Finite Group Databasebeta

← Group #344049

Character table — Group #344049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-11-1-11-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-11-1-1-1-11-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1111111-1-1-1-1-1-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-111111-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-1-111-1-1-1-11-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1111111-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-11-1-11111-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-111111111-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-11-1-1-1-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-11111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-11-1-111-1-111-1-111
χ172222222222-2-2-222-2-2-2000000002222-2-2-2-200000000220000220-200-20000000000000
χ182222222222-2-2-222-2-2-2000000002222-2-2-2-200000000-2-20000-2-2020020000000000000
χ192222222222-2-2-222-2-2-200000000-2-2-2-2222200000000220000-2-20200-20000000000000
χ202222222222-2-2-222-2-2-200000000-2-2-2-2222200000000-2-20000220-20020000000000000
χ2122222222-2-2222-2-22-2-22222-2-2-2-200000000000000000022-2-200-200002000000000000
χ2222222222-2-2222-2-22-2-22222-2-2-2-2000000000000000000-2-2220020000-2000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-22222000000000000000000222200-20000-2000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-22222000000000000000000-2-2-2-200200002000000000000
χ252-22-22-22-2-2-22-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i00000000002-2002i−2i0000000000
χ262-22-22-22-2-2-22-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000-2200−2i2i0000000000
χ272-22-22-22-2-2-22-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i00000000002-200−2i2i0000000000
χ282-22-22-22-2-2-22-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000-22002i−2i0000000000
χ292-22-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i22-200002-200000000i2−i2i2−i2000000
χ302-22-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2-220000-2200000000−i2i2−i2i2000000
χ312-22-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i22-20000-2200000000i2−i2−i2i2000000
χ322-22-2-22-222-20002-2000i2i2−i2−i2i2i2−i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i2-2200002-200000000−i2i2i2−i2000000
χ332-22-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i22-200002-200000000−i2i2−i2i2000000
χ342-22-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2-220000-2200000000i2−i2i2−i2000000
χ352-22-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i2-2-2220000i2i2−i2−i2i2i2−i2−i22-20000-2200000000−i2i2i2−i2000000
χ362-22-2-22-222-20002-2000−i2−i2i2i2−i2−i2i2i2-2-2220000i2i2−i2−i2i2i2−i2−i2-2200002-200000000i2−i2−i2i2000000
χ372-2-222-2-2200-22200-20000002i−2i2i−2ii2−i2i2−i2i2i2−i2−i22−22−22−22−2002-22i−2i00000000000000i2−i22−200
χ382-2-222-2-2200-22200-20000002i−2i2i−2ii2−i2i2−i2i2i2−i2−i22−22−22−22−200-22−2i2i00000000000000−i2i2−2200
χ392-2-222-2-2200-22200-20000002i−2i2i−2i−i2i2−i2i2−i2−i2i2i2−22−22−22−22002-22i−2i00000000000000−i2i2−2200
χ402-2-222-2-2200-22200-20000002i−2i2i−2i−i2i2−i2i2−i2−i2i2i2−22−22−22−2200-22−2i2i00000000000000i2−i22−200
χ412-2-222-2-2200-22200-2000000−2i2i−2i2ii2−i2i2−i2i2i2−i2−i2−22−22−22−22002-2−2i2i00000000000000i2−i2−2200
χ422-2-222-2-2200-22200-2000000−2i2i−2i2ii2−i2i2−i2i2i2−i2−i2−22−22−22−2200-222i−2i00000000000000−i2i22−200
χ432-2-222-2-2200-22200-2000000−2i2i−2i2i−i2i2−i2i2−i2−i2i2i22−22−22−22−2002-2−2i2i00000000000000−i2i22−200
χ442-2-222-2-2200-22200-2000000−2i2i−2i2i−i2i2−i2i2−i2−i2i2i22−22−22−22−200-222i−2i00000000000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-44-4000-440000000000000004-44-40000000000000000000000000000000000
χ474444-4-4-4-44-4000-44000000000000000-44-440000000000000000000000000000000000
χ484444-4-4-4-4-440004-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ494444-4-4-4-4-440004-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5044-4-444-4-40044-400-4004-44-40000000000000000000000000000000000000000000000
χ5144-4-444-4-40044-400-400-44-440000000000000000000000000000000000000000000000
χ5244-4-444-4-400-4-440040000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ5344-4-444-4-400-4-44004000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ5444-4-4-4-4440000000000000022−22−22222i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ5544-4-4-4-4440000000000000022−22−2222−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5644-4-4-4-44400000000000000−222222−222i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5744-4-4-4-44400000000000000−222222−22−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ584-44-44-44-4444-44-4-4-4-4400000000000000000000000000000000000000000000000000
χ594-44-44-44-444-44-4-4-444-400000000000000000000000000000000000000000000000000
χ604-44-44-44-4-4-4-44-4444-4400000000000000000000000000000000000000000000000000
χ614-44-4-44-44-44000-440002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ624-44-4-44-44-44000-44000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ634-4-444-4-44004-4-400400000000002i2−2i22i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ644-4-444-4-44004-4-40040000000000−2i22i2−2i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ654-4-44-444-400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i22-2-22-222-200000000000000000000000000
χ664-4-44-444-400000000002i2−2i2−2i22i200000000−2i22i22i2−2i2-222-22-2-2200000000000000000000000000
χ674-4-44-444-40000000000−2i22i22i2−2i2000000002i2−2i2−2i22i2-222-22-2-2200000000000000000000000000
χ684-4-44-444-40000000000−2i22i22i2−2i200000000−2i22i22i2−2i22-2-22-222-200000000000000000000000000

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