Finite Group Databasebeta

← Group #10691152

Character table — Group #10691152

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666224466661212121212124444688881212121212121212124444441212121224242424244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1
χ91111111-1-1-1-1111-1-11111-1-111-1-1-1-1ii−i−i-1ii−i−i1iiii−i−i−i−i11-1-11-111-1-1ii−i−i1-1ii−i−iii−i−i1-1
χ101111111-1-1-1-1111-1-11111-1-111-1-1-1-1ii−i−i-1ii−i−i1iiii−i−i−i−i-1-1111-111-1-1ii−i−i-11−i−iii−i−iii-11
χ111111111-1-1-1-1111-1-11111-1-111-1-1-1-1ii−i−i-1−i−iii1iiii−i−i−i−i11-1-1-11-1-111−i−iii1-1ii−i−i−i−iii-11
χ121111111-1-1-1-1111-1-11111-1-111-1-1-1-1ii−i−i-1−i−iii1iiii−i−i−i−i-1-111-11-1-111−i−iii-11−i−iiiii−i−i1-1
χ131111111-1-1-1-1111-1-11111-1-111-1-1-1-1−i−iii-1ii−i−i1−i−i−i−iiiii11-1-1-11-1-111ii−i−i1-1−i−iiiii−i−i-11
χ141111111-1-1-1-1111-1-11111-1-111-1-1-1-1−i−iii-1ii−i−i1−i−i−i−iiiii-1-111-11-1-111ii−i−i-11ii−i−i−i−iii1-1
χ151111111-1-1-1-1111-1-11111-1-111-1-1-1-1−i−iii-1−i−iii1−i−i−i−iiiii11-1-11-111-1-1−i−iii1-1−i−iii−i−iii1-1
χ161111111-1-1-1-1111-1-11111-1-111-1-1-1-1−i−iii-1−i−iii1−i−i−i−iiiii-1-1111-111-1-1−i−iii-11ii−i−iii−i−i-11
χ1722222222222222-2-2-2-222-2-2-2-222220000-20000-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-222-2-2-2-222220000-20000-200000000-2-2-2-20000000000220000000000
χ192222222-2-2-2-222222-2-22222-2-2-2-2-2-2000020000-20000000022-2-20000000000-220000000000
χ202222222-2-2-2-222222-2-22222-2-2-2-2-2-2000020000-200000000-2-22200000000002-20000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1111111110000-2-21111-1-1-1-1000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-111111111000022-1-1-1-11111000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-111-1-111112i2i−2i−2i12i2i−2i−2i-1−i−i−i−iiiii00002-2-1-111−i−iii000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-111-1-111112i2i−2i−2i1−2i−2i2i2i-1−i−i−i−iiiii0000-2211-1-1ii−i−i000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-111-1-11111−2i−2i2i2i12i2i−2i−2i-1iiii−i−i−i−i0000-2211-1-1−i−iii000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-111-1-11111−2i−2i2i2i1−2i−2i2i2i-1iiii−i−i−i−i00002-2-1-111ii−i−i000000000000
χ292222-2-2222-2-22222-22-2-2-2222222-2-20000-20000-200000000000000000000000000002i−2i2i−2i00
χ302222-2-2222-2-22222-22-2-2-2222222-2-20000-20000-20000000000000000000000000000−2i2i−2i2i00
χ312222-2-2222-2-2222-22-22-2-2-2-2-2-222-2-2000022i−2i2i−2i20000000000000000002i−2i2i−2i000000000000
χ322222-2-2222-2-2222-22-22-2-2-2-2-2-222-2-200002−2i2i−2i2i2000000000000000000−2i2i−2i2i000000000000
χ332222-2-22-2-2222222-2-22-2-222-2-2-2-2220000-22-2-2220000000000000000002-2-22000000000000
χ342222-2-22-2-2222222-2-22-2-222-2-2-2-2220000-2-222-22000000000000000000-222-2000000000000
χ352222-2-22-2-222222-222-2-2-2-2-222-2-222000020000-200000000000000000000000000002-2-2200
χ362222-2-22-2-222222-222-2-2-2-2-222-2-222000020000-20000000000000000000000000000-222-200
χ372222-2-2-122-2-2-1-1-1-22-22111111-1-1110000-12i−2i2i−2i-133−3−333−3−3000000−i3i3−i3i3−ii−ii000000000000
χ382222-2-2-122-2-2-1-1-1-22-22111111-1-1110000-12i−2i2i−2i-1−3−333−3−333000000i3−i3i3−i3−ii−ii000000000000
χ392222-2-2-122-2-2-1-1-1-22-22111111-1-1110000-1−2i2i−2i2i-133−3−333−3−3000000i3−i3i3−i3i−ii−i000000000000
χ402222-2-2-122-2-2-1-1-1-22-22111111-1-1110000-1−2i2i−2i2i-1−3−333−3−333000000−i3i3−i3i3i−ii−i000000000000
