Finite Group Databasebeta

← Group #11756741

Character table — Group #11756741

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size112444444445566881010101010161616161616161620202020242430303030303040404040404040404040
order12433566102020222412124444415153030606060606666102024444412121212121212121212
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111-1-11111-1ii−i−i11111111-1-1-1-111-1-1ii−i−i-1-1iiii−i−i−i−i
χ411111111111-1-11111-1−i−iii11111111-1-1-1-111-1-1−i−iii-1-1−i−i−i−iiiii
χ5111−1−i32−1+i321−1−i32−1+i321111111−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ6111−1−i32−1+i321−1−i32−1+i321111111−1−i32−1+i321-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ7111−1−i32−1+i321−1−i32−1+i32111-1-111−1−i32−1+i32-1ii−i−i−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i3211-1-1ii−i−i1+i321−i32−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59
χ8111−1−i32−1+i321−1−i32−1+i32111-1-111−1−i32−1+i32-1−i−iii−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i3211-1-1−i−iii1+i321−i32ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59
χ9111−1+i32−1−i321−1+i32−1−i321111111−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ10111−1+i32−1−i321−1+i32−1−i321111111−1+i32−1−i321-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ11111−1+i32−1−i321−1+i32−1−i32111-1-111−1+i32−1−i32-1ii−i−i−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i3211-1-1ii−i−i1−i321+i32−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43
χ12111−1+i32−1−i321−1+i32−1−i32111-1-111−1+i32−1−i32-1−i−iii−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i3211-1-1−i−iii1−i321+i32ζ11+ζ23+ζ47+ζ59ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43−ζ7−ζ19−ζ31−ζ43
χ1311-1111111-1-111-11-1-1-11-11-11111-1-1-1-11111-11-111-11-1-1-11-11-11-11-1
χ1411-1111111-1-111-11-1-1-1-11-111111-1-1-1-11111-11-11-11-11-1-1-11-11-11-11
χ1511-1111111-1-1-1-1-11-1-11i−i−ii1111-1-1-1-1-1-1-1-1-111-1i−i−ii11i−ii−i−ii−ii
χ1611-1111111-1-1-1-1-11-1-11−iii−i1111-1-1-1-1-1-1-1-1-111-1−iii−i11−ii−iii−ii−i
χ1711-1−1−i32−1+i321−1−i32−1+i321-1-111-111+i321−i32-11-11-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11-111-11-11+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ1811-1−1−i32−1+i321−1−i32−1+i321-1-111-111+i321−i32-1-11-11−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11-11-11-111+i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ1911-1−1−i32−1+i321−1−i32−1+i321-1-1-1-1-111+i321−i321i−i−ii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i321+i321−i32-111-1i−i−ii−1−i32−1+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59
χ2011-1−1−i32−1+i321−1−i32−1+i321-1-1-1-1-111+i321−i321−iii−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i321+i321−i32-111-1−iii−i−1−i32−1+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59
χ2111-1−1+i32−1−i321−1+i32−1−i321-1-111-111−i321+i32-11-11-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11-111-11-11−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ2211-1−1+i32−1−i321−1+i32−1−i321-1-111-111−i321+i32-1-11-11−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11-11-11-111−i321+i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ2311-1−1+i32−1−i321−1+i32−1−i321-1-1-1-1-111−i321+i321i−i−ii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i321−i321+i32-111-1i−i−ii−1+i32−1−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43
