Finite Group Databasebeta

← Group #72322280

Character table — Group #72322280

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222222222222244444444444444448888888888888888888816161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222244444444444422444444888888888888888888888888888822224444888888881616161616161616161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1
χ10111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−iii-1-111
χ11111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111
χ12111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1
χ13111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111
χ14111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1
χ15111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1
χ16111111111-1-111-1-1-1-11-1-11-1-1-11111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−iii−i−i-1-111
χ171111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−ii−ii−i1-11-1
χ181111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i-1-111-1-111−i−iii−i−iii−ii−ii-11-11
χ191111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111i−ii−i−ii−ii11-1-111-1-1ii−i−iii−i−i−ii−ii-11-11
χ201111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111i−ii−i−ii−ii-1-111-1-111−i−iii−i−iiii−ii−i1-11-1
χ211111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−ii−iii−ii−i11-1-111-1-1−i−iii−i−iiii−ii−i-11-11
χ221111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−ii−iii−ii−i-1-111-1-111ii−i−iii−i−i−ii−ii1-11-1
χ231111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii−ii−ii1-11-1
χ241111-1-11-1-11111-1-1-1-111-1-111-11-1-1-1-1-111-1-11-111−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii-1-111-1-111ii−i−iii−i−ii−ii−i-11-11
χ251111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1111-1-1-1-11111-1-1-1-1111-1-111-1-11
χ261111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-11-1-11111-1-1-1-11111-1-1-111-1-111-1
χ271111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-11-1-11-111-111-1-1-1-11111-1-1-1-111-111-1-111-1
χ281111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-11-1-11-111-1-1-11111-1-1-1-11111-1-11-1-111-1-11
χ291111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-111-11-1-1111-1-1-1-111-1-11111-1-11-1-11-111-1
χ301111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-111-11-1-11-1-11111-1-111-1-1-1-111-111-11-1-11
χ311111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-111-1-111-111-1-1-1-111-1-11111-1-1-111-11-1-11
χ321111-1-11-1-1-1-11111111-11-1-1-111-1-1-11111111-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-111-1-111-1-1-11111-1-111-1-1-1-1111-1-11-111-1
χ3322222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-20000000000000000000000000000
χ3422222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000000000000000
χ35222222222-2-222-2-2-2-22-2-22-2-2-222-2-222-2-222-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i0000000000000000000000000000
χ36222222222-2-222-2-2-2-22-2-22-2-2-222-2-222-2-222-2-222−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i0000000000000000000000000000
χ37222222-2-2-222222222-2-2-222-2-2-2-222-2-2-2-2222-22-200000000000000002-22-22-22-200000000000000000000000000000000
χ38222222-2-2-222222222-2-2-222-2-2-2-222-2-2-2-2222-22-20000000000000000-22-22-22-2200000000000000000000000000000000
χ39222222-2-2-222222222-2-2-222-2-2-2-2-2-22222-2-2-22-220000000022222222000000000000-2-2-2-2000000000000000000000000
χ40222222-2-2-222222222-2-2-222-2-2-2-2-2-22222-2-2-22-2200000000-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ41222222-2-2-222-2-2-2-222-222-2-2-2-2220000000000002-22-22-22-2000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ42222222-2-2-222-2-2-2-222-222-2-2-2-2220000000000002-22-22-22-2000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ43222222-2-2-222-2-2-2-222-222-2-2-2-222000000000000-22-22-22-22000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ44222222-2-2-222-2-2-2-222-222-2-2-2-222000000000000-22-22-22-22000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ45222222-2-2-2-2-222-2-2-2-2-2222-222-2-22222-2-2-2-22-2-2200000000000000002-22-2-22-2200000000000000000000000000000000
χ46222222-2-2-2-2-222-2-2-2-2-2222-222-2-22222-2-2-2-22-2-220000000000000000-22-222-22-200000000000000000000000000000000
χ47222222-2-2-2-2-222-2-2-2-2-2222-222-2-2-2-2-2-22222-222-2000000002i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i000000000000000000000000
χ48222222-2-2-2-2-222-2-2-2-2-2222-222-2-2-2-2-2-22222-222-200000000−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i000000000000000000000000
χ49222222-2-2-2-2-2-2-222-2-2-2-2-2-2222220000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ50222222-2-2-2-2-2-2-222-2-2-2-2-2-2222220000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ51222222-2-2-2-2-2-2-222-2-2-2-2-2-222222000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ52222222-2-2-2-2-2-2-222-2-2-2-2-2-222222000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ532222-2-22-2-22222-2-2-2-222-2-222-22-22222-2-222-22-2-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i0000000000000000000000000000
