Finite Group Databasebeta

← Group #313243

Character table — Group #313243

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-11-1-1-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11-11111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-111-11-1-111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-11111111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11-111-1-1-1-11111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111-1-1-1-1-11111-1-11-1
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-200000000000022-2-2-220000000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-2000000000000-2-2222-20000000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-20000222200000000000022-2-22-20000000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-200002222000000000000-2-222-220000000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-200000000000022-2-2000000002-2000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-22200000000-22000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002222000000000000222200000000-2-2000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-2-2-20000000022000000000000
χ252-2-222-22-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i00000000000000002i−2i2i−2i00000000002-2000000
χ262-2-222-22-222-2-222-2-2-222i2i−2i−2i00002i2i−2i−2i0000000000000000−2i2i−2i2i0000000000-22000000
χ272-2-222-22-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i00000000000000002i−2i2i−2i0000000000-22000000
χ282-2-222-22-222-2-222-2-2-22−2i−2i2i2i0000−2i−2i2i2i0000000000000000−2i2i−2i2i00000000002-2000000
χ292-2-222-22-22-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i00002i−2i−2i2i000000000000002-200
χ302-2-222-22-22-2-222-2-222-200000000000000002i2i2i2i−2i−2i−2i−2i0000−2i2i2i−2i00000000000000-2200
χ312-2-222-22-22-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i00002i−2i−2i2i00000000000000-2200
χ322-2-222-22-22-2-222-2-222-20000000000000000−2i−2i−2i−2i2i2i2i2i0000−2i2i2i−2i000000000000002-200
χ332-2-222-22-2-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000002-2002i−2i0000000000
χ342-2-222-22-2-222-2-222-22-22i2i−2i−2i0000−2i−2i2i2i0000000000000000000000-2200−2i2i0000000000
χ352-2-222-22-2-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000002-200−2i2i0000000000
χ362-2-222-22-2-222-2-222-22-2−2i−2i2i2i00002i2i−2i−2i0000000000000000000000-22002i−2i0000000000
χ372-2-22-22-2202020-20-200000022−2−22i−2i2i−2i22−2−2i2i2−i2−i2i2i2−i2−i22i−2i2-20000000000002−200i2−i20000
χ382-2-22-22-2202020-20-200000022−2−22i−2i2i−2i22−2−2i2i2−i2−i2i2i2−i2−i2−2i2i-22000000000000−2200−i2i20000
χ392-2-22-22-2202020-20-200000022−2−2−2i2i−2i2i22−2−2−i2−i2i2i2−i2−i2i2i22i−2i-22000000000000−2200i2−i20000
χ402-2-22-22-2202020-20-200000022−2−2−2i2i−2i2i22−2−2−i2−i2i2i2−i2−i2i2i2−2i2i2-20000000000002−200−i2i20000
χ412-2-22-22-2202020-20-2000000−2−2222i−2i2i−2i−2−222−i2−i2i2i2−i2−i2i2i22i−2i2-2000000000000−2200−i2i20000
χ422-2-22-22-2202020-20-2000000−2−2222i−2i2i−2i−2−222−i2−i2i2i2−i2−i2i2i2−2i2i-220000000000002−200i2−i20000
χ432-2-22-22-2202020-20-2000000−2−222−2i2i−2i2i−2−222i2i2−i2−i2i2i2−i2−i22i−2i-220000000000002−200−i2i20000
χ442-2-22-22-2202020-20-2000000−2−222−2i2i−2i2i−2−222i2i2−i2−i2i2i2−i2−i2−2i2i2-2000000000000−2200i2−i20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-4040-40-40400000000004-4-4400000000000000000000000000000000000000
χ474444-4-4-4-4040-40-4040000000000-444-400000000000000000000000000000000000000
χ484444-4-4-4-40-404040-40000000000000000002222−22−22−22−22222200000000000000000000000000
χ494444-4-4-4-40-404040-4000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5044-4-444-4-44040-40-4000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ5144-4-444-4-44040-40-40000000000000000000−2222−2222−2222−222200000000000000000000000000
χ5244-4-444-4-4-40-4040400000004i−4i4i−4i000000000000000000000000000000000000000000
χ5344-4-444-4-4-40-404040000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5444-4-4-4-44400000000002i2−2i22i2−2i2000000002i2−2i22i2−2i22-2-22-222-200000000000000000000000000
χ5544-4-4-4-44400000000002i2−2i22i2−2i200000000−2i22i2−2i22i2-222-22-2-2200000000000000000000000000
χ5644-4-4-4-4440000000000−2i22i2−2i22i2000000002i2−2i22i2−2i2-222-22-2-2200000000000000000000000000
χ5744-4-4-4-4440000000000−2i22i2−2i22i200000000−2i22i2−2i22i22-2-22-222-200000000000000000000000000
χ584-44-44-4-4440-40-40400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ594-44-44-4-4440-40-4040000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ604-44-44-4-44-404040-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ614-44-44-4-44-404040-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ624-44-4-444-4000000000022−22−22222i2−2i2−2i22i2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ634-44-4-444-4000000000022−22−2222−2i22i22i2−2i200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ644-44-4-444-40000000000−222222−222i2−2i2−2i22i200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ654-44-4-444-40000000000−222222−22−2i22i22i2−2i2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ664-4-444-44-4-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ674-4-44-44-440-40-404040000002222−22−220000−22−2222220000000000000000000000000000000000
χ684-4-44-44-440-40-40404000000−22−22222200002222−22−220000000000000000000000000000000000

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