Finite Group Databasebeta

← Group #13149883

Character table — Group #13149883

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222224444444466661212121212121212121218181818181818181818242424242424242424243636363636363636363636363636367272727272727272
order1223446121268812242424243366366612121212121222448824242424612242424242424242422222244668121224246666661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11-1-1-1-1-1-1-1-1111-1-1-11-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111-11-1-1-1-1-1-1-1-1-1-1111-11
χ51111111111-1-11-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1-1111-111-1-111-11-1-1-11
χ61111111111-1-11-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1111-111-111-1-1-1-11-1111-1
χ71111111111-1-11-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-11111-1-111-1-1
χ81111111111-1-11-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-111-1-111-1-111
χ911-11-11111-11-1-111-1-111111-1-11-1-111111-11-1111111-1-11111-1-1-1-11-1111-1-1-11-1-11-1-1-11-1111-1-1-1
χ1011-11-11111-11-1-111-1-111111-1-11-1-111111-11-1111111-1-11111-1-1-1-1-11-1-1-11111-1-11-1-1-1-11-1-1-1111
χ1111-11-11111-11-1-111-1-111111-1-11-1-11111-11-11-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-11-11-111-11111-11-1-11-11
χ1211-11-11111-11-1-111-1-111111-1-11-1-11111-11-11-1-1-1-1-1-1-1-11111-1-1-1-1-11-111-11-1-111-1111-11-111-11-1
χ1311-11-11111-1-11-1-1-11111111-1-11-1-111111-11-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-111-11-111-1111-1-11-111-1
χ1411-11-11111-1-11-1-1-11111111-1-11-1-111111-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11-1-111-111-111-111-11-1-11
χ1511-11-11111-1-11-1-1-11111111-1-11-1-11111-11-11111111-1-1-1-1-1-111111-1-1-11-111-11-1-11-1-11-1-1-11-111
χ1611-11-11111-1-11-1-1-11111111-1-11-1-11111-11-11111111-1-1-1-1-1-11111-1111-11-1-1-11-1-11-1-1-1111-11-1-1
χ17222222222222222222-12-1-12-1-12-12-1-1-10000000000-1-12-1-1-12-1-1-1000222020000000000-1-1-10-1
χ18222222222222222222-12-1-12-1-12-12-1-1-10000000000-1-12-1-1-12-1-1-1000-2-2-20-2000000000011101
χ1922222222222222222-12-12-1-12-1-12-12-1-10000000000-1-1-12-1-1-12-1-1222000200000000-1-1-1000-10
χ2022222222222222222-12-12-1-12-1-12-12-1-10000000000-1-1-12-1-1-12-1-1-2-2-2000-20000000011100010
χ212222222222-2-22-2-2-2-22-12-1-12-1-12-12-1-1-10000000000-1-1-2111-21110002-2-2020000000000-1110-1
χ222222222222-2-22-2-2-2-22-12-1-12-1-12-12-1-1-10000000000-1-1-2111-2111000-2220-200000000001-1-101
χ232222222222-2-22-2-2-2-2-12-12-1-12-1-12-12-1-10000000000-1-11-2111-21122-2000-200000000-1-1100010
χ242222222222-2-22-2-2-2-2-12-12-1-12-1-12-12-1-10000000000-1-11-2111-211-2-2200020000000011-1000-10
χ252222-2-22-2-2200-2000022222222-2-2-2-2-2-22-2-220000002-200000000000000002-20-220000000000
χ262222-2-22-2-2200-2000022222222-2-2-2-2-2-2-222-20000002-20000000000000000-2202-20000000000
χ2722-222-22-2-2-2002000022222-2-2222-2-2-2-222-2-2000000-220000000000000000220-2-20000000000
χ2822-222-22-2-2-2002000022222-2-2222-2-2-2-2-2-222000000-220000000000000000-2-20220000000000
χ2922-22-22222-22-2-222-2-22-12-1-1-21-1-212-1-1-10000000000112-1-1-1-211100022-20-20000000000-1-1101
χ3022-22-22222-22-2-222-2-22-12-1-1-21-1-212-1-1-10000000000112-1-1-1-2111000-2-2202000000000011-10-1
χ3122-22-22222-22-2-222-2-2-12-12-11-2-11-2-12-1-1000000000011-12-1-11-2112-22000-200000000-11-100010
χ3222-22-22222-22-2-222-2-2-12-12-11-2-11-2-12-1-1000000000011-12-1-11-211-22-20002000000001-11000-10
χ3322-22-22222-2-22-2-2-2222-12-1-1-21-1-212-1-1-1000000000011-21112-1-1-10002-220-20000000000-11-101
χ3422-22-22222-2-22-2-2-2222-12-1-1-21-1-212-1-1-1000000000011-21112-1-1-1000-22-20200000000001-110-1
χ3522-22-22222-2-22-2-2-222-12-12-11-2-11-2-12-1-10000000000111-211-12-1-12-2-2000200000000-111000-10
