Finite Group Databasebeta

← Group #67192

Character table — Group #67192

Order 360.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size112121520112121520112121520112121520112121520112121520
order1552331515633151563210102663030666303066
χ1111111111111111111111111111111
χ231−521+52-1031−521+52-1031−521+52-1031−521+52-1031−521+52-1031−521+52-10
χ331+521−52-1031+521−52-1031+521−52-1031+521−52-1031+521−52-1031+521−52-10
χ44-1-1014-1-1014-1-1014-1-1014-1-1014-1-101
χ55001-15001-15001-15001-15001-15001-1
χ611111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ731−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i32031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320
χ831+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i32031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320
χ94-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i324-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i32
χ105001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i325001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i32
χ1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ1231−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i32031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320
χ1331+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i32031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320
χ144-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i324-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i32
χ155001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i325001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i32
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1731−521+52-1031−521+52-1031−521+52-10-3−1+52−1−5210-3−1+52−1−5210-3−1+52−1−5210
χ1831+521−52-1031+521−52-1031+521−52-10-3−1−52−1+5210-3−1−52−1+5210-3−1−52−1+5210
χ194-1-1014-1-1014-1-101-4110-1-4110-1-4110-1
χ205001-15001-15001-1-500-11-500-11-500-11
χ2111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i32
χ2231−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320-3−1+52−1−52103−3i32ζ2+ζ8ζ11+ζ14−1+i3203+3i32ζ7+ζ13ζ+ζ4−1−i320
χ2331+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320-3−1−52−1+52103−3i32ζ11+ζ14ζ2+ζ8−1+i3203+3i32ζ+ζ4ζ7+ζ13−1−i320
χ244-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i32-4110-12−2i3−1+i32−1+i3201−i322+2i3−1−i32−1−i3201+i32
χ255001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i32-500-115−5i32001−i32−1+i325+5i32001+i32−1−i32
χ2611111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−i321−i321−i321−i32
χ2731−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320-3−1+52−1−52103+3i32ζ7+ζ13ζ+ζ4−1−i3203−3i32ζ2+ζ8ζ11+ζ14−1+i320
χ2831+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320-3−1−52−1+52103+3i32ζ+ζ4ζ7+ζ13−1−i3203−3i32ζ11+ζ14ζ2+ζ8−1+i320
χ294-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i32-4110-12+2i3−1−i32−1−i3201+i322−2i3−1+i32−1+i3201−i32
χ305001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i32-500-115+5i32001+i32−1−i325−5i32001−i32−1+i32

Here ζ is a primitive root of unity of order 15 (ζ15 = 1); i = ζ3.