Finite Group Databasebeta

← Group #403115

Character table — Group #403115

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12222222224444444488888888888822224444444488888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ12111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-11111-1-1-1-11111-1-1
χ172222222222-2-2-2-2-2-2-2-20000000000002-22-22-22-22-22-200000000000000000000000000
χ182222222222-2-2-2-2-2-2-2-20000000000002-2-22-222-2-22-2200000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2000000000000-222-2-22-222-2-2200000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2000000000000-22-222-2-22-222-200000000000000000000000000
χ2122222-2-2-2-222222-2-2-2-20000000000000000220000-2-2002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222-2-2-2-222222-2-2-2-20000000000000000220000-2-200−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222-2-2-2-222222-2-2-2-20000000000000000-2-2000022002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222-2-2-2-222222-2-2-2-20000000000000000-2-200002200−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2522222-2-2-2-22-2-2-2-2222222222222-2-2-2-200002-20000-22-2-2000000000000000000000000
χ2622222-2-2-2-22-2-2-2-222222222-2-2-2-222220000-2200002-2-2-2000000000000000000000000
χ2722222-2-2-2-22-2-2-2-22222-2-2-2-22222-2-2-2-20000-2200002-222000000000000000000000000
χ2822222-2-2-2-22-2-2-2-22222-2-2-2-2-2-2-2-2222200002-20000-2222000000000000000000000000
χ292222-222-2-2-222-2-222-2-200002i2i−2i−2i2i2i−2i−2i00220000-2-200002i−2i2i−2i00000000000000000000
χ302222-222-2-2-222-2-222-2-200002i2i−2i−2i2i2i−2i−2i00-2-20000220000−2i2i−2i2i00000000000000000000
χ312222-222-2-2-222-2-222-2-20000−2i−2i2i2i−2i−2i2i2i00220000-2-20000−2i2i−2i2i00000000000000000000
χ322222-222-2-2-222-2-222-2-20000−2i−2i2i2i−2i−2i2i2i00-2-200002200002i−2i2i−2i00000000000000000000
χ332222-222-2-2-2-2-222-2-22222-2-200000000002-20000-22002-200002-22-20000000000000000
χ342222-222-2-2-2-2-222-2-22222-2-20000000000-2200002-2002-20000-22-220000000000000000
χ352222-222-2-2-2-2-222-2-222-2-22200000000002-20000-2200-220000-22-220000000000000000
χ362222-222-2-2-2-2-222-2-222-2-2220000000000-2200002-200-2200002-22-20000000000000000
χ372222-2-2-222-222-2-2-2-22222-2-2000000002-20000-220000-222-2-2200000000000000000000
χ382222-2-2-222-222-2-2-2-22222-2-200000000-2200002-20000-22-222-200000000000000000000
χ392222-2-2-222-222-2-2-2-222-2-222000000002-20000-2200002-2-222-200000000000000000000
χ402222-2-2-222-222-2-2-2-222-2-22200000000-2200002-200002-22-2-2200000000000000000000
χ412222-2-2-222-2-2-22222-2-200002i2i−2i−2i−2i−2i2i2i220000-2-200000000002i−2i−2i2i0000000000000000
χ422222-2-2-222-2-2-22222-2-200002i2i−2i−2i−2i−2i2i2i-2-20000220000000000−2i2i2i−2i0000000000000000
χ432222-2-2-222-2-2-22222-2-20000−2i−2i2i2i2i2i−2i−2i220000-2-20000000000−2i2i2i−2i0000000000000000
χ442222-2-2-222-2-2-22222-2-20000−2i−2i2i2i2i2i−2i−2i-2-200002200000000002i−2i−2i2i0000000000000000
χ452-22-222-22-2-22-22-22-2-2200002-22-22-22-200000000000000000000000000002i−2i002i−2i0000
χ462-22-222-22-2-22-22-22-2-2200002-22-22-22-20000000000000000000000000000−2i2i00−2i2i0000
χ472-22-222-22-2-22-22-22-2-220000-22-22-22-2200000000000000000000000000002i−2i00−2i2i0000
χ482-22-222-22-2-22-22-22-2-220000-22-22-22-220000000000000000000000000000−2i2i002i−2i0000
χ492-22-22-22-22-2-22-222-2-2200002-22-2-22-22000000000000000000000000002i−2i002i−2i000000
χ502-22-22-22-22-2-22-222-2-2200002-22-2-22-2200000000000000000000000000−2i2i00−2i2i000000
χ512-22-22-22-22-2-22-222-2-220000-22-222-22-2000000000000000000000000002i−2i00−2i2i000000
χ522-22-22-22-22-2-22-222-2-220000-22-222-22-200000000000000000000000000−2i2i002i−2i000000
χ532-22-2-22-2-2222-2-222-22-200002i−2i−2i2i2i−2i−2i2i00000000000000000000002i−2i00000000002-200
χ542-22-2-22-2-2222-2-222-22-200002i−2i−2i2i2i−2i−2i2i0000000000000000000000−2i2i0000000000-2200
χ552-22-2-22-2-2222-2-222-22-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000002i−2i0000000000-2200
χ562-22-2-22-2-2222-2-222-22-20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000−2i2i00000000002-200
χ572-22-2-2-222-22-222-22-22-200002i−2i−2i2i−2i2i2i−2i0000000000000000000000002i−2i00000000002-2
χ582-22-2-2-222-22-222-22-22-200002i−2i−2i2i−2i2i2i−2i000000000000000000000000−2i2i0000000000-22
χ592-22-2-2-222-22-222-22-22-20000−2i2i2i−2i2i−2i−2i2i0000000000000000000000002i−2i0000000000-22
χ602-22-2-2-222-22-222-22-22-20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2i2i00000000002-2
χ614-44-444-44-4-4-44-44-444-400000000000000000000000000000000000000000000000000
χ624-44-44-44-44-44-44-4-444-400000000000000000000000000000000000000000000000000
χ634-44-4-44-4-444-444-4-44-4400000000000000000000000000000000000000000000000000
χ644-44-4-4-444-444-4-44-44-4400000000000000000000000000000000000000000000000000
χ6588-8-8000000000000000042−420000000000000000000000000000000000000000000000
χ6688-8-80000000000000000−42420000000000000000000000000000000000000000000000
χ678-8-880000000000000042−42000000000000000000000000000000000000000000000000
χ688-8-8800000000000000−4242000000000000000000000000000000000000000000000000

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