Finite Group Databasebeta

← Group #13137398

Character table — Group #13137398

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12442346661212121244121212123366121212123666661212121212121212121212121212121212121212121288882244888888242424242424242466121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111-1-1-1-11-11-1-1-111
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111-1-1-1-11111-1-1-1-1-11-1111-1-1
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111
χ911-1-1-1111-1-111-1-1i−iii−i−i1111-1-1-1-11-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1i−ii−i1-1ii−i−i11-1-111-1-1i−ii−i
χ1011-1-1-1111-1-111-1-1i−iii−i−i1111-1-1-1-11-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i-1-111−ii−ii1-1ii−i−i11-1-1-1-111−ii−ii
χ1111-1-1-1111-1-111-1-1i−iii−i−i1111-1-1-1-11-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii1-1-11i−i−ii-11−i−iii-1-1111-1-11i−i−ii
χ1211-1-1-1111-1-111-1-1i−iii−i−i1111-1-1-1-11-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-111-1−iii−i-11−i−iii-1-111-111-1−iii−i
χ1311-1-1-1111-1-111-1-1−ii−i−iii1111-1-1-1-11-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i1-1-11−iii−i-11ii−i−i-1-1111-1-11−iii−i
χ1411-1-1-1111-1-111-1-1−ii−i−iii1111-1-1-1-11-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-111-1i−i−ii-11ii−i−i-1-111-111-1i−i−ii
χ1511-1-1-1111-1-111-1-1−ii−i−iii1111-1-1-1-11-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−ii−ii1-1−i−iii11-1-111-1-1−ii−ii
χ1611-1-1-1111-1-111-1-1−ii−i−iii1111-1-1-1-11-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii-1-111i−ii−i1-1−i−iii11-1-1-1-111i−ii−i
χ17222222222222222222222-12-122-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000202002200000000000-10-100-1-1
χ18222222222222222222222-12-122-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000-20-200-2-2000000000001010011
χ1922222222222222222222-12-12-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000202022000000000000-10-10-1-100
χ2022222222222222222222-12-12-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-20-20-2-200000000000010101100
χ2122222222222222-2-2-2-2-2-22-12-122-1-1-12-1-1-1-12-1-1-1-1-1-2-2111111-2-21111110000020200-2-200000000000-10-10011
χ2222222222222222-2-2-2-2-2-22-12-122-1-1-12-1-1-1-12-1-1-1-1-1-2-2111111-2-211111100000-20-200220000000000010100-1-1
χ2322222222222222-2-2-2-2-2-2-12-12-1-122-1-12-1-1-1-12-1-1-1-111-2-2111111-2-2111100002020-2-2000000000000-10-101100
χ2422222222222222-2-2-2-2-2-2-12-12-1-122-1-12-1-1-1-12-1-1-1-111-2-2111111-2-211110000-20-20220000000000001010-1-100
χ252222-22-22-2-2-2-222000000222222222-2-22-2-2-2-2-2-22200000000000000002-22-200000000002-22-2000000000000
χ262222-22-22-2-2-2-222000000222222222-2-22-2-2-2-2-2-2220000000000000000-22-220000000000-22-22000000000000
χ2722-2-222-2222-2-2-2-20000002222-2-2-2-2222222-2-2-2-2-2-200000000000000002i−2i−2i2i00000000002i−2i−2i2i000000000000
χ2822-2-222-2222-2-2-2-20000002222-2-2-2-2222222-2-2-2-2-2-20000000000000000−2i2i2i−2i0000000000−2i2i2i−2i000000000000
χ2922-2-2-2222-2-222-2-22i−2i2i2i−2i−2i2-12-1-2-211-1-21-1112-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii0000020-2002i−2i00000000000-10100−ii
χ3022-2-2-2222-2-222-2-22i−2i2i2i−2i−2i2-12-1-2-211-1-21-1112-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00000-20200−2i2i0000000000010-100i−i
χ3122-2-2-2222-2-222-2-22i−2i2i2i−2i−2i-12-1211-2-2-11-2-111-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii000020-202i−2i000000000000-1010−ii00
χ3222-2-2-2222-2-222-2-22i−2i2i2i−2i−2i-12-1211-2-2-11-2-111-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii0000-2020−2i2i00000000000010-10i−i00
χ3322-2-2-2222-2-222-2-2−2i2i−2i−2i2i2i2-12-1-2-211-1-21-1112-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i0000020-200−2i2i00000000000-10100i−i
χ3422-2-2-2222-2-222-2-2−2i2i−2i−2i2i2i2-12-1-2-211-1-21-1112-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00000-202002i−2i0000000000010-100−ii
χ3522-2-2-2222-2-222-2-2−2i2i−2i−2i2i2i-12-1211-2-2-11-2-111-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i000020-20−2i2i000000000000-1010i−i00
χ3622-2-2-2222-2-222-2-2−2i2i−2i−2i2i2i-12-1211-2-2-11-2-111-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000-20202i−2i00000000000010-10−ii00
χ3744444444444444444444-2-2-2-2-2-2-2-21-2-2111-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000000000
χ3844444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21-2-2111-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000000000
χ394444-44-44-4-4-4-4440000004-24-244-2-2-2-42-222-4222-2-20000000000000000000000000000000000000000000000
χ404444-44-44-4-4-4-444000000-24-24-2-244-22-4-2222-422-2-20000000000000000000000000000000000000000000000
χ414444-44-44-4-4-4-444000000-2-2-2-2-2-2-2-21221-1-122-1-11100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000
χ424444-44-44-4-4-4-444000000-2-2-2-2-2-2-2-21221-1-122-1-1110000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000
χ4344-4-444-4444-4-4-4-40000004-24-2-4-422-24-2-2-2-2-4222220000000000000000000000000000000000000000000000
χ4444-4-444-4444-4-4-4-4000000-24-2422-4-4-2-24-2-2-22-422220000000000000000000000000000000000000000000000
χ4544-4-444-4444-4-4-4-4000000-2-2-2-222221-2-211122-1-1-1-1000033-3-30000-3-333000000000000000000000000000000
χ4644-4-444-4444-4-4-4-4000000-2-2-2-222221-2-211122-1-1-1-10000-3-333000033-3-3000000000000000000000000000000
χ4744-4-4-4444-4-444-4-44i−4i4i4i−4i−4i-2-2-2-222221221-1-1-2-211-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000
