Finite Group Databasebeta

← Group #13154859

Character table — Group #13154859

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222444444444444444444888888888888888881212121212121212121212121212121212123636363672727272727272216216216
order1223623366666666666666633666666666666666441212121212121212121212121212121224121268824242424444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1i−iii−i−i-1i−i
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1−ii−i−iii-1−ii
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−iii−i−i1−ii
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−iii1i−i
χ922222-22222222-2-2-2-2-2-2-2-22222-2222222-2-2-2-2-2-2-2-20000000000000000002-2-2-22000000000
χ1022222-22222222-2-2-2-2-2-2-2-22222-2222222-2-2-2-2-2-2-2-2000000000000000000-2222-2000000000
χ11222-1-1222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-122-1-1-1-1000
χ12222-1-1222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-2-21111000
χ13222-1-1222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21112i−2i−i−iii000
χ14222-1-1222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2111−2i2iii−i−i000
χ15222-1-1-222-12222-2-2-2-2-2-2-2-222-1-11-1-1-1-1-1-1111111110000000000000000002-211-1003−33−3000
χ16222-1-1-222-12222-2-2-2-2-2-2-2-222-1-11-1-1-1-1-1-1111111110000000000000000002-211-100−33−33000
χ17222-1-1-222-12222-2-2-2-2-2-2-2-222-1-11-1-1-1-1-1-111111111000000000000000000-22-1-1100−i3i3i3−i3000
χ18222-1-1-222-12222-2-2-2-2-2-2-2-222-1-11-1-1-1-1-1-111111111000000000000000000-22-1-1100i3−i3−i3i3000
χ194444441-2411-2-21111-2-2-2-21-21-24111-2-2-21111-2-2-2-24411111111-2-2-2-2-2-2-2-200000000000000
χ204444441-2411-2-21111-2-2-2-21-21-24111-2-2-21111-2-2-2-2-4-4-1-1-1-1-1-1-1-12222222200000000000000
χ21444444-214-2-211-2-2-2-21111-21-214-2-2-2111-2-2-2-2111144-2-2-2-2-2-2-2-21111111100000000000000
χ22444444-214-2-211-2-2-2-21111-21-214-2-2-2111-2-2-2-21111-4-422222222-1-1-1-1-1-1-1-100000000000000
χ2344444-41-2411-2-2-1-1-1-122221-21-2-4111-2-2-2-1-1-1-12222003333-3-3-3-30000000000000000000000
χ2444444-41-2411-2-2-1-1-1-122221-21-2-4111-2-2-2-1-1-1-1222200-3-3-3-333330000000000000000000000
χ2544444-4-214-2-2112222-1-1-1-1-21-21-4-2-2-21112222-1-1-1-100000000003333-3-3-3-300000000000000
χ2644444-4-214-2-2112222-1-1-1-1-21-21-4-2-2-21112222-1-1-1-10000000000-3-3-3-3333300000000000000
χ2744-44401-2-4-1-12233-3-300001-21-201-1-122-233-3-3000000−i3−i3i3i3−i3−i3i3i30000−2i3−2i32i32i300000000000000
χ2844-44401-2-4-1-12233-3-300001-21-201-1-122-233-3-3000000i3i3−i3−i3i3i3−i3−i300002i32i3−2i3−2i300000000000000
χ2944-44401-2-4-1-122-3-33300001-21-201-1-122-2-3-333000000−i3−i3i3i3i3i3−i3−i3−2i3−2i32i32i3000000000000000000
χ3044-44401-2-4-1-122-3-33300001-21-201-1-122-2-3-333000000i3i3−i3−i3−i3−i3i3i32i32i3−2i3−2i3000000000000000000
