Finite Group Databasebeta

← Group #131713

Character table — Group #131713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122244444444888822244448888882488881616161616161616161616161616161624444444888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-111
χ611111111111111111-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ711111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1
χ811111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-1-1-1-111
χ91111111-1-1-1-11-1-1-1-1-1111-1-1-11111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1111-1-1-1ii−i−ii−i
χ101111111-1-1-1-11-1-1-1-1-1111-1-1-11111-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-1-1111−i−iii−ii
χ111111111-1-1-1-11-1-1-1-1-1111-1-1-11111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1111-1-1-1−i−iii−ii
χ121111111-1-1-1-11-1-1-1-1-1111-1-1-11111-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-1-1111ii−i−ii−i
χ131111111-1-1-1-11-1-1-1-1-1-1-11-1111111-1-11-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111−i−iiii−i
χ141111111-1-1-1-11-1-1-1-1-1-1-11-1111111-1-11-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1ii−i−i−ii
χ151111111-1-1-1-11-1-1-1-1-1-1-11-1111111-1-11-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111ii−i−i−ii
χ161111111-1-1-1-11-1-1-1-1-1-1-11-1111111-1-11-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1−i−iiii−i
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-22-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ192222222-2-2-2-222222-2222-2-2-2-2-2-2-222-22-2-222000000000000000000000000000000
χ202222222-2-2-2-222222-2-2-22-222-2-2-2-2222-222-2-2000000000000000000000000000000
χ21222222-22222-20000-222-2-222000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ22222222-22222-20000-222-2-222000000-2-20000−2−222−2−222−2−222−2−22200000000000000
χ23222222-22222-20000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−22200000000000000
χ24222222-22222-20000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−200000000000000
χ25222222-2-2-2-2-2-20000222-22-2-20000002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ26222222-2-2-2-2-2-20000222-22-2-20000002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ27222222-2-2-2-2-2-200002-2-2-2222000000-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ28222222-2-2-2-2-2-200002-2-2-2222000000-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ292222-2-2222-2-222222-200-220022-2-2-2-200000000000000000000000002-202-2000000
χ302222-2-2222-2-222222-200-220022-2-2-2-20000000000000000000000000-220-22000000
χ312222-2-2222-2-22-2-2-2-2-200-2200-2-2222200000000000000000000002-2-200200000000
χ322222-2-2222-2-22-2-2-2-2-200-2200-2-222220000000000000000000000-22200-200000000
χ332222-2-22-2-22222222200-2-200-2-222-2-2000000000000000000000022-200-200000000
χ342222-2-22-2-22222222200-2-200-2-222-2-20000000000000000000000-2-2200200000000
χ352222-2-22-2-2222-2-2-2-2200-2-20022-2-22200000000000000000000000002-20-22000000
χ362222-2-22-2-2222-2-2-2-2200-2-20022-2-2220000000000000000000000000-2202-2000000
χ372-22-22-202i−2i2i−2i0i2i2−i2−i202-2002i−2i2−22−2i2−i2002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ300000000000000
χ382-22-22-202i−2i2i−2i0i2i2−i2−i202-2002i−2i2−22−2i2−i2002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ300000000000000
χ392-22-22-202i−2i2i−2i0i2i2−i2−i20-2200−2i2i2−22−2i2−i200−22−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ300000000000000
χ402-22-22-202i−2i2i−2i0i2i2−i2−i20-2200−2i2i2−22−2i2−i200−22−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ300000000000000
χ412-22-22-202i−2i2i−2i0−i2−i2i2i202-2002i−2i−22−22−i2i200−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ700000000000000
χ422-22-22-202i−2i2i−2i0−i2−i2i2i202-2002i−2i−22−22−i2i200−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ700000000000000
χ432-22-22-202i−2i2i−2i0−i2−i2i2i20-2200−2i2i−22−22−i2i2002−2i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ700000000000000
χ442-22-22-202i−2i2i−2i0−i2−i2i2i20-2200−2i2i−22−22−i2i2002−2i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ700000000000000
χ452-22-22-20−2i2i−2i2i0i2i2−i2−i202-200−2i2i−22−22i2−i200−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ300000000000000
χ462-22-22-20−2i2i−2i2i0i2i2−i2−i202-200−2i2i−22−22i2−i200−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ300000000000000
χ472-22-22-20−2i2i−2i2i0i2i2−i2−i20-22002i−2i−22−22i2−i2002−2−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ300000000000000
χ482-22-22-20−2i2i−2i2i0i2i2−i2−i20-22002i−2i−22−22i2−i2002−2−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ300000000000000
χ492-22-22-20−2i2i−2i2i0−i2−i2i2i202-200−2i2i2−22−2−i2i2002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ700000000000000
χ502-22-22-20−2i2i−2i2i0−i2−i2i2i202-200−2i2i2−22−2−i2i2002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ700000000000000
χ512-22-22-20−2i2i−2i2i0−i2−i2i2i20-22002i−2i2−22−2−i2i200−22i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ700000000000000
χ522-22-22-20−2i2i−2i2i0−i2−i2i2i20-22002i−2i2−22−2−i2i200−22i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ700000000000000
χ534444-4-4-444-4-4-400004004-400000000000000000000000000000000000000000000
χ544444-4-4-4-4-444-40000-4004400000000000000000000000000000000000000000000
χ554-44-4-4404i−4i−4i4i02i22i2−2i2−2i2000000022−22−2222−2i22i2000000000000000000000000000000000000
χ564-44-4-4404i−4i−4i4i0−2i2−2i22i22i20000000−222222−222i2−2i2000000000000000000000000000000000000
χ574-44-4-440−4i4i4i−4i02i22i2−2i2−2i20000000−222222−22−2i22i2000000000000000000000000000000000000
χ584-44-4-440−4i4i4i−4i0−2i2−2i22i22i2000000022−22−22222i2−2i2000000000000000000000000000000000000
χ594-4-440040000-44i−4i4i−4i00000000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ200
χ604-4-440040000-44i−4i4i−4i0000000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ200
χ614-4-440040000-4−4i4i−4i4i00000000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ600
χ624-4-440040000-4−4i4i−4i4i0000000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ600
χ6388-8-80000000042−42−42420000000000000000000000000000000000000000000000000
χ6488-8-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-8-8800-80000800000000000000000000000000000000000000000000000000000

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