Finite Group Databasebeta

← Group #313233

Character table — Group #313233

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-111-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-11-1-1-1-1-1-111-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1111111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1111-1-1-1-1-1-111-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111-11111-1-1-1-111-1-1-1-11-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-111-1-1-111-1-111111-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-111111111-1-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-1-1-111-1-11111-1-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1111-1-1-1-1-1-1-11111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1111-1-11111-1-1-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-111111-1-1-1-1111-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-2000000002200-2-200-200002000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-200000000-2-200220020000-2000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-200002222000000002200-2-20020000-2000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-20000222200000000-2-2002200-200002000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-2000000000000002200-2-20-22000000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-200000000000000-2-2002202-2000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002222000000000000002200220-2-2000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000222200000000000000-2-200-2-2022000000000000000
χ252-22-22-2-2222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i0000000000002i−2i002i−2i00000000002-200000000
χ262-22-22-2-2222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i000000000000−2i2i00−2i2i0000000000-2200000000
χ272-22-22-2-2222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i0000000000002i−2i002i−2i0000000000-2200000000
χ282-22-22-2-2222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i000000000000−2i2i00−2i2i00000000002-200000000
χ292-22-22-2-222-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i2i−2i00−2i2i000000000000002-20000
χ302-22-22-2-222-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i−2i2i002i−2i00000000000000-220000
χ312-22-22-2-222-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i2i−2i00−2i2i00000000000000-220000
χ322-22-22-2-222-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i−2i2i002i−2i000000000000002-20000
χ332-22-22-2-22-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i000000000000000000000002i−2i02-20000000000
χ342-22-22-2-22-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000000−2i2i0-220000000000
χ352-22-22-2-22-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i000000000000000000000002i−2i0-220000000000
χ362-22-22-2-22-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000000−2i2i02-20000000000
χ372-2-2-2-22220-20-2020200000022−2−22-22-222−2−222−2−222−2−2002-2002-200000000002−2002−200
χ382-2-2-2-22220-20-2020200000022−2−22-22-222−2−222−2−222−2−200-2200-220000000000−2200−2200
χ392-2-2-2-22220-20-2020200000022−2−2-22-2222−2−2−2−222−2−222002-200-220000000000−22002−200
χ402-2-2-2-22220-20-2020200000022−2−2-22-2222−2−2−2−222−2−22200-22002-200000000002−200−2200
χ412-2-2-2-22220-20-20202000000−2−2222-22-2−2−222−2−222−2−222002-2002-20000000000−2200−2200
χ422-2-2-2-22220-20-20202000000−2−2222-22-2−2−222−2−222−2−22200-2200-2200000000002−2002−200
χ432-2-2-2-22220-20-20202000000−2−222-22-22−2−22222−2−222−2−2002-200-2200000000002−200−2200
χ442-2-2-2-22220-20-20202000000−2−222-22-22−2−22222−2−222−2−200-22002-20000000000−22002−200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-400000004-44-4000000000000000000000000000000000000000000
χ47444-4-4-44-44040-40-40000000-44-44000000000000000000000000000000000000000000
χ48444-4-4-44-4-40-4040400000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ49444-4-4-44-4-40-404040000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ5044-44-4-4-44040-40-4040000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5144-44-4-4-44040-40-404000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5244-44-4-4-440-404040-400000000004i−4i−4i4i00000000000000000000000000000000000000
χ5344-44-4-4-440-404040-40000000000−4i4i4i−4i00000000000000000000000000000000000000
χ5444-4-444-4-4000000000022−2222−220000000022−2222−222-2-22-222-200000000000000000000000000
χ5544-4-444-4-4000000000022−2222−2200000000−2222−2222-222-22-2-2200000000000000000000000000
χ5644-4-444-4-40000000000−2222−22220000000022−2222−22-222-22-2-2200000000000000000000000000
χ5744-4-444-4-40000000000−2222−222200000000−2222−22222-2-22-222-200000000000000000000000000
χ584-444-44-4-440-40-4040000000000000004-4-440000000000000000000000000000000000
χ594-444-44-4-440-40-404000000000000000-444-40000000000000000000000000000000000
χ604-444-44-4-4-404040-4000000000000000000022−2222−22−2222−222200000000000000000000000000
χ614-444-44-4-4-404040-40000000000000000000−2222−222222−2222−2200000000000000000000000000
χ624-44-44-4-44-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ634-4-444-44-400000000002i2−2i2−2i22i222−22−2222000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ644-4-444-44-400000000002i2−2i2−2i22i2−222222−2200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ654-4-444-44-40000000000−2i22i22i2−2i222−22−222200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ664-4-444-44-40000000000−2i22i22i2−2i2−222222−22000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ674-4-4-4-444404040-40-40000002222−22−220000−22−2222220000000000000000000000000000000000
χ684-4-4-4-444404040-40-4000000−22−22222200002222−22−220000000000000000000000000000000000

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