Finite Group Databasebeta

← Group #72253802

Character table — Group #72253802

Order 3840.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1333334566666666121212121212121212121212121212121212121212151515151520203030303030303030606060606060606060606464256256320320320320320320
order122222522222222210101010101010101010101010101010101010101022222442222222244444444443315156612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ4111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ5111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ6111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ71111111-111111111111111111111111111111-1-1-1-1-1i−i-1-1-1-1-1-1-1-1i−iiiii−i−i−i−i1111-1-1i−ii−i
χ81111111-111111111111111111111111111111-1-1-1-1-1i−i-1-1-1-1-1-1-1-1i−iiiii−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321−i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59
χ91111111-111111111111111111111111111111-1-1-1-1-1i−i-1-1-1-1-1-1-1-1i−iiiii−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321+i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43
χ101111111-111111111111111111111111111111-1-1-1-1-1−ii-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii1111-1-1−ii−ii
χ111111111-111111111111111111111111111111-1-1-1-1-1−ii-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−1−i32−1+i32−1−i32−1+i321+i321−i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59
χ121111111-111111111111111111111111111111-1-1-1-1-1−ii-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−1+i32−1−i32−1+i32−1−i321−i321+i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43
χ1333333333-1-1-1-1-1-1-1-133333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-10000000000
χ1433333333-1-1-1-1-1-1-1-133333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333-3-3-1-1-1-1-1-1-1-1-3-3111111110000000000
χ153333333-3-1-1-1-1-1-1-1-133333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3-33i−3i111111113i−3i−i−i−i−iiiii0000000000
χ163333333-3-1-1-1-1-1-1-1-133333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3-3−3i3i11111111−3i3iiiii−i−i−i−i0000000000
χ1733-1-1-1-13333-1-1-1-1-1-13-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333-1-1-1-1-1-1-1-13-1-1-13-1-1-10000000000
χ1833-1-1-1-13333-1-1-1-1-1-13-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-3-333-1-1-1-1-1-111-3111-31110000000000
χ1933-1-1-1-133-1-133-1-1-1-13-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1333-1-133-1-1-1-1-1-1-13-1-1-13-1-10000000000
χ2033-1-1-1-133-1-133-1-1-1-13-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-13-3-3-1-133-1-1-1-1111-3111-3110000000000
χ2133-1-1-1-133-1-1-1-133-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1333-1-1-1-133-1-1-1-1-1-13-1-1-13-10000000000
χ2233-1-1-1-133-1-1-1-133-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-13-3-3-1-1-1-133-1-11111-3111-310000000000
χ2333-1-1-1-133-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1333-1-1-1-1-1-133-1-1-1-1-13-1-1-130000000000
χ2433-1-1-1-133-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-13-3-3-1-1-1-1-1-13311111-3111-30000000000
χ2533-1-1-1-13-333-1-1-1-1-1-13-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-11111-33i−3i-3-3111111−ii3i−i−i−i−3iiii0000000000
χ2633-1-1-1-13-333-1-1-1-1-1-13-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-11111-3−3i3i-3-3111111i−i−3iiii3i−i−i−i0000000000
χ2733-1-1-1-13-3-1-133-1-1-1-13-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-11111-33i−3i11-3-31111−ii−i3i−i−ii−3iii0000000000
χ2833-1-1-1-13-3-1-133-1-1-1-13-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-11111-3−3i3i11-3-31111i−ii−3iii−i3i−i−i0000000000
χ2933-1-1-1-13-3-1-1-1-133-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-11111-33i−3i1111-3-311−ii−i−i3i−iii−3ii0000000000
χ3033-1-1-1-13-3-1-1-1-133-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-11111-3−3i3i1111-3-311i−iii−3ii−i−i3i−i0000000000
χ3133-1-1-1-13-3-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133331111-33i−3i111111-3-3−ii−i−i−i3iiii−3i0000000000
χ3233-1-1-1-13-3-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133331111-3−3i3i111111-3-3i−iiii−3i−i−i−i3i0000000000
χ33444444-1044444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000044-1-1000000
