Finite Group Databasebeta

← Group #13141086

Character table — Group #13141086

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222244444444466666612121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order12234462466612121212336612123666121212121266666121212121224444466121212121212121212122668824242424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-111
χ51111111-1-11-1-111-1-1111111111111111-1-11-1-1-1-11-1-111-1-1111111-1-1-1-11111-1-1-1-11-1-111
χ61111111-1-11-1-111-1-1111111111111111-1-11-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1
χ71111111-1-11-1-111-1-1111111111111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1
χ81111111-1-11-1-111-1-1111111111111111-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111
χ922222222222222222-12-122-1-1-122-1-1-1-12-1-1-1-12-1-1-1-10000000000000000002-1-10200-1-1
χ1022222222222222222-12-122-1-1-122-1-1-1-12-1-1-1-12-1-1-1-1000000000000000000-2110-20011
χ112222222222222222-12-12-1-1-12-1-1-12-1-12-12-1-1-1-12-1-1-100002200000000-1-1-1-100020-1-100
χ122222222222222222-12-12-1-1-12-1-1-12-1-12-12-1-1-1-12-1-1-10000-2-2000000001111000-201100
χ132222222-2-22-2-222-2-22-12-122-1-1-122-1-1-1-1-21-111-21-1110000000000000000002-1-10-20011
χ142222222-2-22-2-222-2-22-12-122-1-1-122-1-1-1-1-21-111-21-111000000000000000000-2110200-1-1
χ152222222-2-22-2-222-2-2-12-12-1-1-12-1-1-12-1-121-2-1111-2-11100002200000000-1-1-1-1000-201100
χ162222222-2-22-2-222-2-2-12-12-1-1-12-1-1-12-1-121-2-1111-2-1110000-2-200000000111100020-1-100
χ172222-2-2200200-2-2002222-2-22222-2-2-2-2-20020000-200002-200000022-2-20000000000000
χ182222-2-2200200-2-2002222-2-22222-2-2-2-2-20020000-20000-22000000-2-2220000000000000
χ1922-222-2200-2002-2002222222-22-2-2222-200-20000-2002-2000022-2-200000000000000000
χ2022-222-2200-2002-2002222222-22-2-2222-200-20000-200-220000-2-22200000000000000000
χ2122-22-2222-2-222-22-2-22222-2-22-22-22-2-2-2222-222-2-22-2-2000000000000000000000000000
χ2222-22-2222-2-222-22-2-22-12-1-2-2-11-1-22111-12-11-1-1-21-1110000000000000000000−i3i30000−i3i3
χ2322-22-2222-2-222-22-2-22-12-1-2-2-11-1-22111-12-11-1-1-21-1110000000000000000000i3−i30000i3−i3
χ2422-22-2222-2-222-22-2-2-12-1211-1-2-11-1-2112-121-1-11-2-1110000000000000033−3−3000003−300
χ2522-22-2222-2-222-22-2-2-12-1211-1-2-11-1-2112-121-1-11-2-11100000000000000−3−33300000−3300
χ2622-22-222-22-2-2-2-22222222-2-22-22-22-2-2-22-2-2-2-2-222222000000000000000000000000000
χ2722-22-222-22-2-2-2-22222-12-1-2-2-11-1-22111-1-211112-1-1-1-10000000000000000000−i3i30000i3−i3
χ2822-22-222-22-2-2-2-22222-12-1-2-2-11-1-22111-1-211112-1-1-1-10000000000000000000i3−i30000−i3i3
χ2922-22-222-22-2-2-2-2222-12-1211-1-2-11-1-21121-2111-12-1-1-10000000000000033−3−300000−3300
χ3022-22-222-22-2-2-2-2222-12-1211-1-2-11-1-21121-2111-12-1-1-100000000000000−3−333000003−300
χ314444444444444444-2-2-2-2-2-21-21-2-2-211-2-2-2111-2-2111000000000000000000000000000
χ324444444-4-44-4-444-4-4-2-2-2-2-2-21-21-2-2-211-2221-1-1221-1-1000000000000000000000000000
χ334444-4-4400400-4-4004-24-2-4-4-2-2-24-4222200-20000200000000000000000000000000000
χ344444-4-4400400-4-400-24-2422-24-2-22-422-400-20000200000000000000000000000000000
