Finite Group Databasebeta

← Group #72319633

Character table — Group #72319633

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size111122222222222244444444444444444448888888888888888888888888881616161616161616161616161616161616161616323232323232323232323232
order1222224444448888444888816161616161616161616161644448888816163232323232323232323232323232323222228888161616163232323232323232224444444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ511111111111111111111111111111111111-1-1-1-11-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ711111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ811111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111
χ9111111-1-111111111-1-1-11-1-1111-1-1-1-111111111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11-1-1-11-111-1-1-1-1
χ10111111-1-111111111-1-1-11-1-1111-1-1-1-111111111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-11-1-11111
χ11111111-1-111111111-1-1-11-1-1111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-11-1-1-1111-1-111
χ12111111-1-111111111-1-1-11-1-1111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111111-1111-1-1-111-1-1
χ13111111-1-111111111-1-1-11-1-1111-1-1-1-1111111-1-111-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-11-1-1-11-1-111-1-1
χ14111111-1-111111111-1-1-11-1-1111-1-1-1-1111111-1-111-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1111-111-1-111
χ15111111-1-111111111-1-1-11-1-1111-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-11-1-1-11111
χ16111111-1-111111111-1-1-11-1-1111-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-1-1111-1111-1-1-1-1
χ171111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111i−ii−i-1i−ii−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−ii−ii−i11-1-111-1-1111-1-1-1i−ii−ii−i
χ181111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111i−ii−i-1i−ii−i11iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iiii−ii−i11-1-111-1-1-1-1-1111−ii−ii−ii
χ191111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111i−ii−i-1i−ii−i11−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iiii−ii−i-1-111-1-111-1-11-111i−ii−i−ii
χ201111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111i−ii−i-1i−ii−i11−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−ii−ii−i-1-111-1-11111-11-1-1−ii−iii−i
χ211111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111−ii−ii-1−ii−ii11iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i−ii−ii-1-111-1-111-1-11-111−ii−iii−i
χ221111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111−ii−ii-1−ii−ii11iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii−ii−ii-1-111-1-11111-11-1-1i−ii−i−ii
χ231111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111−ii−ii-1−ii−ii11−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−ii−ii11-1-111-1-1111-1-1-1−ii−ii−ii
χ241111-1-11111-1-111111-1-1-111-111-1-1-1-1-1-1-1-111−ii−ii-1−ii−ii11−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i−ii−ii11-1-111-1-1-1-1-1111i−ii−ii−i
χ251111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111i−i−ii1i−i−ii-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−ii−i−ii11-1-1-1-1111-1-11-11i−i−ii−ii
χ261111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111i−i−ii1i−i−ii-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiii−i−ii11-1-1-1-111-111-11-1−iii−ii−i
χ271111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111i−i−ii1i−i−ii-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiii−i−ii-1-11111-1-1-11-111-1i−i−iii−i
χ281111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111i−i−ii1i−i−ii-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−ii−i−ii-1-11111-1-11-11-1-11−iii−i−ii
χ291111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111−iii−i1−iii−i-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−iii−i-1-11111-1-1-11-111-1−iii−i−ii
χ301111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111−iii−i1−iii−i-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii−iii−i-1-11111-1-11-11-1-11i−i−iii−i
