Finite Group Databasebeta

← Group #134549

Character table — Group #134549

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1222224444444488888888224444444488888888888824448888888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11-1-11-1-111ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11-1-11-1-111−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-111-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-111-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ192222222-2-2222-2-222222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ202222222-2-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222-2-22222000000000000000000000000
χ212222-2-22222-2-2-2-2000022222-20000000022-2-2-2-200000000002i−2i2i−2i0000000000000000
χ222222-2-22222-2-2-2-2000022222-20000000022-2-2-2-20000000000−2i2i−2i2i0000000000000000
χ232222-2-22222-2-2-2-20000-2-2-2-22-200000000-2-2222200000022-2-200000000000000000000
χ242222-2-22222-2-2-2-20000-2-2-2-22-200000000-2-22222000000-2-22200000000000000000000
χ252222-2-22-2-22-2-22200002222-2200000000-2-222-2-20000002-22-200000000000000000000
χ262222-2-22-2-22-2-22200002222-2200000000-2-222-2-2000000-22-2200000000000000000000
χ272222-2-22-2-22-2-2220000-2-2-2-2-220000000022-2-22200000000002i−2i−2i2i0000000000000000
χ282222-2-22-2-22-2-2220000-2-2-2-2-220000000022-2-2220000000000−2i2i2i−2i0000000000000000
χ292222-2-2-222-222-2-222220000-2200000000000000-2-222-2-20000000000000000i2−i2i2−i2i2−i2i2−i2
χ302222-2-2-222-222-2-222220000-2200000000000000-2-222-2-20000000000000000−i2i2−i2i2−i2i2−i2i2
χ312222-2-2-222-222-2-2-2-2-2-20000-220000000000000022-2-2220000000000000000i2−i2i2−i2−i2i2−i2i2
χ322222-2-2-222-222-2-2-2-2-2-20000-220000000000000022-2-2220000000000000000−i2i2−i2i2i2−i2i2−i2
χ332222-2-2-2-2-2-22222222200002-200000000000000-2-2-2-22200000000000000002−2−222−2−22
χ342222-2-2-2-2-2-22222222200002-200000000000000-2-2-2-2220000000000000000−222−2−222−2
χ352222-2-2-2-2-2-22222-2-2-2-200002-2000000000000002222-2-200000000000000002−2−22−222−2
χ362222-2-2-2-2-2-22222-2-2-2-200002-2000000000000002222-2-20000000000000000−222−22−2−22
χ372-2-22-22200-22-2002i2i−2i−2i2i2i−2i−2i00000022-2-200002i−2i2i−2i0000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ382-2-22-22200-22-2002i2i−2i−2i2i2i−2i−2i00000022-2-200002i−2i2i−2i000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ392-2-22-22200-22-2002i2i−2i−2i−2i−2i2i2i000000-2-2220000−2i2i2i−2i0000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ402-2-22-22200-22-2002i2i−2i−2i−2i−2i2i2i000000-2-2220000−2i2i2i−2i000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ412-2-22-22200-22-200−2i−2i2i2i2i2i−2i−2i000000-2-22200002i−2i−2i2i0000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ422-2-22-22200-22-200−2i−2i2i2i2i2i−2i−2i000000-2-22200002i−2i−2i2i000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ432-2-22-22200-22-200−2i−2i2i2i−2i−2i2i2i00000022-2-20000−2i2i−2i2i0000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ442-2-22-22200-22-200−2i−2i2i2i−2i−2i2i2i00000022-2-20000−2i2i−2i2i000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ45444444-444-4-4-44400000000-4-400000000000000000000000000000000000000000000
χ46444444-4-4-4-4-4-4-4-4000000004400000000000000000000000000000000000000000000
χ4744-4-4000000004i−4i2i2−2i22i2−2i22i2−2i22i2−2i2002i2i−2i−2i2-22-20022−2200000022−22000000000000000000000000
χ4844-4-4000000004i−4i2i2−2i22i2−2i2−2i22i2−2i22i200−2i−2i2i2i-22-2200−222200000022−22000000000000000000000000
χ4944-4-4000000004i−4i−2i22i2−2i22i22i2−2i22i2−2i200−2i−2i2i2i-22-220022−22000000−2222000000000000000000000000
χ5044-4-4000000004i−4i−2i22i2−2i22i2−2i22i2−2i22i2002i2i−2i−2i2-22-200−2222000000−2222000000000000000000000000
χ5144-4-400000000−4i4i2i2−2i22i2−2i22i2−2i22i2−2i200−2i−2i2i2i2-22-200−2222000000−2222000000000000000000000000
χ5244-4-400000000−4i4i2i2−2i22i2−2i2−2i22i2−2i22i2002i2i−2i−2i-22-220022−22000000−2222000000000000000000000000
χ5344-4-400000000−4i4i−2i22i2−2i22i22i2−2i22i2−2i2002i2i−2i−2i-22-2200−222200000022−22000000000000000000000000
χ5444-4-400000000−4i4i−2i22i2−2i22i2−2i22i2−2i22i200−2i−2i2i2i2-22-20022−2200000022−22000000000000000000000000
χ554-44-40004i−4i0000022−22−222222−22−2222002i−2i2i−2i2-2-222i2−2i20000002i2−2i200000000000000000000000000
χ564-44-40004i−4i0000022−22−2222−222222−2200−2i2i−2i2i-222-2−2i22i20000002i2−2i200000000000000000000000000
χ574-44-40004i−4i00000−222222−2222−22−222200−2i2i−2i2i-222-22i2−2i2000000−2i22i200000000000000000000000000
χ584-44-40004i−4i00000−222222−22−222222−22002i−2i2i−2i2-2-22−2i22i2000000−2i22i200000000000000000000000000
χ594-44-4000−4i4i0000022−22−222222−22−222200−2i2i−2i2i2-2-22−2i22i2000000−2i22i200000000000000000000000000
χ604-44-4000−4i4i0000022−22−2222−222222−22002i−2i2i−2i-222-22i2−2i2000000−2i22i200000000000000000000000000
χ614-44-4000−4i4i00000−222222−2222−22−2222002i−2i2i−2i-222-2−2i22i20000002i2−2i200000000000000000000000000
χ624-44-4000−4i4i00000−222222−22−222222−2200−2i2i−2i2i2-2-222i2−2i20000002i2−2i200000000000000000000000000
χ634-4-444-4400-4-440000004i4i−4i−4i00000000000000−4i4i000000000000000000000000000000
χ644-4-444-4400-4-44000000−4i−4i4i4i000000000000004i−4i000000000000000000000000000000
χ654-4-444-4-40044-4004i4i−4i−4i00000000000000000000−4i4i0000000000000000000000000000
χ664-4-444-4-40044-400−4i−4i4i4i000000000000000000004i−4i0000000000000000000000000000
χ674-4-44-44-4004-440000000000004-4-440000000000000000000000000000000000000000
χ684-4-44-44-4004-44000000000000-444-40000000000000000000000000000000000000000

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