Finite Group Databasebeta

← Group #13180846

Character table — Group #13180846

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222334444446666688889912121212121216161616161616161616161616161616182727363636363636363654727272727272727272727272
order1233466223612121212466663612122266121212123333666612121212121212124224444444446612121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11111111111111111111111-1-1-111-1-111-1-1-1-1-111-1-111-1-1-1-1
χ4111111111111111111111111-1-11111111111111111111111-1-1-1-1-111-1-111-1-1-1-1-111-1-111-1-1
χ51111-1111111-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-11-11-11-1-1111-11-11-11-1-1-1
χ61111-1111111-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11-11-11-11-111-11-11-11-11-1-1
χ71111-1111111-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-11-1-111-1-1111
χ81111-1111111-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11-1-1-111-1-111-111
χ922222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222000000002-1-100000000-1-1
χ1022222222222222222222-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-200000000-2110000000011
χ112222-2222222-2-2-2-2-22222-1-1112222-2-2-2-2-1-1-1-1-1-1-1-111111111-22200000000-2-1-10000000011
χ122222-2222222-2-2-2-2-22222-1-111-2-222-2-2-2-2-1-1-1-1-1-1-1-1111111112-2-20000000021100000000-1-1
χ13222-122-122-1-12-1-1-122-12-1222200-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000022002200000-1-100-1-100
χ14222-122-122-1-12-1-1-122-12-1222200-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-100000-2-200-2-20000011001100
χ15222-1-22-122-1-1-2111-22-12-122-2-200-1-1-21112-1-1-12-1-1-1-2-2111111000002-2002-200000-1100-1100
χ16222-1-22-122-1-1-2111-22-12-122-2-200-1-1-21112-1-1-12-1-1-1-2-211111100000-2200-22000001-1001-100
χ1722-122-1222-1-1-12-1-12-12-12222200-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-100022002200000-1-100-1-10000
χ1822-122-1222-1-1-12-1-12-12-12222200-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1000-2-200-2-2000001100110000
χ1922-12-2-1222-1-11-211-2-12-1222-2-200-1-11-211-12-1-1-12-1-111-2-211110002-2002-200000-1100-110000
χ2022-12-2-1222-1-11-211-2-12-1222-2-200-1-11-211-12-1-1-12-1-111-2-21111000-2200-22000001-1001-10000
χ212-2220-2-22-22-20000022-2-22-2002-22-200002222-2-2-2-20000000002-20000000002-20000000000
χ222-2220-2-22-22-20000022-2-22-200-222-200002222-2-2-2-2000000000-22000000000-220000000000
χ232-2220-2-22-22-20000022-2-2-113−32-22-20000-1-1-1-111113−33−333−3−302-2000000000-11000000003−3
χ242-2220-2-22-22-20000022-2-2-113−3-222-20000-1-1-1-111113−33−333−3−30-220000000001-100000000−33
χ252-2220-2-22-22-20000022-2-2-11−332-22-20000-1-1-1-11111−33−33−3−33302-2000000000-1100000000−33
χ262-2220-2-22-22-20000022-2-2-11−33-222-20000-1-1-1-11111−33−33−3−3330-220000000001-1000000003−3
χ273333333-1-1333333-1-1-1-1-1000033-1-1-1-1-1-100000000000000003-1-11111-1-1-1-1-1001111-1-1-1-100
χ283333333-1-1333333-1-1-1-1-1000033-1-1-1-1-1-100000000000000003-1-1-1-1-1-11111-100-1-1-1-1111100
χ293333333-1-1333333-1-1-1-1-10000-3-3-1-1-1-1-1-10000000000000000-31111-1-1-1-11110011-1-1-1-11100
χ303333333-1-1333333-1-1-1-1-10000-3-3-1-1-1-1-1-10000000000000000-311-1-11111-1-1100-1-11111-1-100
χ313333-333-1-133-3-3-3-31-1-1-1-1000033-1-111110000000000000000-3-1-11-11-1-11-111001-11-1-11-1100
χ323333-333-1-133-3-3-3-31-1-1-1-1000033-1-111110000000000000000-3-1-1-11-111-11-1100-11-111-11-100
χ333333-333-1-133-3-3-3-31-1-1-1-10000-3-3-1-1111100000000000000003111-1-11-111-1-1001-1-11-111-100
χ343333-333-1-133-3-3-3-31-1-1-1-10000-3-3-1-111110000000000000000311-111-11-1-11-100-111-11-1-1100
χ35444-244-244-2-24-2-2-244-24-2-2-2-2-200-2-24-2-2-2-2111-2111-2-2111111000000000000000000000000
χ36444-2-44-244-2-2-4222-44-24-2-2-22200-2-2-4222-2111-211122-1-1-1-1-1-1000000000000000000000000
