Finite Group Databasebeta

← Group #314312

Character table — Group #314312

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-11-1-1111-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11111-1-11-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1-1-1-111-111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-11-111-1-1-11111-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1111-1-11-1-1-1-111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1111-1-11111-1-1-11
χ17222222222-22-22-22-2-2-222220000-2-2-2-2000000000000000022-2-2-220000000000000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-20000000000000000-2-2222-20000000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000222200000000000000002222-2-20000000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000022220000000000000000-2-2-2-2220000000000000000
χ2122222222-22-22-22-22-2-2000022220000-2-2-2-20000000022-2-2000000-2000020000000000
χ2222222222-22-22-22-22-2-2000022220000-2-2-2-200000000-2-22200000020000-20000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-2000022220000000022-2-200000020000-20000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-20000222200000000-2-222000000-2000020000000000
χ252-2-222-22-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i0000000000002-22-200000000000000002i−2i0000
χ262-2-222-22-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i000000000000-22-220000000000000000−2i2i0000
χ272-2-222-22-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i0000000000002-22-20000000000000000−2i2i0000
χ282-2-222-22-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i000000000000-22-2200000000000000002i−2i0000
χ292-2-222-22-22-2-222-2-222-22i2i−2i−2i0000−2i−2i2i2i000000000000000000000002i−2i2-200000000000
χ302-2-222-22-22-2-222-2-222-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000000−2i2i-2200000000000
χ312-2-222-22-22-2-222-2-222-2−2i−2i2i2i00002i2i−2i−2i000000000000000000000002i−2i-2200000000000
χ322-2-222-22-22-2-222-2-222-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000000−2i2i2-200000000000
χ332-2-222-22-2-222-2-222-22-200000000000000002i2i2i2i−2i−2i−2i−2i2-2-220000000000002i−2i00000000
χ342-2-222-22-2-222-2-222-22-200000000000000002i2i2i2i−2i−2i−2i−2i-222-2000000000000−2i2i00000000
χ352-2-222-22-2-222-2-222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i2-2-22000000000000−2i2i00000000
χ362-2-222-22-2-222-2-222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i-222-20000000000002i−2i00000000
χ372-2-22-22-222020-20-2000000022−2−22i−2i2i−2i22−2−2i2i2−i2−i2i2i2−i2−i200002i−2i2-20000000000i2−i2002−200
χ382-2-22-22-222020-20-2000000022−2−22i−2i2i−2i22−2−2i2i2−i2−i2i2i2−i2−i20000−2i2i-220000000000−i2i200−2200
χ392-2-22-22-222020-20-2000000022−2−2−2i2i−2i2i22−2−2−i2−i2i2i2−i2−i2i2i200002i−2i-220000000000i2−i200−2200
χ402-2-22-22-222020-20-2000000022−2−2−2i2i−2i2i22−2−2−i2−i2i2i2−i2−i2i2i20000−2i2i2-20000000000−i2i2002−200
χ412-2-22-22-222020-20-20000000−2−2222i−2i2i−2i−2−222−i2−i2i2i2−i2−i2i2i200002i−2i2-20000000000−i2i200−2200
χ422-2-22-22-222020-20-20000000−2−2222i−2i2i−2i−2−222−i2−i2i2i2−i2−i2i2i20000−2i2i-220000000000i2−i2002−200
χ432-2-22-22-222020-20-20000000−2−222−2i2i−2i2i−2−222i2i2−i2−i2i2i2−i2−i200002i−2i-220000000000−i2i2002−200
χ442-2-22-22-222020-20-20000000−2−222−2i2i−2i2i−2−222i2i2−i2−i2i2i2−i2−i20000−2i2i2-20000000000i2−i200−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-440-40-404000000000004-4-4400000000000000000000000000000000000000
χ474444-4-4-4-440-40-40400000000000-444-400000000000000000000000000000000000000
χ484444-4-4-4-4-404040-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ494444-4-4-4-4-404040-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5044-4-44-4-44000000000022−2222−22000000002i2−2i22i2−2i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ5144-4-44-4-44000000000022−2222−2200000000−2i22i2−2i22i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ5244-4-44-4-440000000000−2222−2222000000002i2−2i22i2−2i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ5344-4-44-4-440000000000−2222−222200000000−2i22i2−2i22i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ5444-4-4-444-4040-40-4040000004i−4i4i−4i000000000000000000000000000000000000000000
χ5544-4-4-444-4040-40-404000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5644-4-4-444-40-404040-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ5744-4-4-444-40-404040-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ584-44-444-4-400000000002i2−2i2−2i22i22i2−2i2−2i22i2000000002-22-2-22-2200000000000000000000000000
χ594-44-444-4-400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000-22-222-22-200000000000000000000000000
χ604-44-444-4-40000000000−2i22i22i2−2i22i2−2i2−2i22i200000000-22-222-22-200000000000000000000000000
χ614-44-444-4-40000000000−2i22i22i2−2i2−2i22i22i2−2i2000000002-22-2-22-2200000000000000000000000000
χ624-44-4-4-44404040-40-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ634-44-4-4-44404040-40-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ644-44-4-4-4440-40-4040400000000000000000022−22−222222−22−222200000000000000000000000000
χ654-44-4-4-4440-40-40404000000000000000000−222222−22−222222−2200000000000000000000000000
χ664-4-444-44-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ674-4-44-44-44-40-4040400000002222−22−220000−22−2222220000000000000000000000000000000000
χ684-4-44-44-44-40-404040000000−22−22222200002222−22−220000000000000000000000000000000000

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