Finite Group Databasebeta

← Group #72234390

Character table — Group #72234390

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size111122222222222244444444444444444448888888888888888888888888881616161616161616161616161616161616161616323232323232323232323232
order1222444444448888244888816161616161616161616161688888888816163232323232323232323232323232323222448888161616163232323232323232224444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-11111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-11-1-1-1-111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111
χ911111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−iii−i−i1111-1-1-1-1-111-11-1ii−i−ii−i
χ1011111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iiiii−i−i1111-1-1-1-11-1-11-11−i−iii−ii
χ1111111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iiiii−i−i-1-1-1-11111-1-1-1111ii−i−i−ii
χ1211111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1iiii−i−i−i−i11−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−iii−i−i-1-1-1-11111111-1-1-1−i−iiii−i
χ1311111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i−i−iii-1-1-1-11111-1-1-1111−i−iiii−i
χ1411111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii−i−iii-1-1-1-11111111-1-1-1ii−i−i−ii
χ1511111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii−i−iii1111-1-1-1-1-111-11-1−i−iii−ii
χ1611111111-1-1-1-11111-11-111-1-1-1-1-1-11111-1-1-1-1-1−i−i−i−iiiii11−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i−i−iii1111-1-1-1-11-1-11-11ii−i−ii−i
χ171111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-11-111-1-111-1-1-11-11-1-11-11-1-1-1
χ181111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11-11-111-11-1111
χ191111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-111-1-111-1-11-1-111-11-111
χ201111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-1-111-1-11111-111-1-11-11-1-1
χ211111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-11-11-1-111-1-111-1-11-1-11-11-11-1-1
χ221111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-111-11-11-111
χ231111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1-11-11-1-1-11-1111
χ241111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-11-11-1111-11-1-1-1
χ251111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11ii−i−i−i−iii-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−ii−i−ii11-1-1-1-11111-1-1-11i−i−ii−ii
χ261111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11ii−i−i−i−iii-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiii−i−ii11-1-1-1-111-1-1111-1−iii−ii−i
χ271111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11ii−i−i−i−iii-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiii−i−ii-1-11111-1-11-111-1-1i−i−iii−i
χ281111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11ii−i−i−i−iii-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−ii−i−ii-1-11111-1-1-11-1-111−iii−i−ii
χ291111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11−i−iiiii−i−i-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−iii−i-1-11111-1-11-111-1-1−iii−i−ii
χ301111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11−i−iiiii−i−i-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii−iii−i-1-11111-1-1-11-1-111i−i−iii−i
χ311111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11−i−iiiii−i−i-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii−iii−i11-1-1-1-11111-1-1-11−iii−ii−i
χ321111-1-111-1-1-1-111111-11-1-1-1-111111111-1-1-1-11−i−iiiii−i−i-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−iii−i11-1-1-1-111-1-1111-1i−i−ii−ii
χ3322222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222-2-2000000000000000000000000-2-2-2-200000000000000000000
χ3422222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000000000
χ35222222222222-2-2-2-2222-2-2-2-2000000000000-22-22-22-22-20022−2−222−2−222−2−222−2−20000000000002−22−22−22−2000000000000
χ36222222222222-2-2-2-2222-2-2-2-2000000000000-22-22-22-22-200−2−222−2−222−2−222−2−222000000000000−22−22−22−22000000000000
χ37222222222222-2-2-2-2222-2-2-2-2000000000000-2-22-22-22-220022−2−222−2−222−2−222−2−2000000000000−22−22−22−22000000000000
χ38222222222222-2-2-2-2222-2-2-2-2000000000000-2-22-22-22-2200−2−222−2−222−2−222−2−2220000000000002−22−22−22−2000000000000
