Finite Group Databasebeta

← Group #10693080

Character table — Group #10693080

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242422244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-111-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-11-1-1-1-111
χ91111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i111-1-1-1-11ii−i−ii−i
χ101111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i-1-1-11111-1−i−iii−ii
χ111111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iii11-111-1-1-1−i−iiii−i
χ121111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1ii−i−i1-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-11-1-1111ii−i−i−ii
χ131111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii111-1-1-1-11−i−iii−ii
χ141111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii-1-1-11111-1ii−i−ii−i
χ151111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−i11-111-1-1-1ii−i−i−ii
χ161111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1−i−iii1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-11-1-1111−i−iiii−i
χ1722222222222-2-2222-2-2-222-2-22222-2-20000-2-2000000000000000000000022-200-2000000
χ1822222222222-2-2222-2-2-222-2-22222-2-20000-2-20000000000000000000000-2-22002000000
χ192222222-2-2-2-222222-2-2222-2-2-2-2-2-2220000-2200000000000000000000002-2200-2000000
χ202222222-2-2-2-222222-2-2222-2-2-2-2-2-2220000-220000000000000000000000-22-2002000000
χ21222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ25222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ26222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-11111112i2i−2i−2i-11−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ27222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ28222222-1-2-2-2-2-2-2-1-1-122-2-1-1-1-1111111−2i−2i2i2i-11iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ292222-2-2222-2-2222222-2-2-2-2-2-2-2-2222200002-200000000000000000000000000002-22-200
χ302222-2-2222-2-2222222-2-2-2-2-2-2-2-2222200002-20000000000000000000000000000-22-2200
χ312222-2-2222-2-2-2-2222-222-2-222-2-222-2-22i−2i2i−2i-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ322222-2-2222-2-2-2-2222-222-2-222-2-222-2-2−2i2i−2i2i-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ332222-2-22-2-22222222-22-2-2-22222-2-2222-2-22-2-222-2-2-2-22200000000000000000000000000
χ342222-2-22-2-22222222-22-2-2-22222-2-222-222-2-2-2-2-22222-2-200000000000000000000000000
χ352222-2-22-2-222-2-22222-22-2-2-2-222-2-2-2-200002200000000000000000000000000002i−2i−2i2i00
χ362222-2-22-2-222-2-22222-22-2-2-2-222-2-2-2-20000220000000000000000000000000000−2i2i2i−2i00
χ372222-2-2-122-2-2-2-2-1-1-1-22211-1-111-1-1112i−2i2i−2i1-1−i−iii−i−iii00003−33−3−i3i3−i3i300000000000000
χ382222-2-2-122-2-2-2-2-1-1-1-22211-1-111-1-1112i−2i2i−2i1-1−i−iii−i−iii0000−33−33i3−i3i3−i300000000000000
χ392222-2-2-122-2-2-2-2-1-1-1-22211-1-111-1-111−2i2i−2i2i1-1ii−i−iii−i−i00003−33−3i3−i3i3−i300000000000000
χ402222-2-2-122-2-2-2-2-1-1-1-22211-1-111-1-111−2i2i−2i2i1-1ii−i−iii−i−i0000−33−33−i3i3−i3i300000000000000
χ412222-2-2-1-2-22222-1-1-1-22-211-1-1-1-111-1-12-2-2211-1-11111-1-100003−3−33−333−300000000000000
χ422222-2-2-1-2-22222-1-1-1-22-211-1-1-1-111-1-12-2-2211-1-11111-1-10000−333−33−3−3300000000000000
χ432222-2-2-1-2-22222-1-1-1-22-211-1-1-1-111-1-1-222-21111-1-1-1-11100003−3−333−3−3300000000000000
χ442222-2-2-1-2-22222-1-1-1-22-211-1-1-1-111-1-1-222-21111-1-1-1-1110000−333−3−333−300000000000000
χ45444444-24444-4-4-2-2-2-4-4-4-2-222-2-2-2-2220000220000000000000000000000000000000000
χ46444444-2-4-4-4-444-2-2-2-4-44-2-2222222-2-200002-20000000000000000000000000000000000
χ474444-4-4-244-4-444-2-2-24-4-4222222-2-2-2-20000-220000000000000000000000000000000000
χ484444-4-4-2-4-444-4-4-2-2-24-442222-2-222220000-2-20000000000000000000000000000000000
χ4944-4-400400004i−4i4-4-4000000000004i−4i000000000000000000000000002-20002i−2i0000000
χ5044-4-400400004i−4i4-4-4000000000004i−4i00000000000000000000000000-22000−2i2i0000000
χ5144-4-40040000−4i4i4-4-400000000000−4i4i000000000000000000000000002-2000−2i2i0000000
χ5244-4-40040000−4i4i4-4-400000000000−4i4i00000000000000000000000000-220002i−2i0000000
χ534-44-44-444i−4i4i−4i00-44-40004-4004i−4i4i−4i000000000000000000000000000000000000000000
χ544-44-44-44−4i4i−4i4i00-44-40004-400−4i4i−4i4i000000000000000000000000000000000000000000
χ554-44-44-4-24i−4i4i−4i002-22000-2200−2i2i−2i2i00000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ564-44-44-4-24i−4i4i−4i002-22000-2200−2i2i−2i2i00000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ574-44-44-4-2−4i4i−4i4i002-22000-22002i−2i2i−2i00000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ584-44-44-4-2−4i4i−4i4i002-22000-22002i−2i2i−2i00000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ594-44-4-4444i−4i−4i4i00-44-4000-4400−4i4i4i−4i000000000000000000000000000000000000000000
χ604-44-4-444−4i4i4i−4i00-44-4000-44004i−4i−4i4i000000000000000000000000000000000000000000
χ614-44-4-44-24i−4i−4i4i002-220002-2002i−2i−2i2i00000000−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
χ624-44-4-44-24i−4i−4i4i002-220002-2002i−2i−2i2i00000000ζ2−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
χ634-44-4-44-2−4i4i4i−4i002-220002-200−2i2i2i−2i00000000−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
χ644-44-4-44-2−4i4i4i−4i002-220002-200−2i2i2i−2i00000000ζ2+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
χ6588-8-800-400008i−8i-44400000000000−4i4i0000000000000000000000000000000000000000
χ6688-8-800-40000−8i8i-444000000000004i−4i0000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-40000043−430000000000000000000000000000000000000000000000
χ698-8-8800-400000044-400000−43430000000000000000000000000000000000000000000000

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