Finite Group Databasebeta

← Group #138652

Character table — Group #138652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order1222224444448888224444488888888161616161616161624888161616161616161616161616888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111-1-111-1-111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111-1-111-1-111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-11-1111-1-1-1-1-1111-111-1-1-111-1-1-1-1iiii−i−i−i−i-1-1111ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-11-1111-1-1-1-1-1111-111-1-1-111-1-1-1-1iiii−i−i−i−i-1-1111ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-11-1111-1-1-1-1-1111-111-1-1-111-1-1-1-1−i−i−i−iiiii-1-1111−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ121111-1-11-1111-1-1-1-1-1111-111-1-1-111-1-1-1-1−i−i−i−iiiii-1-1111−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ131111-1-11-1111-1-1-1-1-1-1-11-1-1-1-1-1-1111111iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ141111-1-11-1111-1-1-1-1-1-1-11-1-1-1-1-1-1111111iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ151111-1-11-1111-1-1-1-1-1-1-11-1-1-1-1-1-1111111−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-11-1111-1-1-1-1-1-1-11-1-1-1-1-1-1111111−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222-2-2-2-22222222-2-2-2-2-2-2-2-20000000022-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2-2-222-2-22-2-2-2-2222200000000-2-2-222000000000000000000000000
χ192222222-2-2-22-2000022-22-2-2-200000000i2i2−i2−i2i2i2−i2−i22-2000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ202222222-2-2-22-2000022-22-2-2-200000000−i2−i2i2i2−i2−i2i2i22-2000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ212222222-2-2-22-20000-2-2-2222-200000000i2i2−i2−i2i2i2−i2−i2-22000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ222222222-2-2-22-20000-2-2-2222-200000000−i2−i2i2i2−i2−i2i2i2-22000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ23222222-2222-22222200-2-200-2-2-22200002222222200-200-2-2-2-200000000000000000000
χ24222222-2222-22222200-2-200-2-2-2220000-2-2-2-2-2-2-2-200-200222200000000000000000000
χ25222222-2222-22-2-2-2-200-2-200-222-2-20000000000000020000002i−2i2i−2i2i−2i2i−2i000000000000
χ26222222-2222-22-2-2-2-200-2-200-222-2-2000000000000002000000−2i2i−2i2i−2i2i−2i2i000000000000
χ27222222-2-2-2-2-2-20000002-200200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i20002i−2i−i2i2−i2i22−2−222−2−22000000000000
χ28222222-2-2-2-2-2-20000002-200200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i20002i−2ii2−i2i2−i2−222−2−222−2000000000000
χ29222222-2-2-2-2-2-20000002-20020000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2000−2i2i−i2i2−i2i2−222−2−222−2000000000000
χ30222222-2-2-2-2-2-20000002-20020000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000−2i2ii2−i2i2−i22−2−222−2−22000000000000
χ312222-2-222-2-222000022-2-2-2-220000000022−2−2−2−222-220002−2−2222−2−2−2−222000000000000
χ322222-2-222-2-222000022-2-2-2-2200000000−2−22222−2−2-22000−222−2−2−22222−2−2000000000000
χ332222-2-222-2-2220000-2-2-2-22220000000022−2−2−2−2222-20002−2−22−2−22222−2−2000000000000
χ342222-2-222-2-2220000-2-2-2-222200000000−2−22222−2−22-2000−222−222−2−2−2−222000000000000
χ352222-2-22-2222-22222222-222-222-2-2222200000000-2-2-2-2-2000000000000000000000000
χ362222-2-22-2222-22222-2-22-2-2-2-222-2-2-2-2-2-20000000022-222000000000000000000000000
χ372222-2-2-22-2-2-220000002200-200002i2i−2i−2i22−2−2−2−222000−2i2i−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ382222-2-2-22-2-2-220000002200-200002i2i−2i−2i−2−22222−2−2000−2i2i2−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ392222-2-2-22-2-2-220000002200-20000−2i−2i2i2i22−2−2−2−2220002i−2i−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ402222-2-2-22-2-2-220000002200-20000−2i−2i2i2i−2−22222−2−20002i−2i2−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ412222-2-2-2-222-2-2222200-22002-2-2-2-20000000000000020000002-22-2-22-22000000000000
χ422222-2-2-2-222-2-2222200-22002-2-2-2-2000000000000002000000-22-222-22-2000000000000
χ432222-2-2-2-222-2-2-2-2-2-200-22002222200002i2i2i2i−2i−2i−2i−2i00-200−2i−2i2i2i00000000000000000000
χ442222-2-2-2-222-2-2-2-2-2-200-2200222220000−2i−2i−2i−2i2i2i2i2i00-2002i2i−2i−2i00000000000000000000
χ452-2-222-202-220-222-2-20000000002-200002i−2i2i−2i2i−2i2i−2i000000000000000002−22−2i2−i2i2−i20000
χ462-2-222-202-220-222-2-20000000002-200002i−2i2i−2i2i−2i2i−2i00000000000000000−22−22−i2i2−i2i20000
χ472-2-222-202-220-222-2-20000000002-20000−2i2i−2i2i−2i2i−2i2i000000000000000002−22−2−i2i2−i2i20000
χ482-2-222-202-220-222-2-20000000002-20000−2i2i−2i2i−2i2i−2i2i00000000000000000−22−22i2−i2i2−i20000
χ492-2-22-220-2-2202-2-2220000000002-200002-22-2-22-22000000000000000002−2−222−2−220000
χ502-2-22-220-2-2202-2-2220000000002-200002-22-2-22-2200000000000000000−222−2−222−20000
χ512-2-22-220-2-2202-2-2220000000002-20000-22-222-22-2000000000000000002−2−22−222−20000
χ522-2-22-220-2-2202-2-2220000000002-20000-22-222-22-200000000000000000−222−22−2−220000
χ5344-4-4004000-4022−2222−224-40000022−220022−2222−220000000000000000000000000000000000000
χ5444-4-4004000-4022−2222−22-440000022−2200−2222−22220000000000000000000000000000000000000
χ5544-4-4004000-40−2222−22224-400000−222200−2222−22220000000000000000000000000000000000000
χ5644-4-4004000-40−2222−2222-4400000−22220022−2222−220000000000000000000000000000000000000
χ5744-4-400-40004022−2222−2200004i−4i0−2222002i2−2i2−2i22i20000000000000000000000000000000000000
χ5844-4-400-40004022−2222−220000−4i4i0−222200−2i22i22i2−2i20000000000000000000000000000000000000
χ5944-4-400-400040−2222−222200004i−4i022−2200−2i22i22i2−2i20000000000000000000000000000000000000
χ6044-4-400-400040−2222−22220000−4i4i022−22002i2−2i2−2i22i20000000000000000000000000000000000000
χ614-4-444-404-440-4-4-444000000000-4400000000000000000000000000000000000000000
χ624-4-444-40-44-404000000000000000000022−22−222222−22−222200000000000000000000000000000
χ634-4-444-40-44-4040000000000000000000−222222−22−222222−2200000000000000000000000000000
χ644-4-44-44044-40-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000
χ654-4-44-44044-40-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000
χ664-4-44-440-4-440444-4-4000000000-4400000000000000000000000000000000000000000
χ678-88-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-88-800000000−424242−420000000000000000000000000000000000000000000000000000

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