Finite Group Databasebeta

← Group #13049537

Character table — Group #13049537

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222222224444444444444444666888888888812121212121212121212121218181818182727363636363636363636363654545454108108
order12333366663333333366666666412123333366666121212121212121212121212444121222121212121212121212121244661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-11-11-1-1-111-1-11-1-1-11-1
χ4111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11-11-1-1-1-111-11-1-1-11
χ511111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-1-1-111-1-1-1-111-1-111
χ711111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-11-11-1-1-111-1-1-1111-11
χ811111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-11-1-1-1-1111-1111-1
χ922222-1-1222222-1-1-1-1-12-1-1-1-122-12-1-12-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1200-1-12220000-1-1000000-1-100
χ1022222-1-1222222-1-1-1-1-12-1-1-1-122-12-1-12-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-20011-2-2-20000110000001100
χ1122222-1-1222222-1-1-1-1-12-1-1-1-122-1-2112-1-1-1-12-1-1-1-1-2-2-2-211111111200-1-1-2-220000-1-10000001100
χ1222222-1-1222222-1-1-1-1-12-1-1-1-122-1-2112-1-1-1-12-1-1-1-1-2-2-2-211111111-2001122-2000011000000-1-100
χ132222-12222-12-1-122-1-1-1-12-1-1-12-12222-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-100200000020-10000-1-102000-1
χ142222-12222-12-1-122-1-1-1-12-1-1-12-12222-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-100-2000000-2010000110-20001
χ152222-12222-12-1-122-1-1-1-12-1-1-12-12-2-2-2-12-1-1-1-12-1-1-1-2111-2-211111100200000020-10000-1-10-20001
χ162222-12222-12-1-122-1-1-1-12-1-1-12-12-2-2-2-12-1-1-1-12-1-1-1-2111-2-211111100-2000000-20100001102000-1
χ17222-12222-12-12-12-12-1-1-1-12-1-1-122222-1-12-1-1-1-12-1-1-12-1-1-1-122-1-1-1-10200000020-1000-1-1002000-10
χ18222-12222-12-12-12-12-1-1-1-12-1-1-122222-1-12-1-1-1-12-1-1-12-1-1-1-122-1-1-1-10-2000000-2010001100-200010
χ19222-12222-12-12-12-12-1-1-1-12-1-1-122-2-2-2-1-12-1-1-1-12-1-11-21111-2-211110200000020-1000-1-100-200010
χ20222-12222-12-12-12-12-1-1-1-12-1-1-122-2-2-2-1-12-1-1-1-12-1-11-21111-2-211110-2000000-20100011002000-10
χ2122-12222-122-1-12-1222222222-1-1-1000-1-1-1-1-1-1-1-1-1-10000000000002222200-1-1-122-1-1-1-1-1-1000000
χ2222-12222-122-1-12-1222222222-1-1-1000-1-1-1-1-1-1-1-1-1-10000000000002-2-22200-111-2-2-1-11111000000
χ2322-12222-122-1-12-1222222222-1-1-1000-1-1-1-1-1-1-1-1-1-1000000000000-22-2-2-2001-112-211-1-111000000
χ2422-12222-122-1-12-1222222222-1-1-1000-1-1-1-1-1-1-1-1-1-1000000000000-2-22-2-20011-1-221111-1-1000000
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
χ272-2222-11-2-2-2222-1-1-1-1-1-21111-2-2103−32-1-1-1-1-2111100003−33−333−3−30003−32-2000003−3000000-1100
χ282-2222-11-2-2-2222-1-1-1-1-1-21111-2-2103−32-1-1-1-1-2111100003−33−333−3−3000−33-2200000−330000001-100
χ292-2222-11-2-2-2222-1-1-1-1-1-21111-2-210−332-1-1-1-1-211110000−33−33−3−3330003−3-22000003−30000001-100
χ302-2222-11-2-2-2222-1-1-1-1-1-21111-2-210−332-1-1-1-1-211110000−33−33−3−333000−332-200000−33000000-1100
χ314444-2-2-244-24-2-2-2-2111-2-21114-2-24-2-2-2-2111-2-21114-2-2-2-2-2111111000000000000000000000000
χ324444-2-2-244-24-2-2-2-2111-2-21114-2-2-422-2-2111-2-2111-422222-1-1-1-1-1-1000000000000000000000000
χ33444-24-2-24-24-24-2-21-211-21-211-24-24-2-2-21-211-21-211-24-2-211-2-21111000000000000000000000000
χ34444-24-2-24-24-24-2-21-211-21-211-24-2-422-21-211-21-2112-422-1-122-1-1-1-1000000000000000000000000
χ35444-2-2444-2-2-2-214-2-2111-2-211-2-244441-2-2111-2-211-2-211-2-2-2-21111000000000000000000000000
χ36444-2-2444-2-2-2-214-2-2111-2-211-2-24-4-4-41-2-2111-2-21122-1-12222-1-1-1-1000000000000000000000000
χ37444-2-2-2-24-2-2-2-21-211−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-24-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
χ38444-2-2-2-24-2-2-2-21-211−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-422111−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
χ39444-2-2-2-24-2-2-2-21-211−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-24-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000