χ34444444-1044444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000−2−2i3−2+2i31+i321−i32000000
χ35444444-1044444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000−2+2i3−2−2i31−i321+i32000000
χ366-26-2-2-2662-22-22-22-2-26-2-2-222-2-222-2-222-2-222-2-26-2-2-2-2002-22-22-22-200000000000000000000
χ376-26-2-2-266-22-22-22-22-26-2-2-2-2-222-2-222-2-222-2-2226-2-2-2-200-22-22-22-2200000000000000000000
χ386-26-2-2-26-62-22-22-22-2-26-2-2-222-2-222-2-222-2-222-2-2-6222200-22-22-22-2200000000000000000000
χ396-26-2-2-26-6-22-22-22-22-26-2-2-2-2-222-2-222-2-222-2-222-62222002-22-22-22-200000000000000000000
χ406-2-26-2-2662-22-2-22-22-2-26-2-222-2-222-2-2-2-222-2-222-26-2-2-2002-22-2-22-2200000000000000000000
χ416-2-26-2-266-22-222-22-2-2-26-2-2-2-222-2-22222-2-222-2-2-26-2-2-200-22-222-22-200000000000000000000
χ426-2-26-2-26-62-22-2-22-22-2-26-2-222-2-222-2-2-2-222-2-2222-622200-22-222-22-200000000000000000000
χ436-2-26-2-26-6-22-222-22-2-2-26-2-2-2-222-2-22222-2-222-2-22-6222002-22-2-22-2200000000000000000000
χ446-2-2-26-2662-2-222-2-22-2-2-26-222-2-2-2-22222-2-2-2-222-2-26-2-2002-2-222-2-2200000000000000000000
χ456-2-2-26-266-222-2-222-2-2-2-26-2-2-22222-2-2-2-22222-2-2-2-26-2-200-222-2-222-200000000000000000000
χ466-2-2-26-26-62-2-222-2-22-2-2-26-222-2-2-2-22222-2-2-2-22222-62200-222-2-222-200000000000000000000
χ476-2-2-26-26-6-222-2-222-2-2-2-26-2-2-22222-2-2-2-22222-2-222-622002-2-222-2-2200000000000000000000
χ486-2-2-2-26662-2-22-222-2-2-2-2-2622-2-2-2-222-2-22222-2-2-2-2-26-2002-2-22-222-200000000000000000000
χ496-2-2-2-2666-222-22-2-22-2-2-2-26-2-22222-2-222-2-2-2-222-2-2-26-200-222-22-2-2200000000000000000000
χ506-2-2-2-266-62-2-22-222-2-2-2-2-2622-2-2-2-222-2-22222-2-2222-6200-222-22-2-2200000000000000000000
χ516-2-2-2-266-6-222-22-2-22-2-2-2-26-2-22222-2-222-2-2-2-222222-62002-2-22-222-200000000000000000000
χ52121212121212-30-4-4-4-4-4-4-4-4-3-3-3-3-3111111111111111100000000000000000000000000000000000
χ531212-4-4-4-4-301212-4-4-4-4-4-4-31111-3-3-3-311111111111100000000000000000000000000000000000
χ541212-4-4-4-4-30-4-41212-4-4-4-4-311111111-3-3-3-31111111100000000000000000000000000000000000
χ551212-4-4-4-4-30-4-4-4-41212-4-4-3111111111111-3-3-3-3111100000000000000000000000000000000000
χ561212-4-4-4-4-30-4-4-4-4-4-41212-31111111111111111-3-3-3-300000000000000000000000000000000000
χ5712-412-4-4-4-304-44-44-44-41-3111−1−25−1+2511−1−25−1+2511−1−25−1+2511−1−25−1+251100000000000000000000000000000000000
χ5812-412-4-4-4-304-44-44-44-41-3111−1+25−1−2511−1+25−1−2511−1+25−1−2511−1+25−1−251100000000000000000000000000000000000
χ5912-412-4-4-4-30-44-44-44-441-311111−1−25−1+2511−1−25−1+2511−1−25−1+2511−1−25−1+2500000000000000000000000000000000000
χ6012-412-4-4-4-30-44-44-44-441-311111−1+25−1−2511−1+25−1−2511−1+25−1−2511−1+25−1−2500000000000000000000000000000000000
χ6112-4-412-4-4-304-44-4-44-4411-311−1−25−1+2511−1+25−1−251111−1−25−1+2511−1+25−1−2500000000000000000000000000000000000
χ6212-4-412-4-4-304-44-4-44-4411-311−1+25−1−2511−1−25−1+251111−1+25−1−2511−1−25−1+2500000000000000000000000000000000000
χ6312-4-412-4-4-30-44-444-44-411-31111−1−25−1+2511−1+25−1−25−1−25−1+2511−1+25−1−251100000000000000000000000000000000000
χ6412-4-412-4-4-30-44-444-44-411-31111−1+25−1−2511−1−25−1+25−1+25−1−2511−1−25−1+251100000000000000000000000000000000000
χ6512-4-4-412-4-304-4-444-4-44111-31−1−25−1+251111−1+25−1−25−1+25−1−251111−1−25−1+2500000000000000000000000000000000000
χ6612-4-4-412-4-304-4-444-4-44111-31−1+25−1−251111−1−25−1+25−1−25−1+251111−1+25−1−2500000000000000000000000000000000000
χ6712-4-4-412-4-30-444-4-444-4111-3111−1−25−1+25−1+25−1−251111−1+25−1−25−1−25−1+251100000000000000000000000000000000000
χ6812-4-4-412-4-30-444-4-444-4111-3111−1+25−1−25−1−25−1+251111−1−25−1+25−1+25−1−251100000000000000000000000000000000000
χ6912-4-4-4-412-304-4-44-444-41111-3−1−25−1+251111−1−25−1+2511−1+25−1−25−1+25−1−251100000000000000000000000000000000000
χ7012-4-4-4-412-304-4-44-444-41111-3−1+25−1−251111−1+25−1−2511−1−25−1+25−1−25−1+251100000000000000000000000000000000000
χ7112-4-4-4-412-30-444-44-4-441111-311−1−25−1+25−1−25−1+2511−1+25−1−251111−1+25−1−2500000000000000000000000000000000000
χ7212-4-4-4-412-30-444-44-4-441111-311−1+25−1−25−1+25−1−2511−1−25−1+251111−1−25−1+2500000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.