Finite Group Databasebeta

← Group #13146690

Character table — Group #13146690

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222121212121212121218181818181818181818181818181818181818181818181818181818181818181818181824242424727272727272727272727272
order12222236666666336666664444888888881212121212121212242424242424242424242424242424246666244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ51111-1-1111-1-1-1-11111111111-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111-1-1111-1-1-1-11111111111-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
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
χ1122-2-20022-20000-222-22-22-2-202i−2i022−2−2−i2−i2i2i2002i2i−2i−2i002222−2−2−2−2−i2−i2−i2−i2i2i2i2i20000000000000000
χ1222-2-20022-20000-222-22-22-2-202i−2i0−2−222i2i2−i2−i2002i2i−2i−2i00−2−2−2−22222i2i2i2i2−i2−i2−i2−i20000000000000000
χ1322-2-20022-20000-222-22-22-2-20−2i2i022−2−2i2i2−i2−i200−2i−2i2i2i002222−2−2−2−2i2i2i2i2−i2−i2−i2−i20000000000000000
χ1422-2-20022-20000-222-22-22-2-20−2i2i0−2−222−i2−i2i2i200−2i−2i2i2i00−2−2−2−22222−i2−i2−i2−i2i2i2i2i20000000000000000
χ152-22-22-22-2222-2-2-2222-2-2-2-220000−i2i2−i2i2−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-2000000000000
χ162-22-22-22-2222-2-2-2222-2-2-2-220000i2−i2i2−i2i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-2000000000000
χ172-22-2-222-22-2-222-2222-2-2-2-220000−i2i2−i2i2i2−i2i2−i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-22-22000000000000
χ182-22-2-222-22-2-222-2222-2-2-2-220000i2−i2i2−i2−i2i2−i2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22-22000000000000
χ192-2-22002-2-20000222-2-22-22-2200-22i−2i−2i2i0000220000-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ202-2-22002-2-20000222-2-22-22-2200-2−2i2i2i−2i0000220000-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ212-2-22002-2-20000222-2-22-22-2-200200002-2-22-2-20000220000000022-2-2-2-2220000000000000000
χ222-2-22002-2-20000222-2-22-22-2-20020000-222-2-2-200002200000000-2-22222-2-20000000000000000
χ23444444444444441-21-2-211-200000000000000000000000000000000000011-2-200220000-1-1-1-1
χ24444444444444441-21-2-211-200000000000000000000000000000000000011-2-200-2-200001111
χ2544444444444444-21-211-2-21000000000000000000000000000000000000-2-2112200-1-1-1-10000
χ2644444444444444-21-211-2-21000000000000000000000000000000000000-2-211-2-20011110000
χ274444-4-4444-4-4-4-441-21-2-211-2000000000000000000000000000000000000-1-122002-20000-1-111
χ284444-4-4444-4-4-4-441-21-2-211-2000000000000000000000000000000000000-1-12200-22000011-1-1
χ294444-4-4444-4-4-4-44-21-211-2-2100000000000000000000000000000000000022-1-12-200-1-1110000
χ304444-4-4444-4-4-4-44-21-211-2-2100000000000000000000000000000000000022-1-1-220011-1-10000
χ314-44-44-44-4444-4-4-41-2122-1-1-20000000000000000000000000000000000001-1-22000000003−33−3
χ324-44-44-44-4444-4-4-41-2122-1-1-20000000000000000000000000000000000001-1-2200000000−33−33
χ334-44-44-44-4444-4-4-4-21-2-1-1221000000000000000000000000000000000000-221-10000−i3i3−i3i30000
χ344-44-44-44-4444-4-4-4-21-2-1-1221000000000000000000000000000000000000-221-10000i3−i3i3−i30000
χ354-44-4-444-44-4-444-41-2122-1-1-2000000000000000000000000000000000000-112-2000000003−3−33
χ364-44-4-444-44-4-444-41-2122-1-1-2000000000000000000000000000000000000-112-200000000−333−3
χ374-44-4-444-44-4-444-4-21-2-1-12210000000000000000000000000000000000002-2-110000−i3i3i3−i30000
χ384-44-4-444-44-4-444-4-21-2-1-12210000000000000000000000000000000000002-2-110000i3−i3−i3i30000
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
χ556-66-66-6-33-3-3-3333000000000000−i2i2−i2i2−i2i2−i2i23−33−33−3−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ566-66-66-6-33-3-3-3333000000000000−i2i2−i2i2−i2i2−i2i2−33−33−333−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ576-66-66-6-33-3-3-3333000000000000i2−i2i2−i2i2−i2i2−i23−33−33−3−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ586-66-66-6-33-3-3-3333000000000000i2−i2i2−i2i2−i2i2−i2−33−33−333−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ596-66-6-66-33-333-3-33000000000000−i2i2−i2i2i2−i2i2−i23−3−33−33−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ606-66-6-66-33-333-3-33000000000000−i2i2−i2i2i2−i2i2−i2−333−33−33−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ616-66-6-66-33-333-3-33000000000000i2−i2i2−i2−i2i2−i2i23−3−33−33−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ626-66-6-66-33-333-3-33000000000000i2−i2i2−i2−i2i2−i2i2−333−33−33−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ636-6-6600-333−3i33i33i3−3i3-300000000200-200002-2-22-1-1−i3i3i3−i311−i3i3i3−i3i3−i3−i3i3-1-11111-1-10000000000000000
χ646-6-6600-333−3i33i33i3−3i3-300000000200-20000-222-2-1-1−i3i3i3−i311i3−i3−i3i3−i3i3i3−i311-1-1-1-1110000000000000000
χ656-6-6600-333−3i33i33i3−3i3-300000000-20022i−2i−2i2i000011i3−i3−i3i3-1-1−i−iiiii−i−i3−3−33−333−30000000000000000
χ666-6-6600-333−3i33i33i3−3i3-300000000-2002−2i2i2i−2i000011i3−i3−i3i3-1-1ii−i−i−i−iii−333−33−3−330000000000000000
χ676-6-6600-3333i3−3i3−3i33i3-300000000200-200002-2-22-1-1i3−i3−i3i311i3−i3−i3i3−i3i3i3−i3-1-11111-1-10000000000000000
χ686-6-6600-3333i3−3i3−3i33i3-300000000200-20000-222-2-1-1i3−i3−i3i311−i3i3i3−i3i3−i3−i3i311-1-1-1-1110000000000000000
χ696-6-6600-3333i3−3i3−3i33i3-300000000-20022i−2i−2i2i000011−i3i3i3−i3-1-1−i−iiiii−i−i−333−33−3−330000000000000000
χ706-6-6600-3333i3−3i3−3i33i3-300000000-2002−2i2i2i−2i000011−i3i3i3−i3-1-1ii−i−i−i−iii3−3−33−333−30000000000000000
χ7188-8-80088-80000-82-4-2-442-240000000000000000000000000000000000000000000000000000
χ7288-8-80088-80000-8-4242-2-44-20000000000000000000000000000000000000000000000000000
χ738-8-88008-8-8000082-4-24-4-2240000000000000000000000000000000000000000000000000000
χ748-8-88008-8-800008-424-224-4-20000000000000000000000000000000000000000000000000000

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