Finite Group Databasebeta

← Group #13146694

Character table — Group #13146694

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222121212121212121218181818181818181818181818181818181818181818181818181818181818181818181824242424727272727272727272727272
order122222366666663366666644448888888812121212121212122424242424242424242424242424242466662244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-111
χ51111-1-1111-1-1-1-11111111111-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111-1-1111-1-1-1-11111111111-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111-1-1111-1-1-1-11111111111-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111
χ81111-1-1111-1-1-1-11111111111-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1
χ92222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-200000000000000002222000000000000
χ102222-2-2222-2-2-2-2222222222-222-200000000-2-22222-2-20000000000000000-2-2-2-2000000000000
χ1122-2-20022-20000-22222-2-2-2-202i−2i022−2−2−i2−i2i2i2002i2i−2i−2i002222−2−2−2−2−i2−i2−i2−i2i2i2i2i20000000000000000
χ1222-2-20022-20000-22222-2-2-2-202i−2i0−2−222i2i2−i2−i2002i2i−2i−2i00−2−2−2−22222i2i2i2i2−i2−i2−i2−i20000000000000000
χ1322-2-20022-20000-22222-2-2-2-20−2i2i022−2−2i2i2−i2−i200−2i−2i2i2i002222−2−2−2−2i2i2i2i2−i2−i2−i2−i20000000000000000
χ1422-2-20022-20000-22222-2-2-2-20−2i2i0−2−222−i2−i2i2i200−2i−2i2i2i00−2−2−2−22222−i2−i2−i2−i2i2i2i2i20000000000000000
χ152-22-2002-2-20000222-2-222-2-2200-200002i−2i2i−2i220000-2-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ162-22-2002-2-20000222-2-222-2-2200-20000−2i2i−2i2i220000-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ172-22-2002-2-20000222-2-222-2-2-20022-22-20000-2-200002222-2-222-2-2000000000000000000000000
χ182-22-2002-2-20000222-2-222-2-2-2002-22-220000-2-2000022-2-222-2-222000000000000000000000000
χ192-2-222-22-2222-2-2-222-2-2-2-22200002−2−222−2−220000000022−2−2−2−22222−2−2−2−22222-2-2000000000000
χ202-2-222-22-2222-2-2-222-2-2-2-2220000−222−2−222−200000000−2−22222−2−2−2−22222−2−222-2-2000000000000
χ212-2-22-222-22-2-222-222-2-2-2-22200002−2−22−222−20000000022−2−2−2−222−2−22222−2−2-2-222000000000000
χ222-2-22-222-22-2-222-222-2-2-2-2220000−222−22−2−2200000000−2−22222−2−222−2−2−2−222-2-222000000000000
χ23444444444444441-21-21-21-20000000000000000000000000000000000001-21-2020200-1-100-1-1
χ24444444444444441-21-21-21-20000000000000000000000000000000000001-21-20-20-200110011
χ2544444444444444-21-21-21-21000000000000000000000000000000000000-21-212020-1-100-1-100
χ2644444444444444-21-21-21-21000000000000000000000000000000000000-21-21-20-2011001100
χ274444-4-4444-4-4-4-441-21-21-21-2000000000000000000000000000000000000-12-12020-200-1-10011
χ284444-4-4444-4-4-4-441-21-21-21-2000000000000000000000000000000000000-12-120-202001100-1-1
χ294444-4-4444-4-4-4-44-21-21-21-210000000000000000000000000000000000002-12-120-20-1-1001100
χ304444-4-4444-4-4-4-44-21-21-21-210000000000000000000000000000000000002-12-1-20201100-1-100
χ314-4-444-44-4444-4-4-41-2-12-121-20000000000000000000000000000000000001-2-12000000−i3i300−i3i3
χ324-4-444-44-4444-4-4-41-2-12-121-20000000000000000000000000000000000001-2-12000000i3−i300i3−i3
χ334-4-444-44-4444-4-4-4-212-12-1-21000000000000000000000000000000000000-212-10000−i3i300−i3i300
χ344-4-444-44-4444-4-4-4-212-12-1-21000000000000000000000000000000000000-212-10000i3−i300i3−i300
χ354-4-44-444-44-4-444-41-2-12-121-2000000000000000000000000000000000000-121-2000000−i3i300i3−i3
χ364-4-44-444-44-4-444-41-2-12-121-2000000000000000000000000000000000000-121-2000000i3−i300−i3i3
χ374-4-44-444-44-4-444-4-212-12-1-210000000000000000000000000000000000002-1-210000−i3i300i3−i300
χ384-4-44-444-44-4-444-4-212-12-1-210000000000000000000000000000000000002-1-210000i3−i300−i3i300
χ39666666-3-3-3-3-3-3-3-300000000222200000000-1-1-1-1-1-1-1-13−33−33−33−33−33−33−33−30000000000000000
χ40666666-3-3-3-3-3-3-3-300000000222200000000-1-1-1-1-1-1-1-1−33−33−33−33−33−33−33−330000000000000000