χ4844-4-4-4444-4-444-4-4−4i4i−4i−4i4i4i-2-2-2-222221221-1-1-2-211-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000000
χ494-44i−4i040-400004i−4i00000044-4-44i−4i4i−4i400-40000004i−4i0000000000000000000000000000000000000000000000
χ504-44i−4i040-400004i−4i0000004-2-424i−4i−2i2i-2002000000−2i2i00−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000000000000
χ514-44i−4i040-400004i−4i0000004-2-424i−4i−2i2i-2002000000−2i2i00ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000000000000
χ524-44i−4i040-400004i−4i000000-242-4−2i2i4i−4i-2002000000−2i2i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000000000000
χ534-44i−4i040-400004i−4i000000-242-4−2i2i4i−4i-2002000000−2i2iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000000000000
χ544-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i100-13-3003i−3ii−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11i3−i33−3−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−33i3−i3000000000000000000000000000000
χ554-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i100-13-3003i−3ii−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−i3i3−33ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ113−3−i3i3000000000000000000000000000000
χ564-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i100-1-3300−3i3ii−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−33−i3i3−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−i3i33−3000000000000000000000000000000
χ574-44i−4i040-400004i−4i000000-2-222−2i2i−2i2i100-1-3300−3i3ii−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ113−3i3−i3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11i3−i3−33000000000000000000000000000000
χ584-4−4i4i040-40000−4i4i00000044-4-4−4i4i−4i4i400-4000000−4i4i0000000000000000000000000000000000000000000000
χ594-4−4i4i040-40000−4i4i0000004-2-42−4i4i2i−2i-20020000002i−2i00−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000000000000
χ604-4−4i4i040-40000−4i4i0000004-2-42−4i4i2i−2i-20020000002i−2i00ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000000000000
χ614-4−4i4i040-40000−4i4i000000-242-42i−2i−4i4i-20020000002i−2i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000000000000
χ624-4−4i4i040-40000−4i4i000000-242-42i−2i−4i4i-20020000002i−2iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000000000000
χ634-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i100-13-300−3i3i−ii−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11i3−i3−33−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ113−3i3−i3000000000000000000000000000000
χ644-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i100-13-300−3i3i−iiζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−i3i33−3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−33−i3i3000000000000000000000000000000
χ654-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i100-1-33003i−3i−ii−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ113−3−i3i3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−i3i3−33000000000000000000000000000000
χ664-4−4i4i040-40000−4i4i000000-2-2222i−2i2i−2i100-1-33003i−3i−iiζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−33i3−i3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11i3−i33−3000000000000000000000000000000
χ6766666-36-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022220000000022-1-1-1-1-1-1-1-100000000
χ6866666-36-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-200000000-2-21111111100000000
χ6966666-36-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000222200000000-2-2-1-1-1-1111100000000
χ7066666-36-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-200000000221111-1-1-1-100000000
χ716666-6-3-6-33333-3-30033−3333−330000000000000000000000000000000000002-22-20000000000-11-113−33−300000000
χ726666-6-3-6-33333-3-30033−3333−33000000000000000000000000000000000000-22-2200000000001-11-1−33−3300000000
χ736666-6-3-6-33333-3-300−3333−33330000000000000000000000000000000000002-22-20000000000-11-11−33−3300000000
χ746666-6-3-6-33333-3-300−3333−3333000000000000000000000000000000000000-22-2200000000001-11-13−33−300000000
χ7566-6-66-3-6-3-3-3333300−3i33i33i3−3i30000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i−333−300000000
χ7666-6-66-3-6-3-3-3333300−3i33i33i3−3i3000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii3−3−3300000000
χ7766-6-66-3-6-3-3-33333003i3−3i3−3i33i30000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i3−3−3300000000
χ7866-6-66-3-6-3-3-33333003i3−3i3−3i33i3000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii−333−300000000
χ7966-6-6-6-36-333-3-3336i−6i−3i−3i3i3i0000000000000000000000000000000000002i2i−2i−2i000000002-2−i−iii-1-11100000000
χ8066-6-6-6-36-333-3-3336i−6i−3i−3i3i3i000000000000000000000000000000000000−2i−2i2i2i00000000-22ii−i−i11-1-100000000
χ8166-6-6-6-36-333-3-333−6i6i3i3i−3i−3i0000000000000000000000000000000000002i2i−2i−2i00000000-22−i−iii11-1-100000000
χ8266-6-6-6-36-333-3-333−6i6i3i3i−3i−3i000000000000000000000000000000000000−2i−2i2i2i000000002-2ii−i−i-1-11100000000
χ8312-1212i−12i0-606−6i36i363−63−6i6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212i−12i0-6066i3−6i3−6363−6i6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12−12i12i0-606−6i36i3−63636i−6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12−12i12i0-6066i3−6i363−636i−6i000000000000000000000000000000000000000000000000000000000000000000000000

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