Finite Group Databasebeta

← Group #13146553

Character table — Group #13146553

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222121212121212121218181818181818181818181818181818181818181818181818181818181818181818181824242424727272727272727272727272
order12223446661212121233666666444488888888121212121212121224242424242424242424242424242424121212122244666612121212
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
χ511111-1-1111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ611111-1-1111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ711111-1-1111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111
χ811111-1-1111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1
χ92222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-200000000000000002222000000000000
χ1022222-2-2222-2-2-2-22222222222-2-2000000002222-2-2-2-20000000000000000-2-2-2-2000000000000
χ1122-2-222-22-2-222-2-222-2-2-222-20000−i2−i2i2i2−i2−i2i2i200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i222-2-2000000000000
χ1222-2-222-22-2-222-2-222-2-2-222-20000i2i2−i2−i2i2i2−i2−i200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i222-2-2000000000000
χ1322-2-22-222-2-2-2-22222-2-2-222-20000−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-2-222000000000000
χ1422-2-22-222-2-2-2-22222-2-2-222-20000i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2-222000000000000
χ152-22-2200-22-200002222-2-2-2-2002-200002i−2i2i−2i000022-2-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ162-22-2200-22-200002222-2-2-2-2002-20000−2i2i−2i2i000022-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ172-22-2200-22-200002222-2-2-2-200-222i−2i2i−2i00000000-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ182-22-2200-22-200002222-2-2-2-200-22−2i2i−2i2i00000000-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ192-2-22200-2-22000022-2-22-2-222-2002−2−222−2−2222-2-2000022−2−2−2−22222−2−2−2−2220000000000000000
χ202-2-22200-2-22000022-2-22-2-222-200−222−2−222−222-2-20000−2−22222−2−2−2−22222−2−20000000000000000
χ212-2-22200-2-22000022-2-22-2-22-22002−2−22−222−2-2-222000022−2−2−2−222−2−22222−2−20000000000000000
χ222-2-22200-2-22000022-2-22-2-22-2200−222−22−2−22-2-2220000−2−22222−2−222−2−2−2−2220000000000000000
χ23444444444444441-21-2-21-210000000000000000000000000000000000001-21-200220000-1-1-1-1
χ24444444444444441-21-2-21-210000000000000000000000000000000000001-21-200-2-200001111
χ2544444444444444-21-211-21-2000000000000000000000000000000000000-21-212200-1-1-1-10000
χ2644444444444444-21-211-21-2000000000000000000000000000000000000-21-21-2-20011110000
χ2744444-4-4444-4-4-4-41-21-2-21-21000000000000000000000000000000000000-12-12002-20000-1-111
χ2844444-4-4444-4-4-4-41-21-2-21-21000000000000000000000000000000000000-12-1200-22000011-1-1
χ2944444-4-4444-4-4-4-4-21-211-21-20000000000000000000000000000000000002-12-12-200-1-1110000
χ3044444-4-4444-4-4-4-4-21-211-21-20000000000000000000000000000000000002-12-1-220011-1-10000
χ3144-4-444-44-4-444-4-41-2-1221-2-10000000000000000000000000000000000001-2-12000000003−33−3
χ3244-4-444-44-4-444-4-41-2-1221-2-10000000000000000000000000000000000001-2-1200000000−33−33
χ3344-4-444-44-4-444-4-4-212-1-1-212000000000000000000000000000000000000-212-10000−i3i3−i3i30000
χ3444-4-444-44-4-444-4-4-212-1-1-212000000000000000000000000000000000000-212-10000i3−i3i3−i30000
χ3544-4-44-444-4-4-4-4441-2-1221-2-1000000000000000000000000000000000000-121-2000000003−3−33
χ3644-4-44-444-4-4-4-4441-2-1221-2-1000000000000000000000000000000000000-121-200000000−333−3
χ3744-4-44-444-4-4-4-444-212-1-1-2120000000000000000000000000000000000002-1-210000−i3i3i3−i30000
χ3844-4-44-444-4-4-4-444-212-1-1-2120000000000000000000000000000000000002-1-210000i3−i3−i3i30000
χ396666-366-3-3-3-3-3-3-300000000222200000000-1-1-1-1-1-1-1-13−33−33−33−33−33−33−33−30000000000000000
χ406666-366-3-3-3-3-3-3-300000000222200000000-1-1-1-1-1-1-1-1−33−33−33−33−33−33−33−330000000000000000