χ354444-4-4400400-4-400-2-2-2-2221-21-222-1-120013-300-13-3000000000000000000000000000
χ364444-4-4400400-4-400-2-2-2-2221-21-222-1-12001-3300-1-33000000000000000000000000000
χ3744-444-4400-4004-4004-24-244-22-2-4-4-2-2-220020000200000000000000000000000000000
χ3844-444-4400-4004-400-24-24-2-2-2-4-2224-2-2-40020000200000000000000000000000000000
χ3944-444-4400-4004-400-2-2-2-2-2-212122-211200-13-300-1-33000000000000000000000000000
χ4044-444-4400-4004-400-2-2-2-2-2-212122-211200-1-3300-13-3000000000000000000000000000
χ4144-44-4444-4-444-44-4-4-2-2-2-2221212-22-1-1-2-2-2-111221-1-1000000000000000000000000000
χ4244-44-444-44-4-4-4-4444-2-2-2-2221212-22-1-1-222-1-1-1-2-2111000000000000000000000000000
χ434-40400-400000000044-4-40040-4000000000000000000002i−2i000000002i−2i2i−2i000000000
χ444-40400-400000000044-4-40040-400000000000000000000−2i2i00000000−2i2i−2i2i000000000
χ454-40400-4000000000-242-423−23-20200023−230000000000000002i−2i00000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000
χ464-40400-4000000000-242-423−23-20200023−23000000000000000−2i2i00000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000
χ474-40400-4000000000-242-4−2323-202000−23230000000000000002i−2i00000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000
χ484-40400-4000000000-242-4−2323-202000−2323000000000000000−2i2i00000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000
χ49666-366-366-3-3-3-3-3-3-30000000000000000000000000222200-1-1-1-1-1-1-1-10000000000000
χ50666-366-366-3-3-3-3-3-3-30000000000000000000000000-2-2-2-200111111110000000000000
χ51666-366-3-6-6-333-3-333000000000000000000000000022-2-200-1-1-1-111110000000000000
χ52666-366-3-6-6-333-3-3330000000000000000000000000-2-222001111-1-1-1-10000000000000
χ53666-3-6-6-300-3−3i33i333−3i33i30000000000000000000000000002-200−i3i3−i3i3-1-1110000000000000
χ54666-3-6-6-300-3−3i33i333−3i33i3000000000000000000000000000-2200i3−i3i3−i311-1-10000000000000
χ55666-3-6-6-300-33i3−3i3333i3−3i30000000000000000000000000002-200i3−i3i3−i3-1-1110000000000000
χ56666-3-6-6-300-33i3−3i3333i3−3i3000000000000000000000000000-2200−i3i3−i3i311-1-10000000000000
χ5766-6-36-6-3003−3i33i3-333i3−3i300000000000000000000000002-20000-1-111−i3i3−i3i30000000000000
χ5866-6-36-6-3003−3i33i3-333i3−3i30000000000000000000000000-22000011-1-1i3−i3i3−i30000000000000
χ5966-6-36-6-30033i3−3i3-33−3i33i300000000000000000000000002-20000-1-111i3−i3i3−i30000000000000
χ6066-6-36-6-30033i3−3i3-33−3i33i30000000000000000000000000-22000011-1-1−i3i3−i3i30000000000000
χ6166-6-3-66-36-63-3-33-3330000000000000000000000000000000−i3i3i3−i3−i3i3i3−i30000000000000
χ6266-6-3-66-36-63-3-33-3330000000000000000000000000000000i3−i3−i3i3i3−i3−i3i30000000000000
χ6366-6-3-66-3-663333-3-3-30000000000000000000000000000000−i3i3i3−i3i3−i3−i3i30000000000000
χ6466-6-3-66-3-663333-3-3-30000000000000000000000000000000i3−i3−i3i3−i3i3i3−i30000000000000
χ658-80800-80000000008-4-8400-4040000000000000000000000000000000000000000000
χ668-80800-8000000000-4-44443−4320-2000−232300000000000000000000000000000000000000
χ678-80800-8000000000-4-444−434320-200023−2300000000000000000000000000000000000000
χ6824-240-1200120000000000000000000000000000000000000000000000000000000000000

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