Finite Group Databasebeta

← Group #312918

Character table — Group #312918

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-111-11
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-11
χ91111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ111111111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-11-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1111-1-111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-1-111-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1-11111-1-1-11
χ17222222222-22-22-22-20000-2-22222-2-2-2-200220000-2-20000000000000000200-200000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-200-2-20000220000000000000000-200200000000
χ19222222222-22-22-22-20000-2-2-2-2-2-2222200220000220000000000000000-200-200000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2222200-2-20000-2-20000000000000000200200000000
χ2122222222-22-22-22-222222-2-2000000002200-2-2-2-200220000-2-200000000000000000000
χ2222222222-22-22-22-222222-2-200000000-2-200-2-22200-2-200002200000000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200000000220022-2-200-2-200002200000000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000000-2-200222200220000-2-200000000000000000000
χ252222-2-2-2-202020-20-222-2-20022−2−222−2−22-2000000002-222−2−20022−2−222−2−2000000000000
χ262222-2-2-2-202020-20-222-2-20022−2−222−2−2-2200000000-2222−2−200−2−222−2−222000000000000
χ272222-2-2-2-202020-20-222-2-200−2−222−2−2222-2000000002-2−2−22200−2−222−2−222000000000000
χ282222-2-2-2-202020-20-222-2-200−2−222−2−222-2200000000-22−2−2220022−2−222−2−2000000000000
χ292222-2-2-2-202020-20-2-2-2220022−2−222−2−22-200000000-22−2−2220022−2−2−2−222000000000000
χ302222-2-2-2-202020-20-2-2-2220022−2−222−2−2-22000000002-2−2−22200−2−22222−2−2000000000000
χ312222-2-2-2-202020-20-2-2-22200−2−222−2−2222-200000000-2222−2−200−2−22222−2−2000000000000
χ322222-2-2-2-202020-20-2-2-22200−2−222−2−222-22000000002-222−2−20022−2−2−2−222000000000000
χ332-2-222-2-2222-2-222-2-22i−2i2i−2i-222i−2i2i−2i2i−2i2i−2i00002i−2i0000002-22-20000000000000000000000
χ342-2-222-2-2222-2-222-2-22i−2i2i−2i-22−2i2i−2i2i−2i2i−2i2i00002i−2i000000-22-220000000000000000000000
χ352-2-222-2-2222-2-222-2-2−2i2i−2i2i-222i−2i2i−2i2i−2i2i−2i0000−2i2i000000-22-220000000000000000000000
χ362-2-222-2-2222-2-222-2-2−2i2i−2i2i-22−2i2i−2i2i−2i2i−2i2i0000−2i2i0000002-22-20000000000000000000000
χ372-2-222-2-222-2-222-2-2200002-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000002i−2i02-2000000
χ382-2-222-2-222-2-222-2-2200002-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000−2i2i0-22000000
χ392-2-222-2-222-2-222-2-2200002-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000002i−2i0-22000000
χ402-2-222-2-222-2-222-2-2200002-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000−2i2i02-2000000
χ412-2-222-2-22-222-2-222-22i−2i2i−2i2-2000000000000−2i2i0000000000002-22-22i−2i2i−2i000000000000
χ422-2-222-2-22-222-2-222-22i−2i2i−2i2-2000000000000−2i2i000000000000-22-22−2i2i−2i2i000000000000
χ432-2-222-2-22-222-2-222-2−2i2i−2i2i2-20000000000002i−2i0000000000002-22-2−2i2i−2i2i000000000000
χ442-2-222-2-22-222-2-222-2−2i2i−2i2i2-20000000000002i−2i000000000000-22-222i−2i2i−2i000000000000
χ452-2-22-222-2020-20-2022i−2i−2i2i00i2−i2−i2i2i2−i2−i2i20000002i−2i00002−2−222-22−2−22i2−i2−i2i2000000000000
χ462-2-22-222-2020-20-2022i−2i−2i2i00i2−i2−i2i2i2−i2−i2i2000000−2i2i00002−2−22-22−222−2−i2i2i2−i2000000000000
χ472-2-22-222-2020-20-2022i−2i−2i2i00−i2i2i2−i2−i2i2i2−i20000002i−2i0000−222−22-2−222−2−i2i2i2−i2000000000000
χ482-2-22-222-2020-20-2022i−2i−2i2i00−i2i2i2−i2−i2i2i2−i2000000−2i2i0000−222−2-222−2−22i2−i2−i2i2000000000000
χ492-2-22-222-2020-20-202−2i2i2i−2i00i2−i2−i2i2i2−i2−i2i20000002i−2i0000−222−2-222−2−22−i2i2i2−i2000000000000
χ502-2-22-222-2020-20-202−2i2i2i−2i00i2−i2−i2i2i2−i2−i2i2000000−2i2i0000−222−22-2−222−2i2−i2−i2i2000000000000
χ512-2-22-222-2020-20-202−2i2i2i−2i00−i2i2i2−i2−i2i2i2−i20000002i−2i00002−2−22-22−222−2i2−i2−i2i2000000000000
χ522-2-22-222-2020-20-202−2i2i2i−2i00−i2i2i2−i2−i2i2i2−i2000000−2i2i00002−2−222-22−2−22−i2i2i2−i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ544444-4-4-4-40-40-404040000002222−22−22−22−22222200000000000000000000000000000000000000
χ554444-4-4-4-40-40-40404000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-4-444-4-440-40-404000000000000000000000000000000000000000000000000022−2200
χ5744-4-444-4-440-40-4040000000000000000000000000000000000000000000000000−222200
χ5844-4-444-4-4-404040-4000000000000000004-40000000000000000000000000000000000
χ5944-4-444-4-4-404040-400000000000000000-440000000000000000000000000000000000
χ604-44-44-44-44040-40-40000000000000000000000000000000000000000000000022−220000
χ614-44-44-44-44040-40-400000000000000000000000000000000000000000000000−22220000
χ624-44-44-44-4-40-40404000000000000000000000004i−4i0000000000000000000000000000
χ634-44-44-44-4-40-4040400000000000000000000000−4i4i0000000000000000000000000000
χ644-4-444-4-44-4-444-4-4440000-440000000000000000000000000000000000000000000000
χ654-4-44-444-40-404040-40000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-44-444-40-404040-4000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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