Finite Group Databasebeta

← Group #313255

Character table — Group #313255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-11-1-11-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-11-1-1-1-11-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-111111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1111-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-11111-1-111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1111111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-1-1-11111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-11-1-11111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1111-1-1-1-1-1-1-11111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-11111-1-11111-1-11-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-2000000000022-2-200-200002000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-20000000000-2-2220020000-2000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200002222000000000022-2-20020000-2000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2000022220000000000-2-22200-200002000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-2000000000000220000220-200-20000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-20000-2-2020020000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002222000000000000220000-2-20-20020000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-20000220200-20000000000000
χ252-22-2-2-22222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i000000000000002i−2i2i−2i0000000000002-2000000
χ262-22-2-2-22222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i00000000000000−2i2i−2i2i000000000000-22000000
χ272-22-2-2-22222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i000000000000002i−2i2i−2i000000000000-22000000
χ282-22-2-2-22222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i00000000000000−2i2i−2i2i0000000000002-2000000
χ292-22-2-2-2222-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i002i−2i−2i2i00000000000000002-200
χ302-22-2-2-2222-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i00−2i2i2i−2i0000000000000000-2200
χ312-22-2-2-2222-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i002i−2i−2i2i0000000000000000-2200
χ322-22-2-2-2222-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i00−2i2i2i−2i00000000000000002-200
χ332-22-2-2-222-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000002i−2i002-20000000000
χ342-22-2-2-222-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i0000000000000000000000−2i2i00-220000000000
χ352-22-2-2-222-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000002i−2i00-220000000000
χ362-22-2-2-222-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i0000000000000000000000−2i2i002-20000000000
χ372-2-22-222-2020-20-202002i−2i2i−2ii2i2−i2−i20000i2i2−i2−i222−2−222−2−22i−2i00002-200000000i2−i2002−20000
χ382-2-22-222-2020-20-202002i−2i2i−2ii2i2−i2−i20000i2i2−i2−i222−2−222−2−2−2i2i0000-2200000000−i2i200−220000
χ392-2-22-222-2020-20-202002i−2i2i−2i−i2−i2i2i20000−i2−i2i2i2−2−222−2−2222i−2i00002-200000000−i2i200−220000
χ402-2-22-222-2020-20-202002i−2i2i−2i−i2−i2i2i20000−i2−i2i2i2−2−222−2−222−2i2i0000-2200000000i2−i2002−20000
χ412-2-22-222-2020-20-20200−2i2i−2i2ii2i2−i2−i20000i2i2−i2−i2−2−222−2−2222i−2i0000-2200000000−i2i2002−20000
χ422-2-22-222-2020-20-20200−2i2i−2i2ii2i2−i2−i20000i2i2−i2−i2−2−222−2−222−2i2i00002-200000000i2−i200−220000
χ432-2-22-222-2020-20-20200−2i2i−2i2i−i2−i2i2i20000−i2−i2i2i222−2−222−2−22i−2i0000-2200000000i2−i200−220000
χ442-2-22-222-2020-20-20200−2i2i−2i2i−i2−i2i2i20000−i2−i2i2i222−2−222−2−2−2i2i00002-200000000−i2i2002−20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-440-40-4040000000000000004-44-40000000000000000000000000000000000
χ474444-4-4-4-440-40-404000000000000000-44-440000000000000000000000000000000000
χ484444-4-4-4-4-404040-4000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ494444-4-4-4-4-404040-40000000000000000000−2222−2222−2222−222200000000000000000000000000
χ5044-4-44-44-404040-40-4004-4-440000000000000000000000000000000000000000000000
χ5144-4-44-44-404040-40-400-444-40000000000000000000000000000000000000000000000
χ5244-4-44-44-40-40-404040000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5344-4-44-44-40-40-40404000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5444-4-4-44-44000000000000002i2−2i22i2−2i222−2222−2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5544-4-4-44-44000000000000002i2−2i22i2−2i2−2222−22220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5644-4-4-44-4400000000000000−2i22i2−2i22i222−2222−220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5744-4-4-44-4400000000000000−2i22i2−2i22i2−2222−222200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ584-44-444-4-44040-40-400000004-4-44000000000000000000000000000000000000000000
χ594-44-444-4-44040-40-40000000-444-4000000000000000000000000000000000000000000
χ604-44-444-4-4-40-4040400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ614-44-444-4-4-40-404040000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ624-44-4-4-444-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ634-4-444-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i22-2-222-2-2200000000000000000000000000
χ644-4-444-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2-222-2-222-200000000000000000000000000
χ654-4-444-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2-222-2-222-200000000000000000000000000
χ664-4-444-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i22-2-222-2-2200000000000000000000000000
χ674-4-44-444-40-404040-40000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ684-4-44-444-40-404040-4000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000

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