Finite Group Databasebeta

← Group #10693015

Character table — Group #10693015

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222222344446662446666121212121212444461212121212121212124488121212122424242422444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
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
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1
χ9111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1111-1-1-1ii−i−ii−i
χ10111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-1-1-1111−i−iii−ii
χ11111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-11−ii-1-111−i−iii1-1-1-11-111ii−i−i−ii
χ12111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-11−ii-1-111−i−iii-1111-11-1-1−i−iiii−i
χ13111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1111-1-1-1−i−iii−ii
χ14111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-1-1-1111ii−i−ii−i
χ15111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-11i−i-1-111ii−i−i1-1-1-11-111−i−iiii−i
χ16111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-11i−i-1-111ii−i−i-1111-11-1-1ii−i−i−ii
χ17222222222-2-2-2-22222-2-22222-2-2-2-2-2-200002-2000000000000000000002200-2-200000000
χ18222222222-2-2-2-22222-2-22222-2-2-2-2-2-200002-200000000000000000000-2-2002200000000
χ1922222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ2122222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ2222222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ23222222-2-222222222-2-2-222-2-2-2-222220000-2-2000000000000000000002-200-2200000000
χ24222222-2-222222222-2-2-222-2-2-2-222220000-2-200000000000000000000-22002-200000000
χ25222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ26222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ27222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ28222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ292222-2-222222-2-2222-22-2-2-222-2-2-2-2220000-2200000000000000000000000000002-22-200
χ302222-2-222222-2-2222-22-2-2-222-2-2-2-2220000-220000000000000000000000000000-22-2200
χ312222-2-2222-2-222222-2-22-2-2222222-2-22-22-2-2-222-2-222-2-200000000000000000000000000
χ322222-2-2222-2-222222-2-22-2-2222222-2-2-22-22-2-2-2-222-2-22200000000000000000000000000
χ332222-2-222-1-2-222-1-1-1-2-2211-1-1-1-1-1-1112-22-211-1-111-1-11100003−33−33−33−300000000000000
χ342222-2-222-1-2-222-1-1-1-2-2211-1-1-1-1-1-1112-22-211-1-111-1-1110000−33−33−33−3300000000000000
χ352222-2-222-1-2-222-1-1-1-2-2211-1-1-1-1-1-111-22-221111-1-111-1-100003−33−3−33−3300000000000000
χ362222-2-222-1-2-222-1-1-1-2-2211-1-1-1-1-1-111-22-221111-1-111-1-10000−33−333−33−300000000000000
χ372222-2-2-2-2222-2-22222-22-2-2-2-222-2-2222i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ382222-2-2-2-2222-2-22222-22-2-2-2-222-2-222−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ392222-2-2-2-22-2-22222222-2-2-2-2-2-2-222-2-200002200000000000000000000000000002i−2i−2i2i00
χ402222-2-2-2-22-2-22222222-2-2-2-2-2-2-222-2-20000220000000000000000000000000000−2i2i2i−2i00
χ412222-2-2-2-2-122-2-2-1-1-12-221111-1-111-1-12i−2i−2i2i-11−i−iiiii−i−i00003−3−33i3−i3−i3i300000000000000
χ422222-2-2-2-2-122-2-2-1-1-12-221111-1-111-1-12i−2i−2i2i-11−i−iiiii−i−i0000−333−3−i3i3i3−i300000000000000
χ432222-2-2-2-2-122-2-2-1-1-12-221111-1-111-1-1−2i2i2i−2i-11ii−i−i−i−iii00003−3−33−i3i3i3−i300000000000000
χ442222-2-2-2-2-122-2-2-1-1-12-221111-1-111-1-1−2i2i2i−2i-11ii−i−i−i−iii0000−333−3i3−i3−i3i300000000000000
χ4544444444-2-4-4-4-4-2-2-24-4-4-2-2-2-22222220000-220000000000000000000000000000000000
χ46444444-4-4-24444-2-2-2-4-4-4-2-22222-2-2-2-20000220000000000000000000000000000000000
χ474444-4-444-244-4-4-2-2-2-44-422-2-22222-2-200002-20000000000000000000000000000000000
χ484444-4-4-4-4-2-4-444-2-2-244-4222222-2-2220000-2-20000000000000000000000000000000000
χ4944-4-4004-440000-4-44000004-400000000000000000000000000000000002i−2i002i−2i000000
χ5044-4-4004-440000-4-44000004-40000000000000000000000000000000000−2i2i00−2i2i000000
χ5144-4-400-4440000-4-4400000-4400000000000000000000000000000000002i−2i00−2i2i000000
χ5244-4-400-4440000-4-4400000-440000000000000000000000000000000000−2i2i002i−2i000000
χ534-44-44-40044i−4i4i−4i4-4-40004-400004i−4i4i−4i0000000000000000000000000000000000000000
χ544-44-44-4004−4i4i−4i4i4-4-40004-40000−4i4i−4i4i0000000000000000000000000000000000000000
χ554-44-44-400-24i−4i4i−4i-222000-220000−2i2i−2i2i000000−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
χ564-44-44-400-24i−4i4i−4i-222000-220000−2i2i−2i2i000000ζ2+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
χ574-44-44-400-2−4i4i−4i4i-222000-2200002i−2i2i−2i000000−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
χ584-44-44-400-2−4i4i−4i4i-222000-2200002i−2i2i−2i000000ζ2−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
χ594-44-4-440044i−4i−4i4i4-4-4000-440000−4i4i4i−4i0000000000000000000000000000000000000000
χ604-44-4-44004−4i4i4i−4i4-4-4000-4400004i−4i−4i4i0000000000000000000000000000000000000000
χ614-44-4-4400-24i−4i−4i4i-2220002-200002i−2i−2i2i000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ624-44-4-4400-24i−4i−4i4i-2220002-200002i−2i−2i2i000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ634-44-4-4400-2−4i4i4i−4i-2220002-20000−2i2i2i−2i000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ644-44-4-4400-2−4i4i4i−4i-2220002-20000−2i2i2i−2i000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ6588-8-8008-8-4000044-400000-440000000000000000000000000000000000000000000000
χ6688-8-800-88-4000044-4000004-40000000000000000000000000000000000000000000000
χ678-8-88000080000-88-800000000000000000000000000000000000000000000000000000
χ688-8-880000-400004-44000000043−4300000000000000000000000000000000000000000000
χ698-8-880000-400004-440000000−434300000000000000000000000000000000000000000000

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