χ311111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111−iii−i1−iii−i-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii−iii−i11-1-1-1-1111-1-11-11−iii−ii−i
χ321111-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-111−iii−i1−iii−i-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−iii−i11-1-1-1-111-111-11-1i−i−ii−ii
χ3322222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222-2-2000000000000000000000000-2-2-2-200000000000000000000
χ3422222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2000000000000000000000000222200000000000000000000
χ35222222222222-2-2-2-2222-2-2-2-20000000000002222-2-2-2-2-20022−2−222−2−222−2−222−2−20000000000002−22−22−22−2000000000000
χ36222222222222-2-2-2-2222-2-2-2-20000000000002222-2-2-2-2-200−2−222−2−222−2−222−2−222000000000000−22−22−22−22000000000000
χ37222222222222-2-2-2-2222-2-2-2-2000000000000-2-2-2-2-222220022−2−222−2−222−2−222−2−2000000000000−22−22−22−22000000000000
χ38222222222222-2-2-2-2222-2-2-2-2000000000000-2-2-2-2-2222200−2−222−2−222−2−222−2−2220000000000002−22−22−22−2000000000000
χ39222222-2-222222222-2-2-22-2-22-2-22222-2-2-2-2-2-222-2-2-222-2-222000000000000000000000000-2-22200000000000000000000
χ40222222-2-222222222-2-2-22-2-22-2-22222-2-2-2-2-2-2-2-222-2-2-2222200000000000000000000000022-2-200000000000000000000
χ41222222-2-22222-2-2-2-2-2-2-2-222-200000000000022-2-22-2-2220022−2−222−2−2−2−222−2−2220000000000002−22−2−22−22000000000000
χ42222222-2-22222-2-2-2-2-2-2-2-222-200000000000022-2-22-2-22200−2−222−2−22222−2−222−2−2000000000000−22−222−22−2000000000000
χ43222222-2-22222-2-2-2-2-2-2-2-222-2000000000000-2-222222-2-20022−2−222−2−2−2−222−2−222000000000000−22−222−22−2000000000000
χ44222222-2-22222-2-2-2-2-2-2-2-222-2000000000000-2-222222-2-200−2−222−2−22222−2−222−2−20000000000002−22−2−22−22000000000000
χ452222-2-22222-2-222222-2-2-222-2-2-222222222-2-22i−2i2i−2i-22i−2i2i−2i-2-2000000000000000000000000−2i2i−2i2i00000000000000000000
χ462222-2-22222-2-222222-2-2-222-2-2-222222222-2-2−2i2i−2i2i-2−2i2i−2i2i-2-20000000000000000000000002i−2i2i−2i00000000000000000000
χ472222-2-22222-2-2-2-2-2-22-2-22-2-220000000000002i−2i2i−2i2−2i2i−2i2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000002−2−222−2−22000000000000
χ482222-2-22222-2-2-2-2-2-22-2-22-2-220000000000002i−2i2i−2i2−2i2i−2i2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−222−2−222−2000000000000
χ492222-2-22222-2-2-2-2-2-22-2-22-2-22000000000000−2i2i−2i2i22i−2i2i−2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000−222−2−222−2000000000000
χ502222-2-22222-2-2-2-2-2-22-2-22-2-22000000000000−2i2i−2i2i22i−2i2i−2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000002−2−222−2−22000000000000
χ512222-2-2-2-222-2-22222-222-2-2-2-2-2-2-2-2-2-22222-2-22i−2i−2i2i22i−2i−2i2i22000000000000000000000000−2i2i2i−2i00000000000000000000
χ522222-2-2-2-222-2-22222-222-2-2-2-2-2-2-2-2-2-22222-2-2−2i2i2i−2i2−2i2i2i−2i220000000000000000000000002i−2i−2i2i00000000000000000000
χ532222-2-2-2-222-2-2-2-2-2-2-22222220000000000002i−2i−2i2i-2−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ542222-2-2-2-222-2-2-2-2-2-2-22222220000000000002i−2i−2i2i-2−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ552222-2-2-2-222-2-2-2-2-2-2-2222222000000000000−2i2i2i−2i-22i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ562222-2-2-2-222-2-2-2-2-2-2-2222222000000000000−2i2i2i−2i-22i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ572-22-22-2002-22-222-2-2000200-2-2-2000022-2-222000000000002i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i000000000000000000000000
χ582-22-22-2002-22-222-2-2000200-2-2-2000022-2-222000000000002i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i000000000000000000000000
χ592-22-22-2002-22-222-2-2000200-2-2-2000022-2-22200000000000−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000000000000000
χ602-22-22-2002-22-222-2-2000200-2-2-2000022-2-22200000000000−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i000000000000000000000000