χ41666666-3-3-3-3-3-3-3-300000000-2-2-2-22222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ42666666-3-3-3-3-3-3-3-300000000-2-2-2-2-2-2-2-2-2-2-2-21111111111111111111111110000000000000000
χ436666-6-6-3-3-33333-3000000002-2-2200000000-1-11111-1-13−33−33−33−3−33−33−33−330000000000000000
χ446666-6-6-3-3-33333-3000000002-2-2200000000-1-11111-1-1−33−33−33−333−33−33−33−30000000000000000
χ456666-6-6-3-3-33333-300000000-222-22222-2-2-2-211-1-1-1-111-1-1-1-1-1-1-1-1111111110000000000000000
χ466666-6-6-3-3-33333-300000000-222-2-2-2-2-2222211-1-1-1-11111111111-1-1-1-1-1-1-1-10000000000000000
χ4766-6-600-3-33−3i33i3−3i33i330000000002i−2i022−2−2i2i2−i2−i23−3−i−iii3−3ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ4866-6-600-3-33−3i33i3−3i33i330000000002i−2i0−2−222−i2−i2i2i23−3−i−iii3−3−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ4966-6-600-3-33−3i33i3−3i33i33000000000−2i2i022−2−2−i2−i2i2i2−33ii−i−i−33ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ5066-6-600-3-33−3i33i3−3i33i33000000000−2i2i0−2−222i2i2−i2−i2−33ii−i−i−33−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ5166-6-600-3-333i3−3i33i3−3i330000000002i−2i022−2−2i2i2−i2−i2−33−i−iii−33ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ5266-6-600-3-333i3−3i33i3−3i330000000002i−2i0−2−222−i2−i2i2i2−33−i−iii−33−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ5366-6-600-3-333i3−3i33i3−3i33000000000−2i2i022−2−2−i2−i2i2i23−3ii−i−i3−3ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ5466-6-600-3-333i3−3i33i3−3i33000000000−2i2i0−2−222i2i2−i2−i23−3ii−i−i3−3−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ556-66-600-333−3i33i33i3−3i3-300000000200-22-22-20000-1-1−i3i3−i3i311-1-111-1-111−i3i3i3−i3−i3i3i3−i30000000000000000
χ566-66-600-333−3i33i33i3−3i3-300000000200-2-22-220000-1-1−i3i3−i3i31111-1-111-1-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ576-66-600-333−3i33i33i3−3i3-300000000-200200002i−2i2i−2i11i3−i3i3−i3-1-13−3−333−3−33−i−iii−i−iii0000000000000000
χ586-66-600-333−3i33i33i3−3i3-300000000-20020000−2i2i−2i2i11i3−i3i3−i3-1-1−333−3−333−3ii−i−iii−i−i0000000000000000
χ596-66-600-3333i3−3i3−3i33i3-300000000200-22-22-20000-1-1i3−i3i3−i311-1-111-1-111i3−i3−i3i3i3−i3−i3i30000000000000000
χ606-66-600-3333i3−3i3−3i33i3-300000000200-2-22-220000-1-1i3−i3i3−i31111-1-111-1-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ616-66-600-3333i3−3i3−3i33i3-300000000-200200002i−2i2i−2i11−i3i3−i3i3-1-1−333−3−333−3−i−iii−i−iii0000000000000000
χ626-66-600-3333i3−3i3−3i33i3-300000000-20020000−2i2i−2i2i11−i3i3−i3i3-1-13−3−333−3−33ii−i−iii−i−i0000000000000000
χ636-6-666-6-33-3-3-33330000000000002−2−222−2−223−33−3−33−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ646-6-666-6-33-3-3-33330000000000002−2−222−2−22−33−333−33−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ656-6-666-6-33-3-3-3333000000000000−222−2−222−23−33−3−33−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ666-6-666-6-33-3-3-3333000000000000−222−2−222−2−33−333−33−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ676-6-66-66-33-333-3-330000000000002−2−22−222−23−3−333−3−33ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ686-6-66-66-33-333-3-330000000000002−2−22−222−2−333−3−333−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ696-6-66-66-33-333-3-33000000000000−222−22−2−223−3−333−3−33−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ706-6-66-66-33-333-3-33000000000000−222−22−2−22−333−3−333−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ7188-8-80088-80000-82-42-4-24-240000000000000000000000000000000000000000000000000000
χ7288-8-80088-80000-8-42-424-24-20000000000000000000000000000000000000000000000000000
χ738-88-8008-8-8000082-4-242-4-240000000000000000000000000000000000000000000000000000
χ748-88-8008-8-800008-424-2-424-20000000000000000000000000000000000000000000000000000

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