Finite Group Databasebeta

← Group #140317

Character table — Group #140317

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122244444444444488888888244444444488888888888816161616161616161616161616161616888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111-1-1111111-1-1-1-1-11iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−ii−i11-1-11-1i−i
χ101111-1-1-1-1-1-111-1-1111111-1-1-1-1-11iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−ii−ii-1-111-11−ii
χ111111-1-1-1-1-1-111-1-1111111-1-1-1-1-11iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111i−ii−i11-1-1-11−ii
χ121111-1-1-1-1-1-111-1-1111111-1-1-1-1-11iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−ii−ii-1-1111-1i−i
χ131111-1-1-1-1-1-111-1-1111111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111i−ii−i-1-1111-1−ii
χ141111-1-1-1-1-1-111-1-1111111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−ii−ii11-1-1-11i−i
χ151111-1-1-1-1-1-111-1-1111111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1i−ii−i-1-111-11i−i
χ161111-1-1-1-1-1-111-1-1111111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii−ii11-1-11-1−ii
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-200000000-2-2-2-200000000000000000000000022-2-200000000
χ20222222222222-2-2-2-222222222-2-200000000-2-2-2-2000000000000000000000000-2-22200000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-2222200000000-2-200000000000022-2-222-2-222−2−222−2−222−2−222−2−2000000000000
χ2422222222-2-2-2-2222200000000-2-200000000000022-2-222-2-2−2−222−2−222−2−222−2−222000000000000
χ2522222222-2-2-2-2222200000000-2-2000000000000-2-222-2-22222−2−222−2−2−2−222−2−222000000000000
χ2622222222-2-2-2-2222200000000-2-2000000000000-2-222-2-222−2−222−2−22222−2−222−2−2000000000000
χ272222-2-2-2-222-2-2-2-222000000002-20000000000002i2i−2i−2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ282222-2-2-2-222-2-2-2-222000000002-20000000000002i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ292222-2-2-2-222-2-2-2-222000000002-2000000000000−2i−2i2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ302222-2-2-2-222-2-2-2-222000000002-2000000000000−2i−2i2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ312222-2-2-2-2-2-22222-2-22222-2-2-2-22-200000000-2-2220000000000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-2-2-22222-2-22222-2-2-2-22-200000000-2-222000000000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-2-2-22222-2-2-2-2-2-222222-20000000022-2-200000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-2-2-22222-2-2-2-2-2-222222-20000000022-2-20000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-2-2-222-2-222-2-2-2-22222-222i2i2i2i−2i−2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ362222-2-2-2-2-2-222-2-222-2-2-2-22222-22−2i−2i−2i−2i2i2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ372-22-22i−2i2i−2i00002i−2i2-222−2−2i2i2−i2−i2001+i1+i−1−i−1−i1−i1−i−1+i−1+i2−2i2−i2002ζ2−2ζ2002ζ6−2ζ6ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ382-22-22i−2i2i−2i00002i−2i2-222−2−2i2i2−i2−i2001+i1+i−1−i−1−i1−i1−i−1+i−1+i2−2i2−i2002ζ2−2ζ2002ζ6−2ζ6−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ392-22-22i−2i2i−2i00002i−2i2-222−2−2i2i2−i2−i200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2−2i2−i200−2ζ22ζ200−2ζ62ζ6ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ402-22-22i−2i2i−2i00002i−2i2-222−2−2i2i2−i2−i200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2−2i2−i200−2ζ22ζ200−2ζ62ζ6−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ412-22-22i−2i2i−2i00002i−2i2-2−2−222−i2−i2i2i2001+i1+i−1−i−1−i1−i1−i−1+i−1+i−22−i2i200−2ζ22ζ200−2ζ62ζ6ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ422-22-22i−2i2i−2i00002i−2i2-2−2−222−i2−i2i2i2001+i1+i−1−i−1−i1−i1−i−1+i−1+i−22−i2i200−2ζ22ζ200−2ζ62ζ6−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ432-22-22i−2