Finite Group Databasebeta

← Group #394359

Character table — Group #394359

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222224444444488888888888888888888888888881616161616161616161616161616
order12222222224444444444444444222244444444444444444444888822244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-111111-1-111
χ9111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ11111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ12111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-111-111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1
χ172222222222-2-2-2-2-2-2-2-2000000002-2002-200000022-2-2000022-2-2000000000000000000
χ182222222222-2-2-2-2-2-2-2-2000000002-2002-2000000-2-2220000-2-222000000000000000000
χ192222222222-2-2-2-2-2-2-2-200000000-2200-2200000022-2-20000-2-222000000000000000000
χ202222222222-2-2-2-2-2-2-2-200000000-2200-22000000-2-222000022-2-2000000000000000000
χ2122222-2-22-2-22222-2-2-2-2000000002200-2-2002i2i−2i−2i00002i2i−2i−2i0000000000000000000000
χ2222222-2-22-2-22222-2-2-2-2000000002200-2-200−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000
χ2322222-2-22-2-22222-2-2-2-200000000-2-20022002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000
χ2422222-2-22-2-22222-2-2-2-200000000-2-2002200−2i−2i2i2i00002i2i−2i−2i0000000000000000000000
χ2522222-2-22-2-2-2-2-2-222222222-2-2-2-22-222-22-2-20000000000000000000000000000000000
χ2622222-2-22-2-2-2-2-2-222222222-2-2-2-2-22-2-22-2220000000000000000000000000000000000
χ2722222-2-22-2-2-2-2-2-22222-2-2-2-222222-2-2-2-22220000000000000000000000000000000000
χ2822222-2-22-2-2-2-2-2-22222-2-2-2-22222-22222-2-2-20000000000000000000000000000000000
χ292222-22-2-22-222-2-2-22-2222-2-222-2-2000000000000000000000000000000200-20000002-2
χ302222-22-2-22-222-2-2-22-2222-2-222-2-2000000000000000000000000000000-2002000000-22
χ312222-22-2-22-222-2-2-22-22-2-222-2-222000000000000000000000000000000200-2000000-22
χ322222-22-2-22-222-2-2-22-22-2-222-2-222000000000000000000000000000000-20020000002-2
χ332222-2-22-2-22-2-222-22-2222-2-2-2-22200000000000000000000000000000002-2000002-200
χ342222-2-22-2-22-2-222-22-2222-2-2-2-2220000000000000000000000000000000-2200000-2200
χ352222-2-22-2-22-2-222-22-22-2-22222-2-200000000000000000000000000000002-200000-2200
χ362222-2-22-2-22-2-222-22-22-2-22222-2-20000000000000000000000000000000-22000002-200
χ372-2-22222-2-2-22-22-22-2-222-22-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ382-2-22222-2-2-22-22-22-2-222-22-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ392-2-22222-2-2-22-22-22-2-22-22-22-22-2200000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ402-2-22222-2-2-22-22-22-2-22-22-22-22-220000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ412-2-22222-2-2-2-22-22-222-200000000002-2002-22i−2i2i−2i000000002i−2i−2i2i000000000000000000
χ422-2-22222-2-2-2-22-22-222-200000000002-2002-2−2i2i−2i2i00000000−2i2i2i−2i000000000000000000
χ432-2-22222-2-2-2-22-22-222-20000000000-2200-222i−2i2i−2i00000000−2i2i2i−2i000000000000000000
χ442-2-22222-2-2-2-22-22-222-20000000000-2200-22−2i2i−2i2i000000002i−2i−2i2i000000000000000000
χ452-2-222-2-2-2222-22-2-222-200000000002-200-2200002-22-22-2-220000000000000000000000
χ462-2-222-2-2-2222-22-2-222-200000000002-200-220000-22-22-222-20000000000000000000000
χ472-2-222-2-2-2222-22-2-222-20000000000-22002-200002-22-2-222-20000000000000000000000
χ482-2-222-2-2-2222-22-2-222-20000000000-22002-20000-22-222-2-220000000000000000000000
χ492-2-222-2-2-222-22-222-2-222-22-2-22-22000000002-2-222-2-2200000000000000000000000000
χ502-2-222-2-2-222-22-222-2-222-22-2-22-2200000000-222-2-222-200000000000000000000000000
χ512-2-222-2-2-222-22-222-2-22-22-222-22-2000000002-2-22-222-200000000000000000000000000
χ522-2-222-2-2-222-22-222-2-22-22-222-22-200000000-222-22-2-2200000000000000000000000000
χ532-2-22-22-22-222-2-22-2-2222-2-222-2-2200000000000000000000000000000000002-22-20000
χ542-2-22-22-22-222-2-22-2-2222-2-222-2-220000000000000000000000000000000000-22-220000
χ552-2-22-22-22-222-2-22-2-222-222-2-222-200000000000000000000000000000000002-2-220000
χ562-2-22-22-22-222-2-22-2-222-222-2-222-20000000000000000000000000000000000-222-20000
χ572-2-22-2-2222-2-222-2-2-2222-2-22-222-200000000000000000000000022-2-22-2000000000000
χ582-2-22-2-2222-2-222-2-2-2222-2-22-222-2000000000000000000000000-2-222-22000000000000
χ592-2-22-2-2222-2-222-2-2-222-222-22-2-2200000000000000000000000022-2-2-22000000000000
χ602-2-22-2-2222-2-222-2-2-222-222-22-2-22000000000000000000000000-2-2222-2000000000000
χ614444-44-4-44-4-4-4444-44-400000000000000000000000000000000000000000000000000
χ624444-4-44-4-4444-4-44-44-400000000000000000000000000000000000000000000000000
χ634-4-44-44-44-44-444-444-4-400000000000000000000000000000000000000000000000000
χ644-4-44-4-4444-44-4-4444-4-400000000000000000000000000000000000000000000000000
χ6588-8-800000000000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ6688-8-80000000000000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ678-88-800000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ688-88-80000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000

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