χ3144-444044-4-4-4-4-400000000444404-4-4-4-440000000000000000000000000000000000000000
χ3244-4440-21-422-1-1000033-3-3-21-210-222-1-11000033-3-3000000−2i3−2i32i32i3−i3−i3i3i3i3i3−i3−i300000000000000
χ3344-4440-21-422-1-1000033-3-3-21-210-222-1-11000033-3-30000002i32i3−2i3−2i3i3i3−i3−i3−i3−i3i3i300000000000000
χ3444-4440-21-422-1-10000-3-333-21-210-222-1-110000-3-33300−2i3−2i32i32i30000i3i3−i3−i3i3i3−i3−i300000000000000
χ3544-4440-21-422-1-10000-3-333-21-210-222-1-110000-3-333002i32i3−2i3−2i30000−i3−i3i3i3−i3−i3i3i300000000000000
χ3644-4-2-20442-4-4-4-40000000044-2-20-22222-20000000000000000000000000000−2i32i30000000000
χ3744-4-2-20442-4-4-4-40000000044-2-20-22222-200000000000000000000000000002i3−2i30000000000
χ384-404-401-203-300−i3i3−i3i300−2i32i3-121-20-13-3002−i3i3−i3i300−2i32i32i−2ii−ii−i−3ζ7−ζ113ζ7+ζ11ζ7+3ζ11−ζ7−3ζ11−2ζ72ζ72ζ11−2ζ112ζ11−2ζ11−2ζ72ζ700000000000000
χ394-404-401-203-300−i3i3−i3i300−2i32i3-121-20-13-3002−i3i3−i3i300−2i32i3−2i2i−ii−ii3ζ7+ζ11−3ζ7−ζ11−ζ7−3ζ11ζ7+3ζ112ζ7−2ζ7−2ζ112ζ11−2ζ112ζ112ζ7−2ζ700000000000000
χ404-404-401-203-300i3−i3i3−i3002i3−2i3-121-20-13-3002i3−i3i3−i3002i3−2i32i−2ii−ii−i−ζ7−3ζ11ζ7+3ζ113ζ7+ζ11−3ζ7−ζ11−2ζ112ζ112ζ7−2ζ72ζ7−2ζ7−2ζ112ζ1100000000000000
χ414-404-401-203-300i3−i3i3−i3002i3−2i3-121-20-13-3002i3−i3i3−i3002i3−2i3−2i2i−ii−iiζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ112ζ11−2ζ11−2ζ72ζ7−2ζ72ζ72ζ11−2ζ1100000000000000
χ424-404-401-20-3300−i3i3i3−i3−2i32i300-121-20-1-33002−i3i3i3−i3−2i32i3002i−2iζ7+3ζ11−ζ7−3ζ113ζ7+ζ11−3ζ7−ζ11−iii−i−2ζ72ζ72ζ11−2ζ112ζ7−2ζ7−2ζ112ζ1100000000000000
χ434-404-401-20-3300−i3i3i3−i3−2i32i300-121-20-1-33002−i3i3i3−i3−2i32i300−2i2i−ζ7−3ζ11ζ7+3ζ11−3ζ7−ζ113ζ7+ζ11i−i−ii2ζ7−2ζ7−2ζ112ζ11−2ζ72ζ72ζ11−2ζ1100000000000000
χ444-404-401-20-3300i3−i3−i3i32i3−2i300-121-20-1-33002i3−i3−i3i32i3−2i3002i−2i3ζ7+ζ11−3ζ7−ζ11ζ7+3ζ11−ζ7−3ζ11−iii−i−2ζ112ζ112ζ7−2ζ72ζ11−2ζ11−2ζ72ζ700000000000000
χ454-404-401-20-3300i3−i3−i3i32i3−2i300-121-20-1-33002i3−i3−i3i32i3−2i300−2i2i−3ζ7−ζ113ζ7+ζ11−ζ7−3ζ11ζ7+3ζ11i−i−ii2ζ11−2ζ11−2ζ72ζ7−2ζ112ζ112ζ7−2ζ700000000000000
χ464-404-40440000000000000-4-4440-40000-4000000002i−2i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000
χ474-404-40440000000000000-4-4440-40000-400000000−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000
χ484-404-40-210003-300−2i32i3−i3i3i3−i32-1-2102003-3-100−2i32i3−i3i3i3−i32i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ11−2ζ72ζ7i−i−ii−ζ7−3ζ11ζ7+3ζ113ζ7+ζ11−3ζ7−ζ1100000000000000
χ494-404-40-210003-300−2i32i3−i3i3i3−i32-1-2102003-3-100−2i32i3−i3i3i3−i3−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ112ζ7−2ζ7−iii−iζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ1100000000000000