χ412222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-1000012-2-22-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3-111-1000000000000
χ422222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-1000012-2-22-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3-111-1000000000000
χ432222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-100001-222-2-1−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i31-1-11000000000000
χ442222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-100001-222-2-1i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i31-1-11000000000000
χ452-22-22-222i−2i2i−2i-22-200002-200002i−2i2i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-20000000000001−i−1+i1+i−1−i000000
χ462-22-22-222i−2i2i−2i-22-200002-200002i−2i2i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i-22000000000000−1+i1−i−1−i1+i000000
χ472-22-22-222i−2i2i−2i-22-200002-200002i−2i2i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-2000000000000−1+i1−i−1−i1+i000000
χ482-22-22-222i−2i2i−2i-22-200002-200002i−2i2i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i-220000000000001−i−1+i1+i−1−i000000
χ492-22-22-22−2i2i−2i2i-22-200002-20000−2i2i−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i-22000000000000−1−i1+i−1+i1−i000000
χ502-22-22-22−2i2i−2i2i-22-200002-20000−2i2i−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-20000000000001+i−1−i1−i−1+i000000
χ512-22-22-22−2i2i−2i2i-22-200002-20000−2i2i−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i-220000000000001+i−1−i1−i−1+i000000
χ522-22-22-22−2i2i−2i2i-22-200002-20000−2i2i−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-2000000000000−1−i1+i−1+i1−i000000
χ53444444-24444-2-2-2-4-4-4-4-2-22222-2-2-2-200002000020000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-244-4-4-2-2-2-22222220000-2000020000000000000000000000000000000000
χ554444-4-4-244-4-4-2-2-24-44-422-2-2-2-2-2-22200002000020000000000000000000000000000000000
χ564444-4-4-2-4-444-2-2-2-444-42222-2-222-2-20000-2000020000000000000000000000000000000000
χ574-44-44-4-24i−4i4i−4i2-220000-220000−2i2i−2i2i2+2i−2−2i2−2i−2+2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ584-44-44-4-24i−4i4i−4i2-220000-220000−2i2i−2i2i−2−2i2+2i−2+2i2−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ594-44-44-4-2−4i4i−4i4i2-220000-2200002i−2i2i−2i2−2i−2+2i2+2i−2−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ604-44-44-4-2−4i4i−4i4i2-220000-2200002i−2i2i−2i−2+2i2−2i−2−2i2+2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ614-44-4-4444i−4i−4i4i-44-40000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ624-44-4-444−4i4i4i−4i-44-40000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ634-44-4-44-24i−4i−4i4i2-2200002-20000−2i2i2i−2i0000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ644-44-4-44-24i−4i−4i4i2-2200002-20000−2i2i2i−2i0000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ654-44-4-44-2−4i4i4i−4i2-2200002-200002i−2i−2i2i0000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ664-44-4-44-2−4i4i4i−4i2-2200002-200002i−2i−2i2i0000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-444000000−4i34i300000000000000000000000000000000000000000000000000
χ6988-8-800-40000-4440000004i3−4i300000000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-400000000−4i34i3000000000000000000000000000000000000000000000000
χ728-8-8800-4000044-4000000004i3−4i3000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.