χ3922222222-2-2-2-22222-22-222-2-22222-2-2-2-22222-22i2i2i2i−2i−2i−2i−2i-2-2000000000000000000000000−2i−2i2i2i00000000000000000000
χ4022222222-2-2-2-22222-22-222-2-22222-2-2-2-22222-2−2i−2i−2i−2i2i2i2i2i-2-20000000000000000000000002i2i−2i−2i00000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-22-2-2-22200000000000022i−2i2i−2i−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000002−22−2−22−22000000000000
χ4222222222-2-2-2-2-2-2-2-2-22-2-2-22200000000000022i−2i2i−2i−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000−22−222−22−2000000000000
χ4322222222-2-2-2-2-2-2-2-2-22-2-2-2220000000000002−2i2i−2i2i2i−2i2i−2i00i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000−22−222−22−2000000000000
χ4422222222-2-2-2-2-2-2-2-2-22-2-2-2220000000000002−2i2i−2i2i2i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000002−22−2−22−22000000000000
χ452222-2-22222222222-2-2-2-2-2222222-2-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000-22-2200000000000000000000
χ462222-2-22222222222-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000000000002-22-200000000000000000000
χ472222-2-2222222-2-2-2-2-2-2-222-2-200000000000022-2-222-2-220022−2−2−2−22222−2−2−2−2220000000000002−2−222−2−22000000000000
χ482222-2-2222222-2-2-2-2-2-2-222-2-200000000000022-2-222-2-2200−2−22222−2−2−2−22222−2−2000000000000−222−2−222−2000000000000
χ492222-2-2222222-2-2-2-2-2-2-222-2-20000000000002-222-2-222-20022−2−2−2−22222−2−2−2−222000000000000−222−2−222−2000000000000
χ502222-2-2222222-2-2-2-2-2-2-222-2-20000000000002-222-2-222-200−2−22222−2−2−2−22222−2−20000000000002−2−222−2−22000000000000
χ512222-2-222-2-2-2-222222-22-2-2-2-2-2-2-2-2-2-2-2-2222222i2i−2i−2i−2i−2i2i2i22000000000000000000000000−2i2i2i−2i00000000000000000000
χ522222-2-222-2-2-2-222222-22-2-2-2-2-2-2-2-2-2-2-2-222222−2i−2i2i2i2i2i−2i−2i220000000000000000000000002i−2i−2i2i00000000000000000000
χ532222-2-222-2-2-2-2-2-2-2-22-222222000000000000-22i−2i−2i2i−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000002−2−22−222−2000000000000
χ542222-2-222-2-2-2-2-2-2-2-22-222222000000000000-22i−2i−2i2i−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000−222−22−2−22000000000000
χ552222-2-222-2-2-2-2-2-2-2-22-222222000000000000-2−2i2i2i−2i2i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000−222−22−2−22000000000000
χ562222-2-222-2-2-2-2-2-2-2-22-222222000000000000-2−2i2i2i−2i2i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000002−2−22−222−2000000000000
χ5722-2-2002-22i−2i2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i000000000002ζ2−2ζ22ζ2−2ζ200002ζ6−2ζ62ζ6−2ζ600002-22i−2i2ζ2−2ζ22ζ6−2ζ6000000000000000000000000
χ5822-2-2002-22i−2i2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i000000000002ζ2−2ζ22ζ2−2ζ200002ζ6−2ζ62ζ6−2ζ60000-22−2i2i−2ζ22ζ2−2ζ62ζ6000000000000000000000000
χ5922-2-2002-22i−2i2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i00000000000−2ζ22ζ2−2ζ22ζ20000−2ζ62ζ6−2ζ62ζ600002-22i−2i−2ζ22ζ2−2ζ62ζ6000000000000000000000000
χ6022-2-2002-22i−2i2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i00000000000−2ζ22ζ2−2ζ22ζ20000−2ζ62ζ6−2ζ62ζ60000-22−2i2i2ζ2−2ζ22ζ6−2ζ6000000000000000000000000
χ6122-2-2002-2−2i2i−2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i000000000002ζ6−2ζ62ζ6−2ζ600002ζ2−2ζ22ζ2−2ζ200002-2−2i2i2ζ6−2ζ62ζ2−2ζ2000000000000000000000000
χ6222-2-2002-2−2i2i−2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i000000000002ζ6−2ζ62ζ6−2ζ600002ζ2−2ζ22ζ2−2ζ20000-222i−2i−2ζ62ζ6−2ζ22ζ2000000000000000000000000
χ6322-2-2002-2−2i2i−2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i00000000000−2ζ62ζ6−2ζ62ζ60000−2ζ22ζ2−2ζ22ζ200002-2−2i2i−2ζ62ζ6−2ζ22ζ2000000000000000000000000
χ6422-2-2002-2−2i2i−2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i00000000000−2ζ62ζ6−2ζ62ζ60000−2ζ22ζ2−2ζ22ζ20000-222i−2i2ζ6−2ζ62ζ2−2ζ2000000000000000000000000
χ65444444-4-444-4-40000-4-4400002222−22−2222−2222−2222−2222−2200000000022−22000000000000000000000000000000000000000000000000
χ66444444-4-444-4-40000-4-440000−22−222222−2222−2222−2222−2222000000000−2222000000000000000000000000000000000000000000000000
