0000000000000000
χ23222222-2-2-2-2222-2-22-2-2-2-2-2-222220000000000000000002i2i−2i−2i−2i2i−2i2i0000000000000000
χ24222222-2-2-2-2222-2-22-2-2-2-2-2-22222000000000000000000−2i−2i2i2i2i−2i2i−2i0000000000000000
χ25222222-2-2-2-2-2-2-222-2220000000022220022-2-200-2-2000000002-2-220000000000000000
χ26222222-2-2-2-2-2-2-222-22200000000222200-2-22200-2-200000000-222-20000000000000000
χ27222222-2-2-2-2-2-2-222-22200000000-2-2-2-20022-2-2002200000000-222-20000000000000000
χ28222222-2-2-2-2-2-2-222-22200000000-2-2-2-200-2-2220022000000002-2-220000000000000000
χ292222-2-222-2-222-222-2-2-2000000000000002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ302222-2-222-2-222-222-2-2-2000000000000002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ312222-2-222-2-222-222-2-2-200000000000000-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ322222-2-222-2-222-222-2-2-200000000000000-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ332222-2-222-2-2-2-22-2-222222-2-222-2-222-2-2000000002-22-2-22000000000000000000000000
χ342222-2-222-2-2-2-22-2-222222-2-222-2-2-2-22200000000-22-222-2000000000000000000000000
χ352222-2-222-2-2-2-22-2-2222-2-222-2-22222-2-2000000002-2-222-2000000000000000000000000
χ362222-2-222-2-2-2-22-2-2222-2-222-2-222-2-22200000000-222-2-22000000000000000000000000
χ372222-2-2-2-22222-2-2-2-2220000000022-2-22-20000-22-2200002-2-2200000000000000000000
χ382222-2-2-2-22222-2-2-2-2220000000022-2-2-2200002-2-220000-222-200000000000000000000
χ392222-2-2-2-22222-2-2-2-22200000000-2-2222-20000-222-20000-222-200000000000000000000
χ402222-2-2-2-22222-2-2-2-22200000000-2-222-2200002-22-200002-2-2200000000000000000000
χ412222-2-2-2-222-2-22222-2-222-2-2-2-2220000222-2-22-2-2000000000000000000000000000000
χ422222-2-2-2-222-2-22222-2-222-2-2-2-2220000-2-2-222-222000000000000000000000000000000
χ432222-2-2-2-222-2-22222-2-2-2-22222-2-2000022-222-2-2-2000000000000000000000000000000
χ442222-2-2-2-222-2-22222-2-2-2-22222-2-20000-2-22-2-2222000000000000000000000000000000
χ452-2-222-22-22-22-222-2-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000002-200000000002i−2i
χ462-2-222-22-22-22-222-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000-220000000000−2i2i
χ472-2-222-22-22-22-222-2-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002-20000000000−2i2i
χ482-2-222-22-22-22-222-2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000-2200000000002i−2i
χ492-2-222-2-22-222-22-22-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000002-2002i−2i000000
χ502-2-222-2-22-222-22-22-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000-2200−2i2i000000
χ512-2-222-2-22-222-22-22-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000002-200−2i2i000000
χ522-2-222-2-22-222-22-22-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000-22002i−2i000000
χ532-2-22-222-2-22-222-22-22-22i−2i−2i2i2i−2i−2i2i000000000000000000000000002-200000000002i−2i00
χ542-2-22-222-2-22-222-22-22-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000-220000000000−2i2i00
χ552-2-22-222-2-22-222-22-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000002-20000000000−2i2i00
χ562-2-22-222-2-22-222-22-22-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000-2200000000002i−2i00
χ572-2-22-22-222-2-2222-2-2-222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000002-2002i−2i0000
χ582-2-22-22-222-2-2222-2-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000-2200−2i2i0000
χ592-2-22-22-222-2-2222-2-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000002-200−2i2i0000
χ602-2-22-22-222-2-2222-2-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000-22002i−2i0000
χ614-4-444-44-44-4-44-4-444-4400000000000000000000000000000000000000000000000000
χ624-4-444-4-44-44-44-44-444-400000000000000000000000000000000000000000000000000
χ634-4-44-444-4-444-4-44-44-4400000000000000000000000000000000000000000000000000
χ644-4-44-44-444-44-4-4-4444-400000000000000000000000000000000000000000000000000
χ6588-8-800000000000000000000000042−4200000000000000000000000000000000000000
χ6688-8-8000000000000000000000000−424200000000000000000000000000000000000000
χ678-88-8000000000000000000000042−420000000000000000000000000000000000000000
χ688-88-80000000000000000000000−42420000000000000000000000000000000000000000

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