i2i−2i00002i−2i2-2−2−222−i2−i2i2i200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−22−i2i2002ζ2−2ζ2002ζ6−2ζ6ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ442-22-22i−2i2i−2i00002i−2i2-2−2−222−i2−i2i2i200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−22−i2i2002ζ2−2ζ2002ζ6−2ζ6−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ452-22-2−2i2i−2i2i0000−2i2i2-222−2−2−i2−i2i2i2001−i1−i−1+i−1+i1+i1+i−1−i−1−i2−2−i2i200−2ζ62ζ600−2ζ22ζ2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ462-22-2−2i2i−2i2i0000−2i2i2-222−2−2−i2−i2i2i2001−i1−i−1+i−1+i1+i1+i−1−i−1−i2−2−i2i200−2ζ62ζ600−2ζ22ζ2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ472-22-2−2i2i−2i2i0000−2i2i2-222−2−2−i2−i2i2i200−1+i−1+i1−i1−i−1−i−1−i1+i1+i2−2−i2i2002ζ6−2ζ6002ζ2−2ζ2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ482-22-2−2i2i−2i2i0000−2i2i2-222−2−2−i2−i2i2i200−1+i−1+i1−i1−i−1−i−1−i1+i1+i2−2−i2i2002ζ6−2ζ6002ζ2−2ζ2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ492-22-2−2i2i−2i2i0000−2i2i2-2−2−222i2i2−i2−i2001−i1−i−1+i−1+i1+i1+i−1−i−1−i−22i2−i2002ζ6−2ζ6002ζ2−2ζ2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ502-22-2−2i2i−2i2i0000−2i2i2-2−2−222i2i2−i2−i2001−i1−i−1+i−1+i1+i1+i−1−i−1−i−22i2−i2002ζ6−2ζ6002ζ2−2ζ2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ512-22-2−2i2i−2i2i0000−2i2i2-2−2−222i2i2−i2−i200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−22i2−i200−2ζ62ζ600−2ζ22ζ2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ522-22-2−2i2i−2i2i0000−2i2i2-2−2−222i2i2−i2−i200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−22i2−i200−2ζ62ζ600−2ζ22ζ2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-444-4-400000000-44000000000000000000000000000000000000000000000000
χ5544-4-444-4-40000000022−2222−2222−2222−22002-22-22-22-2000022−220022−22000000000000000000000000000000
χ5644-4-444-4-40000000022−2222−2222−2222−2200-22-22-22-220000−222200−2222000000000000000000000000000000
χ5744-4-444-4-400000000−2222−2222−2222−2222002-22-22-22-20000−222200−2222000000000000000000000000000000
χ5844-4-444-4-400000000−2222−2222−2222−222200-22-22-22-22000022−220022−22000000000000000000000000000000
χ5944-4-4-4-4440000000022−2222−22−2222−2222002i−2i2i−2i−2i2i−2i2i00002i2−2i200−2i22i2000000000000000000000000000000
χ6044-4-4-4-4440000000022−2222−22−2222−222200−2i2i−2i2i2i−2i2i−2i0000−2i22i2002i2−2i2000000000000000000000000000000
χ6144-4-4-4-44400000000−2222−222222−2222−22002i−2i2i−2i−2i2i−2i2i0000−2i22i2002i2−2i2000000000000000000000000000000
χ6244-4-4-4-44400000000−2222−222222−2222−2200−2i2i−2i2i2i−2i2i−2i00002i2−2i200−2i22i2000000000000000000000000000000
χ634-44-44i−4i4i−4i0000−4i4i-442222−22−222i22i2−2i2−2i20000000000−2222−2i22i2000000000000000000000000000000000000
χ644-44-44i−4i4i−4i0000−4i4i-44−22−222222−2i2−2i22i22i2000000000022−222i2−2i2000000000000000000000000000000000000
χ654-44-4−4i4i−4i4i00004i−4i-442222−22−22−2i2−2i22i22i20000000000−22222i2−2i2000000000000000000000000000000000000
χ664-44-4−4i4i−4i4i00004i−4i-44−22−2222222i22i2−2i2−2i2000000000022−22−2i22i2000000000000000000000000000000000000
χ674-4-444i−4i−4i4i4i−4i4-4000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000
χ684-4-444i−4i−4i4i4i−4i4-400000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000
χ694-4-444i−4i−4i4i−4i4i-4400004-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000
χ704-4-444i−4i−4i4i−4i4i-440000-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ714-4-44−4i4i4i−4i4i−4i-4400004-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ724-4-44−4i4i4i−4i4i−4i-440000-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000
χ734-4-44−4i4i4i−4i−4i4i4-4000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000
χ744-4-44−4i4i4i−4i−4i4i4-400000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000

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