Finite Group Databasebeta

← Group #405609

Character table — Group #405609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12222222224444444444448888888822444444448888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1
χ10111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111
χ11111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111
χ12111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-111-1-1-1-111
χ1722222-2-22-2-222-222-2-2-200002i2i2i2i−2i−2i−2i−2i0022-2-2000000002i2i−2i−2i00000000000000000000
χ1822222-2-22-2-222-222-2-2-200002i2i2i2i−2i−2i−2i−2i00-2-22200000000−2i−2i2i2i00000000000000000000
χ1922222-2-22-2-222-222-2-2-20000−2i−2i−2i−2i2i2i2i2i0022-2-200000000−2i−2i2i2i00000000000000000000
χ2022222-2-22-2-222-222-2-2-20000−2i−2i−2i−2i2i2i2i2i00-2-222000000002i2i−2i−2i00000000000000000000
χ212222-22-2-22-22-222-22-2-200002i2i−2i−2i2i2i−2i−2i220000-2-200000000002i2i−2i−2i0000000000000000
χ222222-22-2-22-22-222-22-2-200002i2i−2i−2i2i2i−2i−2i-2-20000220000000000−2i−2i2i2i0000000000000000
χ232222-22-2-22-22-222-22-2-20000−2i−2i2i2i−2i−2i2i2i220000-2-20000000000−2i−2i2i2i0000000000000000
χ242222-22-2-22-22-222-22-2-20000−2i−2i2i2i−2i−2i2i2i-2-200002200000000002i2i−2i−2i0000000000000000
χ252222-2-22-2-222-2-22-2-222222222-2-2-2-22200000000-2-222-2-2000000000000000000000000
χ262222-2-22-2-222-2-22-2-2222222-2-22222-2-200000000-2-2-2-222000000000000000000000000
χ272222-2-22-2-222-2-22-2-222-2-2-2-222-2-2-2-2220000000022-2-222000000000000000000000000
χ282222-2-22-2-222-2-22-2-222-2-2-2-2-2-22222-2-2000000002222-2-2000000000000000000000000
χ292-2-2222-2-2-22222-2-2-22-222-2-200000000002i−2i2i−2i002-2000000002i−2i2i−2i0000000000000000
χ302-2-2222-2-2-22222-2-2-22-222-2-20000000000−2i2i−2i2i002-200000000−2i2i−2i2i0000000000000000
χ312-2-2222-2-2-22222-2-2-22-2-2-22200000000002i−2i2i−2i00-2200000000−2i2i−2i2i0000000000000000
χ322-2-2222-2-2-22222-2-2-22-2-2-2220000000000−2i2i−2i2i00-22000000002i−2i2i−2i0000000000000000
χ332-2-2222-2-2-22-2-2-2222-2200002-22-22-22-20000000000000000000000002-20000002-20000
χ342-2-2222-2-2-22-2-2-2222-2200002-22-22-22-2000000000000000000000000-22000000-220000
χ352-2-2222-2-2-22-2-2-2222-220000-22-22-22-220000000000000000000000002-2000000-220000
χ362-2-2222-2-2-22-2-2-2222-220000-22-22-22-22000000000000000000000000-220000002-20000
χ372-2-222-22-22-222-2-2-22-220000000000002-22i−2i−2i2i2-2002i−2i2i−2i000000000000000000000000
χ382-2-222-22-22-222-2-2-22-220000000000002-2−2i2i2i−2i2-200−2i2i−2i2i000000000000000000000000
χ392-2-222-22-22-222-2-2-22-22000000000000-222i−2i−2i2i-2200−2i2i−2i2i000000000000000000000000
χ402-2-222-22-22-222-2-2-22-22000000000000-22−2i2i2i−2i-22002i−2i2i−2i000000000000000000000000
χ412-2-222-22-22-2-2-2222-22-200002i−2i2i−2i−2i2i−2i2i000000000000000000000000002-22i−2i00000000
χ422-2-222-22-22-2-2-2222-22-200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000-22−2i2i00000000
χ432-2-222-22-22-2-2-2222-22-20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000002-2−2i2i00000000
χ442-2-222-22-22-2-2-2222-22-20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000-222i−2i00000000
χ452-2-22-2222-2-22-22-22-2-2200000000000000000000002i−2i−2i2i2i−2i2i−2i2-2-220000000000000000
χ462-2-22-2222-2-22-22-22-2-2200000000000000000000002i−2i−2i2i−2i2i−2i2i-222-20000000000000000
χ472-2-22-2222-2-22-22-22-2-220000000000000000000000−2i2i2i−2i2i−2i2i−2i-222-20000000000000000
χ482-2-22-2222-2-22-22-22-2-220000000000000000000000−2i2i2i−2i−2i2i−2i2i2-2-220000000000000000
χ492-2-22-2222-2-2-22-22-222-200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000002-22i−2i
χ502-2-22-2222-2-2-22-22-222-200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000-22−2i2i
χ512-2-22-2222-2-2-22-22-222-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000002-2−2i2i
χ522-2-22-2222-2-2-22-22-222-20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000-222i−2i
χ532-2-22-2-2-22222-2-2-2222-222-2-2000000002-20000-22-220000-222-200000000000000000000
χ542-2-22-2-2-22222-2-2-2222-222-2-200000000-2200002-2-2200002-2-2200000000000000000000
χ552-2-22-2-2-22222-2-2-2222-2-2-222000000002-20000-222-200002-2-2200000000000000000000
χ562-2-22-2-2-22222-2-2-2222-2-2-22200000000-2200002-22-20000-222-200000000000000000000
χ572-2-22-2-2-2222-2222-2-2-2200002-2-22-222-200000000000000000000002-20000002-2000000
χ582-2-22-2-2-2222-2222-2-2-2200002-2-22-222-20000000000000000000000-22000000-22000000
χ592-2-22-2-2-2222-2222-2-2-220000-222-22-2-2200000000000000000000002-2000000-22000000
χ602-2-22-2-2-2222-2222-2-2-220000-222-22-2-220000000000000000000000-220000002-2000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ6244444-4-44-4-4-4-44-4-444400000000000000000000000000000000000000000000000000
χ634444-44-4-44-4-44-4-44-44400000000000000000000000000000000000000000000000000
χ644444-4-44-4-44-444-444-4-400000000000000000000000000000000000000000000000000
χ6588-8-8000000000000004-44-40000000000000000000000000000000000000000000000
χ6688-8-800000000000000-44-440000000000000000000000000000000000000000000000
χ678-88-8000000000000004-4-440000000000000000000000000000000000000000000000
χ688-88-800000000000000-444-40000000000000000000000000000000000000000000000

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