χ612-22-2-22002-2-2222-2-2000-2002-2-20000-2-22222000000000002-22-2-22-22000000002-2-222-2-22000000000000000000000000
χ622-22-2-22002-2-2222-2-2000-2002-2-20000-2-22222000000000002-22-2-22-2200000000-222-2-222-2000000000000000000000000
χ632-22-2-22002-2-2222-2-2000-2002-2-20000-2-2222200000000000-22-222-22-2000000002-2-22-222-2000000000000000000000000
χ642-22-2-22002-2-2222-2-2000-2002-2-20000-2-2222200000000000-22-222-22-200000000-222-22-2-22000000000000000000000000
χ6544444444-4-4-4-40000-4-44000022−222222−22−2222−2222−2222−2200000000022−22000000000000000000000000000000000000000000000000
χ6644444444-4-4-4-40000-4-440000−2222−22−222222−2222−2222−2222000000000−2222000000000000000000000000000000000000000000000000
χ67444444-4-4-4-4-4-4000044-4000022−22−22−22222222−2222−2222−22000000000−2222000000000000000000000000000000000000000000000000
χ68444444-4-4-4-4-4-4000044-40000−22222222−22−22−2222−2222−222200000000022−22000000000000000000000000000000000000000000000000
χ694444-4-444-4-4440000-44-4000022−22−22−222222−2222−222222−2200000000022−22000000000000000000000000000000000000000000000000
χ704444-4-444-4-4440000-44-40000−22222222−22−2222−2222−22−2222000000000−2222000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-4-44400004-44000022−222222−22−22−2222−222222−22000000000−2222000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-4-44400004-440000−2222−22−22222222−2222−22−222200000000022−22000000000000000000000000000000000000000000000000
χ734-44-44-4004-44-444-4-4000400-4440000-4-444-4-400000000000000000000000000000000000000000000000000000000000
χ744-44-44-4004-44-4-4-444000-4004000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ754-44-44-4004-44-4-4-444000-400400000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ764-44-44-400-44-440000000000022−220000−222222−22−222200000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ774-44-44-400-44-440000000000022−220000−222222−22−22220000000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ784-44-44-400-44-4400000000000−2222000022−22−222222−2200000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ794-44-44-400-44-4400000000000−2222000022−22−222222−220000000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ804-44-4-44004-4-4444-4-4000-400444000044-4-4-4-400000000000000000000000000000000000000000000000000000000000
χ814-44-4-44004-4-44-4-444000400-40000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ824-44-4-44004-4-44-4-444000400-400000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ834-44-4-4400-444-40000000000022−22000022−22−2222−222200000000000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000
χ844-44-4-4400-444-40000000000022−22000022−22−2222−22220000000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000
χ854-44-4-4400-444-400000000000−22220000−222222−2222−2200000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000
χ864-44-4-4400-444-400000000000−22220000−222222−2222−220000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000
χ8788-8-80000000042−4242−420000000004ζ3+4ζ5−4ζ3−4ζ54ζ+4ζ7−4ζ−4ζ700000000000000000000000000000000000000000000000000000000000000000
χ8888-8-80000000042−4242−42000000000−4ζ3−4ζ54ζ3+4ζ5−4ζ−4ζ74ζ+4ζ700000000000000000000000000000000000000000000000000000000000000000
χ8988-8-800000000−4242−42420000000004ζ+4ζ7−4ζ−4ζ7−4ζ3−4ζ54ζ3+4ζ500000000000000000000000000000000000000000000000000000000000000000
χ9088-8-800000000−4242−4242000000000−4ζ−4ζ74ζ+4ζ74ζ3+4ζ5−4ζ3−4ζ500000000000000000000000000000000000000000000000000000000000000000
χ918-8-88008-8000042−42−4242000042−42000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88008-80000−424242−420000−4242000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-88000042−42−42420000−4242000000000000000000000000000000000000000000000000000000000000000000000000
χ948-8-8800-880000−424242−42000042−42000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.