χ2411-1−1+i32−1−i321−1+i32−1−i321-1-1-1-1-111−i321+i321−iii−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i321−i321+i32-111-1−iii−i−1+i32−1−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43
χ253330030033333-1-10033333000000000000-1-1-1-1-1-1-1-10000000000
χ263330030033333-1-1003-3-3-3-3000000000000-1-1-1-111110000000000
χ2733300300333-3-3-1-100-33i3i−3i−3i000000000000-1-111−i−iii0000000000
χ2833300300333-3-3-1-100-3−3i−3i3i3i000000000000-1-111ii−i−i0000000000
χ2933-3003003-3-3331-100-33-33-30000000000001-11-1-11-110000000000
χ3033-3003003-3-3331-100-3-33-330000000000001-11-11-11-10000000000
χ3133-3003003-3-3-3-31-10033i−3i−3i3i0000000000001-1-11−iii−i0000000000
χ3233-3003003-3-3-3-31-1003−3i3i3i−3i0000000000001-1-11i−i−ii0000000000
χ3344444-144-1-1-100444400000-1-1-1-1-1-1-1-10000-1-10000000000000000
χ34444−2−2i3−2+2i3-1−2−2i3−2+2i3-1-1-10044−2−2i3−2+2i3000001+i321−i321+i321−i321+i321+i321−i321−i320000-1-10000000000000000
χ35444−2+2i3−2−2i3-1−2+2i3−2−2i3-1-1-10044−2+2i3−2−2i3000001−i321+i321−i321+i321−i321−i321+i321+i320000-1-10000000000000000
χ3644-444-144-11100-44-4-400000-1-1-1-1111100001-10000000000000000
χ3744-4−2−2i3−2+2i3-1−2−2i3−2+2i3-11100-442+2i32−2i3000001+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i3200001-10000000000000000
χ3844-4−2+2i3−2−2i3-1−2+2i3−2−2i3-11100-442−2i32+2i3000001−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i3200001-10000000000000000
χ394-40-2-2422-4004-4000000000-2-222000022-2-2000000000000000000
χ404-40-2-2422-400-44000000000-2-2220000-2-222000000000000000000
χ414-401+i31−i34−1−i3−1+i3-4004-40000000001+i31−i3−1−i3−1+i30000−1−i3−1+i31+i31−i3000000000000000000
χ424-401+i31−i34−1−i3−1+i3-400-440000000001+i31−i3−1−i3−1+i300001+i31−i3−1−i3−1+i3000000000000000000
χ434-401−i31+i34−1+i3−1−i3-4004-40000000001−i31+i3−1+i3−1−i30000−1+i3−1−i31−i31+i3000000000000000000
χ444-401−i31+i34−1+i3−1−i3-400-440000000001−i31+i3−1+i3−1−i300001−i31+i3−1+i3−1−i3000000000000000000
χ458-80-4-4-2442−2i52i50000000000011-1-1−i5i5−i5i50000000000000000000000
χ468-80-4-4-24422i5−2i50000000000011-1-1i5−i5i5−i50000000000000000000000
χ478-802+2i32−2i3-2−2−2i3−2+2i32−2i52i500000000000−1−i32−1+i321+i321−i32−ζ7+ζ19+ζ31−ζ43ζ7−ζ19−ζ31+ζ43ζ11−ζ23−ζ47+ζ59−ζ11+ζ23+ζ47−ζ590000000000000000000000
χ488-802+2i32−2i3-2−2−2i3−2+2i322i5−2i500000000000−1−i32−1+i321+i321−i32ζ7−ζ19−ζ31+ζ43−ζ7+ζ19+ζ31−ζ43−ζ11+ζ23+ζ47−ζ59ζ11−ζ23−ζ47+ζ590000000000000000000000
χ498-802−2i32+2i3-2−2+2i3−2−2i32−2i52i500000000000−1+i32−1−i321−i321+i32ζ11−ζ23−ζ47+ζ59−ζ11+ζ23+ζ47−ζ59−ζ7+ζ19+ζ31−ζ43ζ7−ζ19−ζ31+ζ430000000000000000000000
χ508-802−2i32+2i3-2−2+2i3−2−2i322i5−2i500000000000−1+i32−1−i321−i321+i32−ζ11+ζ23+ζ47−ζ59ζ11−ζ23−ζ47+ζ59ζ7−ζ19−ζ31+ζ43−ζ7+ζ19+ζ31−ζ430000000000000000000000
χ5112121200-300-3-3-300-4-40000000000000000000110000000000000000
χ521212-1200-300-333004-40000000000000000000-110000000000000000

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