Finite Group Databasebeta

← Group #150296

Character table — Group #150296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112244444488888888881616161616161616161111224444448888888888161616161616161616
order124424248888241616161616161616448888888224424248888241616161616161616448888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11-1-1-1-11111111111111111111111-1-1-1-11-1-1-1-1
χ311111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111
χ511111111-1-1-1-1-1-1iiii−i−i−i−i11-1-11ii−i−i11111111-1-1-1-1-1-1iiii−i−i−i−i11-1-11ii−i−i
χ611111111-1-1-1-1-1-1iiii−i−i−i−i-1-1111−i−iii11111111-1-1-1-1-1-1iiii−i−i−i−i-1-1111−i−iii
χ711111111-1-1-1-1-1-1−i−i−i−iiiii11-1-11−i−iii11111111-1-1-1-1-1-1−i−i−i−iiiii11-1-11−i−iii
χ811111111-1-1-1-1-1-1−i−i−i−iiiii-1-1111ii−i−i11111111-1-1-1-1-1-1−i−i−i−iiiii-1-1111ii−i−i
χ9222222222222-2-2000000000000-20000222222222222-2-2000000000000-20000
χ1022222222-2-2-2-222000000000000-2000022222222-2-2-2-222000000000000-20000
χ1122-2-22-22-22i2i−2i−2i0000000000000001+i−1−i1−i−1+i22-2-22-22-22i2i−2i−2i0000000000000001+i−1−i1−i−1+i
χ1222-2-22-22-22i2i−2i−2i000000000000000−1−i1+i−1+i1−i22-2-22-22-22i2i−2i−2i000000000000000−1−i1+i−1+i1−i
χ1322-2-22-22-2−2i−2i2i2i0000000000000001−i−1+i1+i−1−i22-2-22-22-2−2i−2i2i2i0000000000000001−i−1+i1+i−1−i
χ1422-2-22-22-2−2i−2i2i2i000000000000000−1+i1−i−1−i1+i22-2-22-22-2−2i−2i2i2i000000000000000−1+i1−i−1−i1+i
χ1522-2-22-2-2200002-222−2−222−2−200000000022-2-22-2-2200002-222−2−222−2−2000000000
χ1622-2-22-2-2200002-2−2−222−2−22200000000022-2-22-2-2200002-2−2−222−2−222000000000
χ1722-2-22-2-220000-22i2i2−i2−i2−i2−i2i2i200000000022-2-22-2-220000-22i2i2−i2−i2−i2−i2i2i2000000000
χ1822-2-22-2-220000-22−i2−i2i2i2i2i2−i2−i200000000022-2-22-2-220000-22−i2−i2i2i2i2i2−i2−i2000000000
χ19444444-4-400000000000000000000000444444-4-400000000000000000000000
χ204444-4-400000000000000002-200000004444-4-400000000000000002-20000000
χ214444-4-40000000000000000-2200000004444-4-40000000000000000-220000000
χ2244-4-4-440000000000000000002i−2i0000044-4-4-440000000000000000002i−2i00000
χ2344-4-4-44000000000000000000−2i2i0000044-4-4-44000000000000000000−2i2i00000
χ244-44i−4i00002ζ2−2ζ22ζ6−2ζ600ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ70000000004-44i−4i00002ζ2−2ζ22ζ6−2ζ600ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7000000000
χ254-44i−4i00002ζ2−2ζ22ζ6−2ζ600−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ70000000004-44i−4i00002ζ2−2ζ22ζ6−2ζ600−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7000000000
χ264-44i−4i0000−2ζ22ζ2−2ζ62ζ600ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ70000000004-44i−4i0000−2ζ22ζ2−2ζ62ζ600ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7000000000
χ274-44i−4i0000−2ζ22ζ2−2ζ62ζ600−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ70000000004-44i−4i0000−2ζ22ζ2−2ζ62ζ600−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7000000000
χ284-4−4i4i00002ζ6−2ζ62ζ2−2ζ200ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ50000000004-4−4i4i00002ζ6−2ζ62ζ2−2ζ200ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5000000000
χ294-4−4i4i00002ζ6−2ζ62ζ2−2ζ200−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ50000000004-4−4i4i00002ζ6−2ζ62ζ2−2ζ200−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5000000000
χ304-4−4i4i0000−2ζ62ζ6−2ζ22ζ200ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ50000000004-4−4i4i0000−2ζ62ζ6−2ζ22ζ200ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5000000000
χ314-4−4i4i0000−2ζ62ζ6−2ζ22ζ200−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ50000000004-4−4i4i0000−2ζ62ζ6−2ζ22ζ200−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5000000000
