Finite Group Databasebeta

← Group #414513

Character table — Group #414513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12222222224444444444444444888844444444444444448888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ511111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-111-1-111
χ611111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-1-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-1111111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-111111-1-1-1-1-1-111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-11-1111111-1-1-1-1-1-1
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11-1-1-1-1-1-1111111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-111-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
χ17222222-2-2-2-222-22-2-2-220000000022-2-2000000002i2i−2i−2i2i2i−2i−2i00002-20000000000000000
χ18222222-2-2-2-222-22-2-2-220000000022-2-200000000−2i−2i2i2i−2i−2i2i2i00002-20000000000000000
χ19222222-2-2-2-222-22-2-2-2200000000-2-222000000002i2i−2i−2i−2i−2i2i2i0000-220000000000000000
χ20222222-2-2-2-222-22-2-2-2200000000-2-22200000000−2i−2i2i2i2i2i−2i−2i0000-220000000000000000
χ21222222-2-2-2-2-2-22-2222-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000020-2000000000002i−2i
χ22222222-2-2-2-2-2-22-2222-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000-20200000000000−2i2i
χ23222222-2-2-2-2-2-22-2222-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000020-200000000000−2i2i
χ24222222-2-2-2-2-2-22-2222-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000-202000000000002i−2i
χ252222-2-222-2-2222-22-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000020-200002i−2i000000
χ262222-2-222-2-2222-22-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000-2020000−2i2i000000
χ272222-2-222-2-2222-22-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000020-20000−2i2i000000
χ282222-2-222-2-2222-22-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000-20200002i−2i000000
χ292222-2-222-2-2-2-2-22-22220000000022-2-222-2-222-2-2000000000000-220000000000000000
χ302222-2-222-2-2-2-2-22-22220000000022-2-2-2-222-2-222000000000000-220000000000000000
χ312222-2-222-2-2-2-2-22-222200000000-2-22222-2-2-2-2220000000000002-20000000000000000
χ322222-2-222-2-2-2-2-22-222200000000-2-222-2-22222-2-20000000000002-20000000000000000
χ332222-2-2-2-222-2-2222-2-2222-2-2-2-2222222000000000000000022-2-2-2-20000000000000000
χ342222-2-2-2-222-2-2222-2-2222-2-2-2-222-2-2-2-20000000000000000-2-222220000000000000000
χ352222-2-2-2-222-2-2222-2-22-2-22222-2-222220000000000000000-2-222-2-20000000000000000
χ362222-2-2-2-222-2-2222-2-22-2-22222-2-2-2-2-2-2000000000000000022-2-2220000000000000000
χ372-22-22-22-22-22-2-2-222-222-22-22-22-2000000002i−2i2i−2i00002i−2i2i−2i0000000000000000000000
χ382-22-22-22-22-22-2-2-222-222-22-22-22-200000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000
χ392-22-22-22-22-22-2-2-222-22-22-22-22-22000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000000000
χ402-22-22-22-22-22-2-2-222-22-22-22-22-2200000000−2i2i−2i2i00002i−2i2i−2i0000000000000000000000
χ412-22-22-2-22-222-22-2-2-2220000000000002i−2i2i−2i000000002-2-222i−2i2i−2i000000000000000000
χ422-22-22-2-22-222-22-2-2-2220000000000002i−2i2i−2i00000000-222-2−2i2i−2i2i000000000000000000
χ432-22-22-2-22-222-22-2-2-222000000000000−2i2i−2i2i000000002-2-22−2i2i−2i2i000000000000000000
χ442-22-22-2-22-222-22-2-2-222000000000000−2i2i−2i2i00000000-222-22i−2i2i−2i000000000000000000
χ452-22-22-2-22-22-22-2222-2-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002-200002i−2i00
χ462-22-22-2-22-22-22-2222-2-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000-220000−2i2i00
χ472-22-22-2-22-22-22-2222-2-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002-20000−2i2i00
χ482-22-22-2-22-22-22-2222-2-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000-2200002i−2i00
χ492-22-2-222-2-222-2-222-22-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000002-200002i−2i0000
χ502-22-2-222-2-222-2-222-22-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000-220000−2i2i0000
χ512-22-2-222-2-222-2-222-22-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000002-20000−2i2i0000
χ522-22-2-222-2-222-2-222-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000-2200002i−2i0000
χ532-22-2-222-2-22-222-2-22-2200000000000000002i−2i−2i2i2-22-200002i−2i−2i2i000000000000000000
χ542-22-2-222-2-22-222-2-22-2200000000000000002i−2i−2i2i-22-220000−2i2i2i−2i000000000000000000
χ552-22-2-222-2-22-222-2-22-220000000000000000−2i2i2i−2i2-22-20000−2i2i2i−2i000000000000000000
χ562-22-2-222-2-22-222-2-22-220000000000000000−2i2i2i−2i-22-2200002i−2i−2i2i000000000000000000
χ572-22-2-22-222-2-22-2-22-2222-2-22-222-200002i−2i−2i2i00002i−2i−2i2i00000000000000000000000000
χ582-22-2-22-222-2-22-2-22-2222-2-22-222-20000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000000000
χ592-22-2-22-222-2-22-2-22-222-222-22-2-2200002i−2i−2i2i0000−2i2i2i−2i00000000000000000000000000
χ602-22-2-22-222-2-22-2-22-222-222-22-2-220000−2i2i2i−2i00002i−2i−2i2i00000000000000000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ624444-4-4-4-44444-4-4-444-400000000000000000000000000000000000000000000000000
χ634-44-44-44-44-4-4444-4-44-400000000000000000000000000000000000000000000000000
χ644-44-4-44-444-44-444-44-4-400000000000000000000000000000000000000000000000000
χ6588-8-800000000000000000000000042−4200000000000000000000000000000000000000
χ6688-8-8000000000000000000000000−424200000000000000000000000000000000000000
χ678-8-88000000000000000000000042−420000000000000000000000000000000000000000
χ688-8-880000000000000000000000−42420000000000000000000000000000000000000000

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