χ3622-22-22222-2-22-2-2-222-12-12-11-2-11-2-12-1-10000000000111-211-12-1-1-222000-2000000001-1-100010
χ3744444444444444444-2-2-2-21-2-21-2-2-2-211000000000011-2-211-2-21100000000000000000000000
χ384444444444-4-44-4-4-4-4-2-2-2-21-2-21-2-2-2-21100000000001122-1-122-1-100000000000000000000000
χ394444-4-44-4-4400-400004-24-2-24-2-2-42-42220000000000-220000000000000000000000000000000
χ404444-4-44-4-4400-40000-24-24-2-24-22-42-4220000000000-220000000000000000000000000000000
χ414444-4-44-4-4400-40000-2-2-2-21-2-212222-1-100000000001-1003i−3i003i−3i00000000000000000000000
χ424444-4-44-4-4400-40000-2-2-2-21-2-212222-1-100000000001-100−3i3i00−3i3i00000000000000000000000
χ4344-444-44-4-4-400400004-24-2-2-42-24-2-422200000000002-20000000000000000000000000000000
χ4444-444-44-4-4-40040000-24-24-22-4-2-242-42200000000002-20000000000000000000000000000000
χ4544-444-44-4-4-40040000-2-2-2-21221-2-222-1-10000000000-11003i−3i00−3i3i00000000000000000000000
χ4644-444-44-4-4-40040000-2-2-2-21221-2-222-1-10000000000-1100−3i3i003i−3i00000000000000000000000
χ4744-44-44444-44-4-444-4-4-2-2-2-2122122-2-2110000000000-1-1-2-21122-1-100000000000000000000000
χ4844-44-44444-4-44-4-4-444-2-2-2-2122122-2-2110000000000-1-122-1-1-2-21100000000000000000000000
χ494-40400-4000000000044-4-4400-4000000000022−222222−22−22000000000000000000000000000000000
χ504-40400-4000000000044-4-4400-40000000000−2222−22−222222000000000000000000000000000000000
χ51666-366-3-3-3-366-3-3-3-3-300000000000000222222-1-1-1-1000000000000000000-1-12-1-1-1-100000000
χ52666-366-3-3-3-366-3-3-3-3-300000000000000-2-2-2-2-2-2111100000000000000000011-2111100000000
χ53666-366-3-3-3-3-6-6-33333000000000000002222-2-21111000000000000000000-1-1-2-1-11100000000
χ54666-366-3-3-3-3-6-6-3333300000000000000-2-2-2-222-1-1-1-100000000000000000011211-1-100000000
χ55666-3-6-6-333-300333−3333−33000000000000002-2-22003−33−3000000000000000000-1101-13−300000000
χ56666-3-6-6-333-300333−3333−3300000000000000-222-200−33−330000000000000000001-10-11−3300000000
χ57666-3-6-6-333-3003−3333−3333000000000000002-2-2200−33−33000000000000000000-1101-1−3300000000
χ58666-3-6-6-333-3003−3333−333300000000000000-222-2003−33−30000000000000000001-10-113−300000000
χ5966-6-36-6-333300-333−33−33330000000000000022-2-2003−33−3000000000000000000-1-1011−3300000000
χ6066-6-36-6-333300-333−33−333300000000000000-2-22200−33−33000000000000000000110-1-13−300000000
χ6166-6-36-6-333300-3−333333−330000000000000022-2-200−33−33000000000000000000-1-10113−300000000
χ6266-6-36-6-333300-3−333333−3300000000000000-2-222003−33−3000000000000000000110-1-1−3300000000
χ6366-6-3-66-3-3-336-63-3-333000000000000002-22-222-1-1-1-1000000000000000000-11-2-111100000000
χ6466-6-3-66-3-3-336-63-3-33300000000000000-22-22-2-211110000000000000000001-121-1-1-100000000
χ6566-6-3-66-3-3-33-66333-3-3000000000000002-22-2-2-21111000000000000000000-112-11-1-100000000
χ6666-6-3-66-3-3-33-66333-3-300000000000000-22-2222-1-1-1-10000000000000000001-1-21-11100000000
χ678-80800-800000000008-4-84-40040000000000000000000000000000000000000000000000000
χ688-80800-80000000000-484-8-40040000000000000000000000000000000000000000000000000
χ698-80800-80000000000-4-444200-200006i−6i0000000000000000000000000000000000000000000
χ708-80800-80000000000-4-444200-20000−6i6i0000000000000000000000000000000000000000000
χ7112-120-600663−630000000000000000000000000022−222ζ13−2ζ232ζ5−2ζ7−2ζ13+2ζ23−2ζ5+2ζ7000000000000000000000000000000000
χ7212-120-600663−6300000000000000000000000000−2222−2ζ13+2ζ23−2ζ5+2ζ72ζ13−2ζ232ζ5−2ζ7000000000000000000000000000000000
χ7312-120-6006−63630000000000000000000000000022−222ζ5−2ζ72ζ13−2ζ23−2ζ5+2ζ7−2ζ13+2ζ23000000000000000000000000000000000
χ7412-120-6006−636300000000000000000000000000−2222−2ζ5+2ζ7−2ζ13+2ζ232ζ5−2ζ72ζ13−2ζ23000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.