χ416666-366-3-3-3-3-3-3-300000000-2-2-2-22222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ426666-366-3-3-3-3-3-3-300000000-2-2-2-2-2-2-2-2-2-2-2-21111111111111111111111110000000000000000
χ436666-3-6-6-3-3-333330000000022-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111110000000000000000
χ446666-3-6-6-3-3-333330000000022-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000
χ456666-3-6-6-3-3-3333300000000-2-222000000001111-1-1-1-13−33−33−33−3−33−33−33−330000000000000000
χ466666-3-6-6-3-3-3333300000000-2-222000000001111-1-1-1-1−33−33−33−333−33−33−33−30000000000000000
χ4766-6-6-36-6-333-3-333000000000000−i2−i2i2i2−i2−i2i2i23−33−33−33−3ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ4866-6-6-36-6-333-3-333000000000000−i2−i2i2i2−i2−i2i2i2−33−33−33−33ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ4966-6-6-36-6-333-3-333000000000000i2i2−i2−i2i2i2−i2−i23−33−33−33−3−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ5066-6-6-36-6-333-3-333000000000000i2i2−i2−i2i2i2−i2−i2−33−33−33−33−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ5166-6-6-3-66-33333-3-3000000000000−i2−i2i2i2i2i2−i2−i23−33−3−33−33ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ70000000000000000
χ5266-6-6-3-66-33333-3-3000000000000−i2−i2i2i2i2i2−i2−i2−33−333−33−3ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ230000000000000000
χ5366-6-6-3-66-33333-3-3000000000000i2i2−i2−i2−i2−i2i2i23−33−3−33−33−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ70000000000000000
χ5466-6-6-3-66-33333-3-3000000000000i2i2−i2−i2−i2−i2i2i2−33−333−33−3−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ230000000000000000
χ556-66-6-3003-3333−3333−3300000000002-22i−2i2i−2i00003−3−33-1-111−i−iii−i−iii−i3i3i3−i3−i3i3i3−i30000000000000000
χ566-66-6-3003-3333−3333−3300000000002-2−2i2i−2i2i00003−3−33-1-111ii−i−iii−i−ii3−i3−i3i3i3−i3−i3i30000000000000000
χ576-66-6-3003-3333−3333−330000000000-2200002i−2i2i−2i−333−311-1-1i3−i3−i3i3i3−i3−i3i3−i−iii−i−iii0000000000000000
χ586-66-6-3003-3333−3333−330000000000-220000−2i2i−2i2i−333−311-1-1−i3i3i3−i3−i3i3i3−i3ii−i−iii−i−i0000000000000000
χ596-66-6-3003-33−3333−333300000000002-22i−2i2i−2i0000−333−3-1-111−i−iii−i−iiii3−i3−i3i3i3−i3−i3i30000000000000000
χ606-66-6-3003-33−3333−333300000000002-2−2i2i−2i2i0000−333−3-1-111ii−i−iii−i−i−i3i3i3−i3−i3i3i3−i30000000000000000
χ616-66-6-3003-33−3333−33330000000000-2200002i−2i2i−2i3−3−3311-1-1−i3i3i3−i3−i3i3i3−i3−i−iii−i−iii0000000000000000
χ626-66-6-3003-33−3333−33330000000000-220000−2i2i−2i2i3−3−3311-1-1i3−i3−i3i3i3−i3−i3i3ii−i−iii−i−i0000000000000000
χ636-6-66-30033-333−33−3333000000002-2002−2−22−222−2-1-111−333−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ646-6-66-30033-333−33−3333000000002-200−222−22−2−22-1-111−333−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ656-6-66-30033-333−33−333300000000-22002−2−222−2−2211-1-13−3−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ666-6-66-30033-333−33−333300000000-2200−222−2−222−211-1-13−3−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ676-6-66-30033-3−333333−33000000002-2002−2−22−222−2-1-1113−3−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000000000
χ686-6-66-30033-3−333333−33000000002-200−222−22−2−22-1-1113−3−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000000000
χ696-6-66-30033-3−333333−3300000000-22002−2−222−2−2211-1-1−333−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000000000
χ706-6-66-30033-3−333333−3300000000-2200−222−2−222−211-1-1−333−3−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000000000
χ718-88-8800-88-800002-42-44-24-20000000000000000000000000000000000000000000000000000
χ728-88-8800-88-80000-42-42-24-240000000000000000000000000000000000000000000000000000
χ738-8-88800-8-8800002-4-24-4-2420000000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-424-224-2-40000000000000000000000000000000000000000000000000000

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