χ67444444-4-4-4-44400004-4-400002222−22−22−2222−222222−2222−22000000000−2222000000000000000000000000000000000000000000000000
χ68444444-4-4-4-44400004-4-40000−22−22222222−2222−22−2222−222200000000022−22000000000000000000000000000000000000000000000000
χ694444-4-4-4-444-4-4000044-400002222−22−22−2222−2222−2222−222200000000022−22000000000000000000000000000000000000000000000000
χ704444-4-4-4-444-4-4000044-40000−22−22222222−2222−2222−2222−22000000000−2222000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-4-4440000-44400002222−22−2222−2222−22−2222−2222000000000−2222000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-4-4440000-4440000−22−222222−2222−222222−2222−2200000000022−22000000000000000000000000000000000000000000000000
χ7344-4-4004-44i−4i4i−4i44-4-4000004i−4i0000-4-444−4i−4i4i4i00000000000000000000000000000000000000000000000000000000000
χ7444-4-4004-44i−4i4i−4i-4-44400000−4i4i000000000000000000000002+2i−2−2i−2−2i2+2i0000−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000
χ7544-4-4004-44i−4i4i−4i-4-44400000−4i4i00000000000000000000000−2−2i2+2i2+2i−2−2i00002−2i−2+2i−2+2i2−2i000000000000000000000000000000000000
χ7644-4-4004-4−4i4i−4i4i44-4-400000−4i4i0000-4-4444i4i−4i−4i00000000000000000000000000000000000000000000000000000000000
χ7744-4-4004-4−4i4i−4i4i-4-444000004i−4i000000000000000000000002−2i−2+2i−2+2i2−2i0000−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000
χ7844-4-4004-4−4i4i−4i4i-4-444000004i−4i00000000000000000000000−2+2i2−2i2−2i−2+2i00002+2i−2−2i−2−2i2+2i000000000000000000000000000000000000
χ7944-4-400-444i−4i−4i4i00000000000000022−22−22222i2−2i2−2i22i20000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ300002ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000
χ8044-4-400-444i−4i−4i4i00000000000000022−22−22222i2−2i2−2i22i2000000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ30000−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000
χ8144-4-400-444i−4i−4i4i000000000000000−222222−22−2i22i22i2−2i20000000000000002ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ70000−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ300000000000000000000000000000000
χ8244-4-400-444i−4i−4i4i000000000000000−222222−22−2i22i22i2−2i2000000000000000−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ700002ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ300000000000000000000000000000000
χ8344-4-400-44−4i4i4i−4i00000000000000022−22−2222−2i22i22i2−2i20000000000000002ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ700002ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ300000000000000000000000000000000
χ8444-4-400-44−4i4i4i−4i00000000000000022−22−2222−2i22i22i2−2i2000000000000000−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ70000−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ300000000000000000000000000000000
χ8544-4-400-44−4i4i4i−4i000000000000000−222222−222i2−2i2−2i22i20000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ30000−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000
χ8644-4-400-44−4i4i4i−4i000000000000000−222222−222i2−2i2−2i22i2000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ300002ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000
χ878-88-88i−8i00000042−4242−420004i2−4i20000000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-88i−8i000000−4242−4242000−4i24i20000000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8−8i8i00000042−4242−42000−4i24i20000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i000000−4242−42420004i2−4i20000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-880000000042−42−424200000004ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ50000000000000000000000000000000000000000000000000000000000000000000
χ928-8-880000000042−42−42420000000−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ50000000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800000000−424242−4200000004ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ70000000000000000000000000000000000000000000000000000000000000000000
χ948-8-8800000000−424242−420000000−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ70000000000000000000000000000000000000000000000000000000000000000000

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