χ40444-2-2-2-24-2-2-2-21-211−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-422111−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000
χ4144-244-2-2-244-2-241-2-2-2-24-2-2-2-2-2-21000-21111-21111000000000000400-2-200-20000110000000000
χ4244-244-2-2-244-2-241-2-2-2-24-2-2-2-2-2-21000-21111-21111000000000000-400220020000-1-10000000000
χ4344-24-244-24-2-21-2-24-2-2-2-24-2-2-2-21-20001-21111-2111000000000000004000000-20-2000011000000
χ4444-24-244-24-2-21-2-24-2-2-2-24-2-2-2-21-20001-21111-211100000000000000-40000002020000-1-1000000
χ4544-2-2444-2-241-2-2-2-24-2-2-2-24-2-21-2-200011-21111-21100000000000004000000-20-20001100000000
χ4644-2-2444-2-241-2-2-2-24-2-2-2-24-2-21-2-200011-21111-2110000000000000-4000000202000-1-100000000
χ474-444-24-4-4-424-2-244-2-2-22-4222-42-4000-24-2-2-22-4222000000000000000000000000000000000000
χ484-444-2-22-4-424-2-2-2-211122-1-1-1-422023−23-2-211122-1-1-1000023−23−33−3−333000000000000000000000000
χ494-444-2-22-4-424-2-2-2-211122-1-1-1-4220−2323-2-211122-1-1-10000−23233−333−3−3000000000000000000000000
χ504-44-244-4-42-4-24-24-24-2-222-4222-4-4000-2-24-2-222-422000000000000000000000000000000000000
χ514-44-24-22-42-4-24-2-21-2112-12-1-12-42023−23-21-2112-12-1-10000−3323−23−3−333000000000000000000000000
χ524-44-24-22-42-4-24-2-21-2112-12-1-12-420−2323-21-2112-12-1-100003−3−232333−3−3000000000000000000000000
χ534-44-2-24-4-422-2-214-2-211-122-1-122-40001-2-211-122-1-1003i−3i00003i−3i−3i3i000000000000000000000000
χ544-44-2-24-4-422-2-214-2-211-122-1-122-40001-2-211-122-1-100−3i3i0000−3i3i3i−3i000000000000000000000000
χ554-44-2-2-22-422-2-21-211−1−3i32−1+3i32-1-1-11+3i321−3i32222023−23111−1−3i32−1+3i32-1-1-11+3i321−3i32003i−3i−33−33ζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11000000000000000000000000
χ564-44-2-2-22-422-2-21-211−1−3i32−1+3i32-1-1-11+3i321−3i322220−2323111−1−3i32−1+3i32-1-1-11+3i321−3i3200−3i3i3−33−3−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ11000000000000000000000000
χ574-44-2-2-22-422-2-21-211−1+3i32−1−3i32-1-1-11−3i321+3i32222023−23111−1+3i32−1−3i32-1-1-11−3i321+3i3200−3i3i−33−33−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000
χ584-44-2-2-22-422-2-21-211−1+3i32−1−3i32-1-1-11−3i321+3i322220−2323111−1+3i32−1−3i32-1-1-11−3i321+3i32003i−3i3−33−32ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000
χ594-4-2444-42-4-4-2-24-24444-4-4-4-4-4222000-2-2-2-2-222222000000000000000000000000000000000000
χ604-4-244-222-4-4-2-241-2-2-2-2-4222222-1000-211112-1-1-1-100000000000000023−230000000−330000000000
χ614-4-244-222-4-4-2-241-2-2-2-2-4222222-1000-211112-1-1-1-1000000000000000−232300000003−30000000000
χ624-4-24-24-42-42-21-2-24-2-2-22-42222-120001-2111-12-1-1-100000000000000000000000000003i−3i000000
χ634-4-24-24-42-42-21-2-24-2-2-22-42222-120001-2111-12-1-1-10000000000000000000000000000−3i3i000000
χ644-4-2-244-422-41-2-2-2-24-2-222-422-12200011-211-1-12-1-1000000000000000000000000003i−3i00000000
χ654-4-2-244-422-41-2-2-2-24-2-222-422-12200011-211-1-12-1-100000000000000000000000000−3i3i00000000
χ6688-48-4-4-4-48-4-42-42-4222-4-4222-42200022-1-1-122-1-1-1000000000000000000000000000000000000
χ6788-4-48-4-4-4-482-4-422-422-42-4222-420002-12-1-12-12-1-1000000000000000000000000000000000000
χ6888-4-4-488-4-4-4222-4-4-4222-4-42222-4000-122-1-1-122-1-1000000000000000000000000000000000000
χ6988-4-4-4-4-4-4-4-4222222−1−3i3−1+3i3222−1−3i3−1+3i3222000-1-1-11+3i321−3i32-1-1-11+3i321−3i32000000000000000000000000000000000000
χ7088-4-4-4-4-4-4-4-4222222−1+3i3−1−3i3222−1+3i3−1−3i3222000-1-1-11−3i321+3i32-1-1-11−3i321+3i32000000000000000000000000000000000000
χ718-8-48-4-444-84-42-42-422244-2-2-24-2-200022-1-1-1-2-2111000000000000000000000000000000000000
χ728-8-4-48-4444-82-4-422-4224-24-2-2-24-20002-12-1-1-21-211000000000000000000000000000000000000
χ738-8-4-4-48-8444222-4-4-422-244-2-2-2-24000-122-1-11-2-211000000000000000000000000000000000000
χ748-8-4-4-4-44444222222−1−3i3−1+3i3-2-2-21+3i31−3i3-2-2-2000-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000000000000000
χ758-8-4-4-4-44444222222−1+3i3−1−3i3-2-2-21−3i31+3i3-2-2-2000-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000000000000000

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