Finite Group Databasebeta

← Group #13049534

Character table — Group #13049534

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222222224444444444444444666888888888812121212121212121212121218181818182727363636363636363636363654545454108108
order1233336666333333336666666641212333336666612121212121212121212121222412122266666666121212226666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-11-111-1-1-1-1-11-1-1-11-1
χ3111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-11-11-1-111-1-1-1-11-1-1-11
χ4111111111111111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1111-1-111-1-1
χ511111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-11-111-1-1-1-1-1-1111-11
χ711111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-11-11-1-111-1-1-11-1111-1
χ811111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111-1-111
χ922222-12-12222-1-1-1-12-12-12-1-1-1-122222-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-10200000020-100-1-100002000-1
χ1022222-12-12222-1-1-1-12-12-12-1-1-1-122222-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-10-2000000-20100110000-20001
χ1122222-12-12222-1-1-1-12-12-12-1-1-1-12-2-2-22-1-1-1-12-1-1-1-1-21-2-2111111110200000020-100-1-10000-20001
χ1222222-12-12222-1-1-1-12-12-12-1-1-1-12-2-2-22-1-1-1-12-1-1-1-1-21-2-2111111110-2000000-201001100002000-1
χ132222-12-12222-12-1-1-1-12-12-12-1-1-12222-12-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1200000020-10-1-1000002000-10
χ142222-12-12222-12-1-1-1-12-12-12-1-1-12222-12-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-2000000-20101100000-200010
χ152222-12-12222-12-1-1-1-12-12-12-1-1-12-2-2-2-12-1-1-1-12-1-1-11-211-2-2111111200000020-10-1-100000-200010
χ162222-12-12222-12-1-1-1-12-12-12-1-1-12-2-2-2-12-1-1-1-12-1-1-11-211-2-2111111-2000000-201011000002000-10
χ17222-122222-1-1-1-12-1-12222-1-12-1-1-12-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1002-1-122000000002-1-100-1-100
χ18222-122222-1-1-1-12-1-12222-1-12-1-1-12-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-100-211-2-200000000-211001100
χ19222-122222-1-1-1-12-1-12222-1-12-1-1-1-211-1-12-1-1-1-12-1-1-2-21111-2-21111002-1-1-2-2000000002-1-1001100
χ20222-122222-1-1-1-12-1-12222-1-12-1-1-1-211-1-12-1-1-1-12-1-1-2-21111-2-2111100-2112200000000-21100-1-100
χ2122-122222-12-122222-1-1-1-122222-1000-1-1-1-1-1-1-1-1-1-10000000000002222200-1-122-1-1-1-1-1-1-1000000
χ2222-122222-12-122222-1-1-1-122222-1000-1-1-1-1-1-1-1-1-1-10000000000002-2-2-2-200-112-2-1-111111000000
χ2322-122222-12-122222-1-1-1-122222-1000-1-1-1-1-1-1-1-1-1-1000000000000-22-2-2-2001-1-2211-1-1111000000
χ2422-122222-12-122222-1-1-1-122222-1000-1-1-1-1-1-1-1-1-1-1000000000000-2-22220011-2-21111-1-1-1000000
χ252-22222-2-2-2-222222222-2-2-2-2-2-2-2-200022222-2-2-2-2-2000000000000000002-200000000000002-200
χ262-22222-2-2-2-222222222-2-2-2-2-2-2-2-200022222-2-2-2-2-200000000000000000-220000000000000-2200
χ272-22-122-2-2-21-1-1-12-1-122-2-211-211103−3-1-12-1-111-211003−33−30033−3−30003−32-20000000003−300-1100
χ282-22-122-2-2-21-1-1-12-1-122-2-211-211103−3-1-12-1-111-211003−33−30033−3−3000−33-22000000000−33001-100
χ292-22-122-2-2-21-1-1-12-1-122-2-211-21110−33-1-12-1-111-21100−33−3300−3−3330003−3-220000000003−3001-100
χ302-22-122-2-2-21-1-1-12-1-122-2-211-21110−33-1-12-1-111-21100−33−3300−3−333000−332-2000000000−3300-1100
χ314444-2-2-2-2444-2-2111-2-2-2-2-2-21114444-2-2111-2-2111-2-2-2-2-2-2111111000000000000000000000000
χ324444-2-2-2-2444-2-2111-2-2-2-2-2-21114-4-4-4-2-2111-2-2111222222-1-1-1-1-1-1000000000000000000000000
χ33444-24-24-24-2-2-21-2114-24-2-21-211-24-2-2-21-211-21-2114-2-2-211-2-21111000000000000000000000000
χ34444-24-24-24-2-2-21-2114-24-2-21-211-2-422-21-211-21-211-4222-1-122-1-1-1-1000000000000000000000000
χ35444-2-24-244-2-21-2-211-24-241-2-211-24-2-21-2-2111-2-211-2411-2-2-2-21111000000000000000000000000
χ36444-2-24-244-2-21-2-211-24-241-2-211-2-4221-2-2111-2-2112-4-1-12222-1-1-1-1000000000000000000000000
χ37444-2-2-2-2-24-2-2111−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i32-24-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
χ38444-2-2-2-2-24-2-2111−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i32-2-422111−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