χ321111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ331111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ3411111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111
χ3511111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1
χ3611111111-1-1-1-1-1-1iiii−i−i−i−i11-1-11ii−i−i-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-111-1−i−iii
χ3711111111-1-1-1-1-1-1iiii−i−i−i−i-1-1111−i−iii-1-1-1-1-1-1-1-1111111−i−i−i−iiiii11-1-1-1ii−i−i
χ3811111111-1-1-1-1-1-1−i−i−i−iiiii11-1-11−i−iii-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-111-1ii−i−i
χ3911111111-1-1-1-1-1-1−i−i−i−iiiii-1-1111ii−i−i-1-1-1-1-1-1-1-1111111iiii−i−i−i−i11-1-1-1−i−iii
χ40222222222222-2-2000000000000-20000-2-2-2-2-2-2-2-2-2-2-2-22200000000000020000
χ4122222222-2-2-2-222000000000000-20000-2-2-2-2-2-2-2-22222-2-200000000000020000
χ4222-2-22-22-22i2i−2i−2i0000000000000001+i−1−i1−i−1+i-2-222-22-22−2i−2i2i2i000000000000000−1−i1+i−1+i1−i
χ4322-2-22-22-22i2i−2i−2i000000000000000−1−i1+i−1+i1−i-2-222-22-22−2i−2i2i2i0000000000000001+i−1−i1−i−1+i
χ4422-2-22-22-2−2i−2i2i2i0000000000000001−i−1+i1+i−1−i-2-222-22-222i2i−2i−2i000000000000000−1+i1−i−1−i1+i
χ4522-2-22-22-2−2i−2i2i2i000000000000000−1+i1−i−1−i1+i-2-222-22-222i2i−2i−2i0000000000000001−i−1+i1+i−1−i
χ4622-2-22-2-2200002-222−2−222−2−2000000000-2-222-222-20000-22−2−222−2−222000000000
χ4722-2-22-2-2200002-2−2−222−2−222000000000-2-222-222-20000-2222−2−222−2−2000000000
χ4822-2-22-2-220000-22i2i2−i2−i2−i2−i2i2i2000000000-2-222-222-200002-2−i2−i2i2i2i2i2−i2−i2000000000
χ4922-2-22-2-220000-22−i2−i2i2i2i2i2−i2−i2000000000-2-222-222-200002-2i2i2−i2−i2−i2−i2i2i2000000000
χ50444444-4-400000000000000000000000-4-4-4-4-4-44400000000000000000000000
χ514444-4-400000000000000002-20000000-4-4-4-4440000000000000000-220000000
χ524444-4-40000000000000000-220000000-4-4-4-44400000000000000002-20000000
χ5344-4-4-440000000000000000002i−2i00000-4-4444-4000000000000000000−2i2i00000
χ5444-4-4-44000000000000000000−2i2i00000-4-4444-40000000000000000002i−2i00000
χ554-44i−4i00002ζ2−2ζ22ζ6−2ζ600ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7000000000-44−4i4i0000−2ζ22ζ2−2ζ62ζ600−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7000000000
χ564-44i−4i00002ζ2−2ζ22ζ6−2ζ600−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7000000000-44−4i4i0000−2ζ22ζ2−2ζ62ζ600ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7000000000
χ574-44i−4i0000−2ζ22ζ2−2ζ62ζ600ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7000000000-44−4i4i00002ζ2−2ζ22ζ6−2ζ600−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7000000000
χ584-44i−4i0000−2ζ22ζ2−2ζ62ζ600−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7000000000-44−4i4i00002ζ2−2ζ22ζ6−2ζ600ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7000000000
χ594-4−4i4i00002ζ6−2ζ62ζ2−2ζ200ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5000000000-444i−4i0000−2ζ62ζ6−2ζ22ζ200−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5000000000
χ604-4−4i4i00002ζ6−2ζ62ζ2−2ζ200−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5000000000-444i−4i0000−2ζ62ζ6−2ζ22ζ200ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5000000000
χ614-4−4i4i0000−2ζ62ζ6−2ζ22ζ200ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5000000000-444i−4i00002ζ6−2ζ62ζ2−2ζ200−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5000000000
χ624-4−4i4i0000−2ζ62ζ6−2ζ22ζ200−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5000000000-444i−4i00002ζ6−2ζ62ζ2−2ζ200ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5000000000

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