Finite Group Databasebeta

← Group #72234389

Character table — Group #72234389

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size111122222222222244444444444444444448888888888888888888888888881616161616161616161616161616161616161616323232323232323232323232
order1222444444448888244888816161616161616161616161688888888816163232323232323232323232323232323288888888161616163232323232323232224444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1111-1-1-111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-111111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1111-1-1-1-1-111
χ911111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1iiii−i−i−i−i-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i111-1-11-1-1i−ii−i
χ1011111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1iiii−i−i−i−i-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iiiii−i−iiiii−i−i−i−i-1-1-111-111−ii−ii
χ1111111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−i−i−iiiii1-11-1-1-111i−i−ii
χ1211111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−iii−i−i−i−i−i−iiiii-11-1111-1-1−iii−i
χ1311111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1−i−i−i−iiiii-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i−i−iii−i−i−i−iiiii-1-1-111-111i−ii−i
χ1411111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1−i−i−i−iiiii-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii111-1-11-1-1−ii−ii
χ1511111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii−i−iiiiiii−i−i−i−i-11-1111-1-1i−i−ii
χ1611111111-1-1-1-11111-11-111-1-111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiiiii−i−i−i−i1-11-1-1-111−iii−i
χ171111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-11-111-1-111-1-111-11-1-11-1-1-1-1-1
χ181111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-11-111-111111
χ191111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-111-1-1111-1-11-11-11-1-111
χ201111-1-11111111111-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-111-11-11-111-1-1
χ211111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-11-11-1-111-1-111-1-11-111-11-1-1-1-1
χ221111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-11-1-11-11111
χ231111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1-111-11-11-1-1-111
χ241111-1-11111111111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-11-1-11-11-1111-1-1
χ251111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11ii−i−i−i−iii111111-1-1-1-1-1-1-1-11111ii−i−iii−i−ii−i−iiii−i−i−i−iii11-1-11-1-11−ii−ii
χ261111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11ii−i−i−i−iii111111-1-1-1-1-1-1-1-11111−i−iii−i−iiii−i−iiii−i−i−i−iii-1-111-111-1i−ii−i
χ271111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11ii−i−i−i−iii11-1-1-1-111111111-1-1-1-1ii−i−i−i−iiii−i−ii−i−iiiii−i−i1-1-1-1111-1−iii−i
χ281111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11ii−i−i−i−iii11-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−ii−i−iiiii−i−i-1111-1-1-11i−i−ii
χ291111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11−i−iiiii−i−i111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−iii−i−i−iiiii−i−i-1-111-111-1−ii−ii
χ301111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11−i−iiiii−i−i111111-1-1-1-1-1-1-1-11111−i−iii−i−iii−iii−i−i−iiiii−i−i11-1-11-1-11i−ii−i
χ311111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11−i−iiiii−i−i11-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−iii−i−i−i−iii-1111-1-1-11−iii−i
χ321111-1-111-1-1-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-11−i−iiiii−i−i11-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−iii−iii−i−i−i−iii1-1-1-1111-1i−i−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
χ3922222222-2-2-2-22222-22-222-2-2-2-2-2-2-2-2-2-22222-22i2i2i2i−2i−2i−2i−2i22000000000000000000000000−2i−2i2i2i00000000000000000000
χ4022222222-2-2-2-22222-22-222-2-2-2-2-2-2-2-2-2-22222-2−2i−2i−2i−2i2i2i2i2i220000000000000000000000002i2i−2i−2i00000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-22-2-2-22200000000000022i−2i2i−2i−2i2i−2i2i0022−2−222−2−2−2−222−2−222000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ4222222222-2-2-2-2-2-2-2-2-22-2-2-22200000000000022i−2i2i−2i−2i2i−2i2i00−2−222−2−22222−2−222−2−2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4322222222-2-2-2-2-2-2-2-2-22-2-2-2220000000000002−2i2i−2i2i2i−2i2i−2i0022−2−222−2−2−2−222−2−222000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ4422222222-2-2-2-2-2-2-2-2-22-2-2-2220000000000002−2i2i−2i2i2i−2i2i−2i00−2−222−2−22222−2−222−2−2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
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
χ512222-2-222-2-2-2-222222-22-2-2-2-22222-2-2-2-2222222i2i−2i−2i−2i−2i2i2i-2-2000000000000000000000000−2i2i2i−2i00000000000000000000
χ522222-2-222-2-2-2-222222-22-2-2-2-22222-2-2-2-222222−2i−2i2i2i2i2i−2i−2i-2-20000000000000000000000002i−2i−2i2i00000000000000000000
χ532222-2-222-2-2-2-2-2-2-2-22-222222000000000000-22i−2i−2i2i−2i2i2i−2i0022−2−2−2−222−2−22222−2−2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ542222-2-222-2-2-2-2-2-2-2-22-222222000000000000-22i−2i−2i2i−2i2i2i−2i00−2−22222−2−222−2−2−2−222000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ552222-2-222-2-2-2-2-2-2-2-22-222222000000000000-2−2i2i2i−2i2i−2i−2i2i0022−2−2−2−222−2−22222−2−2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ562222-2-222-2-2-2-2-2-2-2-22-222222000000000000-2−2i2i2i−2i2i−2i−2i2i00−2−22222−2−222−2−2−2−222000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ5722-2-2002-22i2i−2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i000000000002-22-200002i−2i2i−2i00002ζ2−2ζ22ζ6−2ζ62ζ2−2ζ22ζ6−2ζ6000000000000000000000000