χ504-404-40-210003-3002i3−2i3i3−i3−i3i32-1-2102003-3-1002i3−2i3i3−i3−i3i32i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ7−2ζ112ζ11i−i−ii−3ζ7−ζ113ζ7+ζ11ζ7+3ζ11−ζ7−3ζ1100000000000000
χ514-404-40-210003-3002i3−2i3i3−i3−i3i32-1-2102003-3-1002i3−2i3i3−i3−i3i3−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ72ζ11−2ζ11−iii−i3ζ7+ζ11−3ζ7−ζ11−ζ7−3ζ11ζ7+3ζ1100000000000000
χ524-404-40-21000-33−2i32i300i3−i3i3−i32-1-210200-33-1−2i32i300i3−i3i3−i32i−2i−2ζ72ζ7−2ζ112ζ112ζ11−2ζ11−2ζ72ζ73ζ7+ζ11−3ζ7−ζ11−ζ7−3ζ11ζ7+3ζ11−iii−i00000000000000
χ534-404-40-21000-33−2i32i300i3−i3i3−i32-1-210200-33-1−2i32i300i3−i3i3−i3−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−3ζ7−ζ113ζ7+ζ11ζ7+3ζ11−ζ7−3ζ11i−i−ii00000000000000
χ544-404-40-21000-332i3−2i300−i3i3−i3i32-1-210200-33-12i3−2i300−i3i3−i3i32i−2i−2ζ112ζ11−2ζ72ζ72ζ7−2ζ7−2ζ112ζ11ζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ11−iii−i00000000000000
χ554-404-40-21000-332i3−2i300−i3i3−i3i32-1-210200-33-12i3−2i300−i3i3−i3i3−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−ζ7−3ζ11ζ7+3ζ113ζ7+ζ11−3ζ7−ζ11i−i−ii00000000000000
χ56888-4-482-4-422-4-42222-4-4-4-42-4-12-4-1-1-1222-1-1-1-1222200000000000000000000000000000000
χ57888-4-48-42-4-4-422-4-4-4-42222-422-1-4222-1-1-12222-1-1-1-100000000000000000000000000000000
χ58888-4-4-82-4-422-4-4-2-2-2-244442-4-124-1-1-12221111-2-2-2-200000000000000000000000000000000
χ59888-4-4-8-42-4-4-4224444-2-2-2-2-422-14222-1-1-1-2-2-2-2111100000000000000000000000000000000
χ6088-8-4-402-44-2-24466-6-600002-4-120-111-2-22-3-333000000000000000000000000000000000000
χ6188-8-4-402-44-2-244-6-66600002-4-120-111-2-2233-3-3000000000000000000000000000000000000
χ6288-8-4-40-42444-2-2000066-6-6-422-102-2-211-10000-3-33300000000000000000000000000000000
χ6388-8-4-40-42444-2-20000-6-666-422-102-2-211-1000033-3-300000000000000000000000000000000
χ648-80-4402-406-600−2i32i3−2i32i300−4i34i3-24-1201-3300-2i3−i3i3−i3002i3−2i300000000000000000000000000000000
χ658-80-4402-406-6002i3−2i32i3−2i3004i3−4i3-24-1201-3300-2−i3i3−i3i300−2i32i300000000000000000000000000000000
χ668-80-4402-40-6600−2i32i32i3−2i3−4i34i300-24-12013-300-2i3−i3−i3i32i3−2i30000000000000000000000000000000000
χ678-80-4402-40-66002i3−2i3−2i32i34i3−4i300-24-12013-300-2−i3i3i3−i3−2i32i30000000000000000000000000000000000
χ688-80-440880000000000000-8-8-4-404000040000000000000000000000000000000000000000
χ698-80-440-420006-600−4i34i3−2i32i32i3−2i34-22-10-200-331002i3−2i3i3−i3−i3i300000000000000000000000000000000
χ708-80-440-420006-6004i3−4i32i3−2i3−2i32i34-22-10-200-33100−2i32i3−i3i3i3−i300000000000000000000000000000000
χ718-80-440-42000-66−4i34i3002i3−2i32i3−2i34-22-10-2003-312i3−2i300−i3i3−i3i300000000000000000000000000000000
χ728-80-440-42000-664i3−4i300−2i32i3−2i32i34-22-10-2003-31−2i32i300i3−i3i3−i300000000000000000000000000000000

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