χ3744-244-2444-2-2-24-2-24-24-24-2-2-2-200-2-2-24-2-21-2111-21111-2-21111000000000000000000000000
χ3844-24-4-2444-2-22-422-4-24-24-2-22200-2-22-4221-2111-211-1-122-1-1-1-1000000000000000000000000
χ3944-2-24-2-24411-2-2114-2-2-2-244440011-2-211-2-211-2-211-2-2-2-21111000000000000000000000000
χ4044-2-24-2-24411-2-2114-2-2-2-2-2-2-2-20011-2-21111−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
χ4144-2-24-2-24411-2-2114-2-2-2-2-2-2-2-20011-2-21111−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000
χ4244-2-2-4-2-2441122-1-1-4-2-2-2-244-4-4001122-1-1-2-211-2-2112222-1-1-1-1000000000000000000000000
χ4344-2-2-4-2-2441122-1-1-4-2-2-2-2-2-222001122-1-111−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
χ4444-2-2-4-2-2441122-1-1-4-2-2-2-2-2-222001122-1-111−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000
χ454-44-20-424-4-22000004-2-424-40000-2200004-2-2-2-422200000000000000000000000000000000
χ464-44-20-424-4-22000004-2-42-2223−2300-220000-21112-1-1-123−23−33−3−333000000000000000000000000
χ474-44-20-424-4-22000004-2-42-22−232300-220000-21112-1-1-1−23233−333−3−3000000000000000000000000
χ484-4-2402-44-4-2200000-242-44-40000-220000-24-2-22-42200000000000000000000000000000000
χ494-4-2402-44-4-2200000-242-4-2223−2300-2200001-211-12-1-1−3323−23−3−333000000000000000000000000
χ504-4-2402-44-4-2200000-242-4-22−232300-2200001-211-12-1-13−3−232333−3−3000000000000000000000000
χ514-4-2-20224-41-1003i−3i0-2-2224-400001-1003i−3i-2-21122-1-100003i−3i−3i3i000000000000000000000000
χ524-4-2-20224-41-1003i−3i0-2-222-2223−23001-1003i−3i11−1−3i32−1+3i32-1-11+3i321−3i32−33−33ζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11000000000000000000000000
χ534-4-2-20224-41-1003i−3i0-2-222-22−2323001-1003i−3i11−1+3i32−1−3i32-1-11−3i321+3i323−33−32ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000
χ544-4-2-20224-41-100−3i3i0-2-2224-400001-100−3i3i-2-21122-1-10000−3i3i3i−3i000000000000000000000000
χ554-4-2-20224-41-100−3i3i0-2-222-2223−23001-100−3i3i11−1+3i32−1−3i32-1-11−3i321+3i32−33−33−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000
χ564-4-2-20224-41-100−3i3i0-2-222-22−2323001-100−3i3i11−1−3i32−1+3i32-1-11+3i321−3i323−33−3−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ11000000000000000000000000
χ57666-366-3-2-2-3-36-3-3-3-2-21-2100000011-21110000000000000000000002200-2-200000-1-1001100
χ58666-366-3-2-2-3-36-3-3-3-2-21-2100000011-2111000000000000000000000-2-20022000001100-1-100
χ59666-3-66-3-2-2-3-3-63332-21-21000000112-1-1-10000000000000000000002-200-2200000-11001-100
χ60666-3-66-3-2-2-3-3-63332-21-21000000112-1-1-1000000000000000000000-22002-2000001-100-1100
χ6166-366-36-2-2-3-3-36-3-3-21-21-2000000111-21100000000000000000002200-2-200000-1-100110000
χ6266-366-36-2-2-3-3-36-3-3-21-21-2000000111-2110000000000000000000-2-20022000001100-1-10000
χ6366-36-6-36-2-2-3-33-63321-21-200000011-12-1-100000000000000000002-200-2200000-11001-10000
χ6466-36-6-36-2-2-3-33-63321-21-200000011-12-1-10000000000000000000-22002-2000001-100-110000
χ656-6660-6-6-226-600000-2-22200006-6-22000000000000000000000-22000000000000000000000
χ666-6660-6-6-226-600000-2-2220000-66-220000000000000000000002-2000000000000000000000
χ671212-6-612-6-6-4-433-6-633-42222000000-1-122-1-10000000000000000000000000000000000000000
χ681212-6-6-12-6-6-4-43366-3-342222000000-1-1-2-2110000000000000000000000000000000000000000
χ6912-1212-60-126-44-6600000-424-20000002-200000000000000000000000000000000000000000000
χ7012-12-61206-12-44-66000002-4-240000002-200000000000000000000000000000000000000000000
χ7112-12-6-6066-443-3009i−9i022-2-2000000-1100−3i3i0000000000000000000000000000000000000000
χ7212-12-6-6066-443-300−9i9i022-2-2000000-11003i−3i0000000000000000000000000000000000000000

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