χ542222-2-22-2-22222-2-2-2-222-2-222-22-22222-2-222-22-2-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i0000000000000000000000000000
χ552222-2-22-2-2-2-22222222-22-2-2-222-222-2-2-2-2-2-2-222222-2-2-2-2220000000000000000-222-20000000000000000000000000000
χ562222-2-22-2-2-2-22222222-22-2-2-222-222-2-2-2-2-2-2-2222-2-22222-2-200000000000000002-2-220000000000000000000000000000
χ572222-2-2-2222222-2-2-2-2-2-22-22-22-2222-2-22222-2-2-22000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i000000000000000000000000
χ582222-2-2-2222222-2-2-2-2-2-22-22-22-2222-2-22222-2-2-2200000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i000000000000000000000000
χ592222-2-2-2222222-2-2-2-2-2-22-22-22-22-2-222-2-2-2-2222-200000000000000002-2-222-2-2200000000000000000000000000000000
χ602222-2-2-2222222-2-2-2-2-2-22-22-22-22-2-222-2-2-2-2222-20000000000000000-222-2-222-200000000000000000000000000000000
χ612222-2-2-22222-2-222-2-2-22-22-2-222-20000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000i2−i2−i2i2i2−i2−i2i2−222−2−222−200000000
χ622222-2-2-22222-2-222-2-2-22-22-2-222-20000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000−i2i2i2−i2−i2i2i2−i22−2−222−2−2200000000
χ632222-2-2-22222-2-222-2-2-22-22-2-222-2000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000i2−i2−i2i2i2−i2−i2i22−2−222−2−2200000000
χ642222-2-2-22222-2-222-2-2-22-22-2-222-2000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−2−222−200000000
χ652222-2-2-222-2-2222222-22-2-2-22-2-22222222-2-2-2-22-20000000022-2-2-2-222000000000000-222-2000000000000000000000000
χ662222-2-2-222-2-2222222-22-2-2-22-2-22222222-2-2-2-22-200000000-2-22222-2-20000000000002-2-22000000000000000000000000
χ672222-2-2-222-2-2222222-22-2-2-22-2-22-2-2-2-2-2-22222-2200000000000000002-2-22-222-200000000000000000000000000000000
χ682222-2-2-222-2-2222222-22-2-2-22-2-22-2-2-2-2-2-22222-220000000000000000-222-22-2-2200000000000000000000000000000000
χ692222-2-2-222-2-2-2-2-2-222-2-22222-22-20000000000002-2-22-222-2000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ702222-2-2-222-2-2-2-2-2-222-2-22222-22-20000000000002-2-22-222-2000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ712222-2-2-222-2-2-2-2-2-222-2-22222-22-2000000000000-222-22-2-22000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ722222-2-2-222-2-2-2-2-2-222-2-22222-22-2000000000000-222-22-2-22000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ7344444444444-4-4-4-4444-4-4-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ74444444444-4-4-4-444-4-4444-44-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ754444-4-44-4-444-4-444-4-44-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ764444-4-44-4-4-4-4-4-4-4-44444-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ7744-4-400000004-44i−4i4i−4i000000000004i−4i4-400000000000000004ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000
χ7844-4-400000004-44i−4i4i−4i000000000004i−4i4-40000000000000000−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000
χ7944-4-400000004-44i−4i4i−4i00000000000−4i4i-44000000000000004ζ−4ζ00004ζ3−4ζ30000000000000000000000000000000000000000
χ8044-4-400000004-44i−4i4i−4i00000000000−4i4i-4400000000000000−4ζ4ζ0000−4ζ34ζ30000000000000000000000000000000000000000
χ8144-4-400000004-4−4i4i−4i4i000000000004i−4i-44000000000000004ζ3−4ζ300004ζ−4ζ0000000000000000000000000000000000000000
χ8244-4-400000004-4−4i4i−4i4i000000000004i−4i-4400000000000000−4ζ34ζ30000−4ζ4ζ0000000000000000000000000000000000000000
χ8344-4-400000004-4−4i4i−4i4i00000000000−4i4i4-400000000000000004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000
χ8444-4-400000004-4−4i4i−4i4i00000000000−4i4i4-40000000000000000−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000
χ8588-8-80000000-888i−8i−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-80000000-88−8i8i8i−8i00000000000000000000000000000000000000000000000000000000000000000000000000000
χ878-88-88-888-800000000-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-88-8-8-880000000080000000000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-888-8800000000-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-80000000080000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88000008-800000000000000042−42000042−42000000000000000000000000000000000000000000000000000000000000
χ928-8-88000008-8000000000000000−42420000−4242000000000000000000000000000000000000000000000000000000000000
χ938-8-8800000-8800000000000000042−420000−4242000000000000000000000000000000000000000000000000000000000000
χ948-8-8800000-88000000000000000−4242000042−42000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.