χ39444-2-2-2-2-24-2-2111−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i32-24-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000
χ40444-2-2-2-2-24-2-2111−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i32-2-422111−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000
χ4144-244-24-2-24-24-2-2-2-2-21-214-2-2-2-2-2000-21111-2111100000000000004000000-20-20011000000000
χ4244-244-24-2-24-24-2-2-2-2-21-214-2-2-2-2-2000-21111-211110000000000000-400000020200-1-1000000000
χ4344-24-24-24-24-2-24-2-2-21-21-2-24-2-2-2-20001-21111-21110000000000004000000-20-201100000000000
χ4444-24-24-24-24-2-24-2-2-21-21-2-24-2-2-2-20001-21111-2111000000000000-40000002020-1-100000000000
χ4544-2-24444-2-21-2-24-2-2-2-2-2-2-2-24-2-2100011-21111-211000000000000004-2-20000000000-211000000
χ4644-2-24444-2-21-2-24-2-2-2-2-2-2-2-24-2-2100011-21111-21100000000000000-42200000000002-1-1000000
χ474-4444-2-42-4-444-2-2-2-24-2-42-42222-40004-2-2-2-2-42222000000000000000000000000000000000000
χ484-444-242-4-4-44-24-2-2-2-242-42-4222-4000-24-2-2-22-4222000000000000000000000000000000000000
χ494-444-2-222-4-44-2-2111-2-22222-1-1-1-4000-2-211122-1-1-10000003i−3i3i−3i−3i3i000000000000000000000000
χ504-444-2-222-4-44-2-2111-2-22222-1-1-1-4000-2-211122-1-1-1000000−3i3i−3i3i3i−3i000000000000000000000000
χ514-44-24-2-42-42-2-21-2114-2-422-12-1-12023−23-21-2112-12-1-10023−23−3300−3−333000000000000000000000000
χ524-44-24-2-42-42-2-21-2114-2-422-12-1-120−2323-21-2112-12-1-100−23233−30033−3−3000000000000000000000000
χ534-44-2-242-4-42-21-2-211-242-4-122-1-12023−231-2-211-122-1-100−3323−2300−3−333000000000000000000000000
χ544-44-2-242-4-42-21-2-211-242-4-122-1-120−23231-2-211-122-1-1003−3−23230033−3−3000000000000000000000000
χ554-44-2-2-222-42-2111−1−3i32−1+3i32-2-222-1-1-11+3i321−3i322023−23111−1−3i32−1+3i32-1-1-11+3i321−3i3200−33−333i−3iζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11000000000000000000000000
χ564-44-2-2-222-42-2111−1−3i32−1+3i32-2-222-1-1-11+3i321−3i3220−2323111−1−3i32−1+3i32-1-1-11+3i321−3i32003−33−3−3i3i−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ11000000000000000000000000
χ574-44-2-2-222-42-2111−1+3i32−1−3i32-2-222-1-1-11−3i321+3i322023−23111−1+3i32−1−3i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000
χ584-44-2-2-222-42-2111−1+3i32−1−3i32-2-222-1-1-11−3i321+3i3220−2323111−1+3i32−1−3i32-1-1-11−3i321+3i32003−33−33i−3i2ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000
χ594-4-2444-4-42-4-244444-2-222-4-4-4-4-42000-2-2-2-2-222222000000000000000000000000000000000000
χ604-4-244-2-422-4-24-2-2-2-2-212-1-422222000-211112-1-1-1-100000000000000000000000003-3000000000
χ614-4-244-2-422-4-24-2-2-2-2-212-1-422222000-211112-1-1-1-10000000000000000000000000-33000000000
χ624-4-24-242-42-4-2-24-2-2-21-2-122-422220001-2111-12-1-1-1000000000000000000000003-300000000000
χ634-4-24-242-42-4-2-24-2-2-21-2-122-422220001-2111-12-1-1-100000000000000000000000-3300000000000
χ644-4-2-244-4-4221-2-24-2-2-2-22222-422-100011-211-1-12-1-100000000000000023−2300000000000−33000000
χ654-4-2-244-4-4221-2-24-2-2-2-22222-422-100011-211-1-12-1-1000000000000000−2323000000000003−3000000
χ6688-48-4-4-4-4-48-4-4-42222222-4-4222-400022-1-1-122-1-1-1000000000000000000000000000000000000
χ6788-4-48-48-4-4-42-42-422-42-42-42-42220002-12-1-12-12-1-1000000000000000000000000000000000000
χ6888-4-4-48-48-4-422-4-4222-42-42-4-4222000-122-1-1-122-1-1000000000000000000000000000000000000
χ6988-4-4-4-4-4-4-4-42222−1−3i3−1+3i32222222−1−3i3−1+3i32000-1-1-11+3i321−3i32-1-1-11+3i321−3i32000000000000000000000000000000000000
χ7088-4-4-4-4-4-4-4-42222−1+3i3−1−3i32222222−1+3i3−1−3i32000-1-1-11−3i321+3i32-1-1-11−3i321+3i32000000000000000000000000000000000000
χ718-8-48-4-4444-8-4-4-422222-2-244-2-2-2400022-1-1-1-2-2111000000000000000000000000000000000000
χ728-8-4-48-4-84442-42-422-424-24-24-2-2-20002-12-1-1-21-211000000000000000000000000000000000000
χ738-8-4-4-484-84422-4-4222-4-24-244-2-2-2000-122-1-11-2-211000000000000000000000000000000000000
χ748-8-4-4-4-444442222−1−3i3−1+3i322-2-2-2-2-21+3i31−3i3-2000-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000000000000000
χ758-8-4-4-4-444442222−1+3i3−1−3i322-2-2-2-2-21−3i31+3i3-2000-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000000000000000

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