χ5822-2-2002-22i2i−2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i000000000002-22-200002i−2i2i−2i0000−2ζ22ζ2−2ζ62ζ6−2ζ22ζ2−2ζ62ζ6000000000000000000000000
χ5922-2-2002-22i2i−2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i00000000000-22-220000−2i2i−2i2i00002ζ2−2ζ22ζ6−2ζ6−2ζ22ζ2−2ζ62ζ6000000000000000000000000
χ6022-2-2002-22i2i−2i−2i22-2-2000002i−2i000022-2-22i2i−2i−2i00000000000-22-220000−2i2i−2i2i0000−2ζ22ζ2−2ζ62ζ62ζ2−2ζ22ζ6−2ζ6000000000000000000000000
χ6122-2-2002-2−2i−2i2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i000000000002-22-20000−2i2i−2i2i00002ζ6−2ζ62ζ2−2ζ22ζ6−2ζ62ζ2−2ζ2000000000000000000000000
χ6222-2-2002-2−2i−2i2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i000000000002-22-20000−2i2i−2i2i0000−2ζ62ζ6−2ζ22ζ2−2ζ62ζ6−2ζ22ζ2000000000000000000000000
χ6322-2-2002-2−2i−2i2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i00000000000-22-2200002i−2i2i−2i00002ζ6−2ζ62ζ2−2ζ2−2ζ62ζ6−2ζ22ζ2000000000000000000000000
χ6422-2-2002-2−2i−2i2i2i22-2-200000−2i2i000022-2-2−2i−2i2i2i00000000000-22-2200002i−2i2i−2i0000−2ζ62ζ6−2ζ22ζ22ζ6−2ζ62ζ2−2ζ2000000000000000000000000
χ65444444-4-44-44-400004-4-400002222−22−2222−2222−2222−2222−2200000000022−22000000000000000000000000000000000000000000000000
χ66444444-4-44-44-400004-4-40000−22−222222−2222−2222−2222−2222000000000−2222000000000000000000000000000000000000000000000000
χ67444444-4-4-44-440000-4-4400002222−22−2222−2222−22−2222−2222000000000−2222000000000000000000000000000000000000000000000000
χ68444444-4-4-44-440000-4-440000−22−222222−2222−222222−2222−2200000000022−22000000000000000000000000000000000000000000000000
χ694444-4-4-4-44-44-40000-44400002222−22−22−2222−2222−2222−222200000000022−22000000000000000000000000000000000000000000000000
χ704444-4-4-4-44-44-40000-4440000−22−22222222−2222−2222−2222−22000000000−2222000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-44-44000044-400002222−22−22−2222−222222−2222−22000000000−2222000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-44-44000044-40000−22−22222222−2222−22−2222−222200000000022−22000000000000000000000000000000000000000000000000
χ7344-4-4004-44i4i−4i−4i44-4-4000004i−4i0000-4-444−4i−4i4i4i00000000000000000000000000000000000000000000000000000000000
χ7444-4-4004-44i4i−4i−4i-4-44400000−4i4i0000000000000000000000022−22−222200002i2−2i2−2i22i2000000000000000000000000000000000000
χ7544-4-4004-44i4i−4i−4i-4-44400000−4i4i00000000000000000000000−222222−220000−2i22i22i2−2i2000000000000000000000000000000000000
χ7644-4-4004-4−4i−4i4i4i44-4-400000−4i4i0000-4-4444i4i−4i−4i00000000000000000000000000000000000000000000000000000000000
χ7744-4-4004-4−4i−4i4i4i-4-444000004i−4i0000000000000000000000022−22−22220000−2i22i22i2−2i2000000000000000000000000000000000000
χ7844-4-4004-4−4i−4i4i4i-4-444000004i−4i00000000000000000000000−222222−2200002i2−2i2−2i22i2000000000000000000000000000000000000
χ7944-4-400-444i−4i−4i4i00000000000000022−22−22222i2−2i2−2i22i20000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ700002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ8044-4-400-444i−4i−4i4i00000000000000022−22−22222i2−2i2−2i22i2000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ70000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ8144-4-400-444i−4i−4i4i000000000000000−222222−22−2i22i22i2−2i20000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ500002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ8244-4-400-444i−4i−4i4i000000000000000−222222−22−2i22i22i2−2i2000000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ50000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ8344-4-400-44−4i4i4i−4i00000000000000022−22−2222−2i22i22i2−2i20000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ70000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ8444-4-400-44−4i4i4i−4i00000000000000022−22−2222−2i22i22i2−2i2000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ700002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ8544-4-400-44−4i4i4i−4i000000000000000−222222−222i2−2i2−2i22i20000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ50000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ8644-4-400-44−4i4i4i−4i000000000000000−222222−222i2−2i2−2i22i2000000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ500002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ878-88-80000000042−4242−4200000004ζ+4ζ7−4ζ−4ζ74ζ3+4ζ5−4ζ3−4ζ50000000000000000000000000000000000000000000000000000000000000000000
χ888-88-80000000042−4242−420000000−4ζ−4ζ74ζ+4ζ7−4ζ3−4ζ54ζ3+4ζ50000000000000000000000000000000000000000000000000000000000000000000
χ898-88-800000000−4242−424200000004ζ3+4ζ5−4ζ3−4ζ5−4ζ−4ζ74ζ+4ζ70000000000000000000000000000000000000000000000000000000000000000000
χ908-88-800000000−4242−42420000000−4ζ3−4ζ54ζ3+4ζ54ζ+4ζ7−4ζ−4ζ70000000000000000000000000000000000000000000000000000000000000000000
χ918-8-888i−8i00000042−42−42420004i2−4i20000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-888i−8i000000−424242−42000−4i24i20000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-88−8i8i00000042−42−4242000−4i24i20000000000000000000000000000000000000000000000000000000000000000000000000
χ948-8-88−8i8i000000−424242−420004i2−4i20000000000000000000000000000000000000000000000000000000000000000000000000

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