Finite Group Databasebeta

← Group #72228895

Character table — Group #72228895

Order 2160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112121520336364560448486080448486080112121520336364560448486080448486080112121520336364560448486080448486080
order1552321010263151563315156331515636303066315156331515633151563630306631515633151563
χ1111111111111111111111111111111111111111111111111111111111111
χ231−521+52-1031−521+52-1031−521+52-1031−521+52-1031−521+52-1031−521+52-1031−521+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+521−52-1031+521−52-1031+521−52-1031+521−52-1031+521−52-1031+521−52-1031+521−52-10
χ44-1-1014-1-1014-1-1014-1-1014-1-1014-1-1014-1-1014-1-1014-1-1014-1-1014-1-1014-1-101
χ55001-15001-15001-15001-15001-15001-15001-15001-15001-15001-15001-15001-1
χ61111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ731−521+52-1031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i32031−521+52-1031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i32031−521+52-1031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320
χ831+521−52-1031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i32031+521−52-1031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i32031+521−52-1031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320
χ94-1-1014-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i324-1-1014-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i324-1-1014-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i32
χ105001-15001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i325001-15001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i325001-15001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i32
χ111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ1231−521+52-1031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i32031−521+52-1031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i32031−521+52-1031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320
χ1331+521−52-1031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i32031+521−52-1031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i32031+521−52-1031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320
χ144-1-1014-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i324-1-1014-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i324-1-1014-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i32
χ155001-15001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i325001-15001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i325001-15001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i32
χ1633333-1-1-1-1-1000000000033333-1-1-1-1-1000000000033333-1-1-1-1-10000000000
χ1793−3523+352-30-3−1+52−1−5210000000000093−3523+352-30-3−1+52−1−5210000000000093−3523+352-30-3−1+52−1−52100000000000
χ1893+3523−352-30-3−1−52−1+5210000000000093+3523−352-30-3−1−52−1+5210000000000093+3523−352-30-3−1−52−1+52100000000000
χ1912-3-303-4110-1000000000012-3-303-4110-1000000000012-3-303-4110-10000000000
χ2015003-3-500-11000000000015003-3-500-11000000000015003-3-500-110000000000
χ2111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2231−521+52-1031−521+52-1031−521+52-1031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320
χ2331+521−52-1031+521−52-1031+521−52-1031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320
χ244-1-1014-1-1014-1-1014-1-101−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32
χ255001-15001-15001-15001-1−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32
χ261111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32
χ2731−521+52-1031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i32031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i32031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320
χ2831+521−52-1031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i32031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i32031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320
χ294-1-1014-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i324-1-101−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i324-1-101−2+2i31−i321−i320−1+i32
χ305001-15001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5−5i3200−1−i321+i325001-1−5−5i3200−1−i321+i32−5−5i3200−1−i321+i325001-1−5+5i3200−1+i321−i32
χ311111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111
χ3231−521+52-1031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i32031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i32031−521+52-10
χ3331+521−52-1031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i32031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i32031+521−52-10
χ344-1-1014-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i324-1-101−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i324-1-101
χ355001-15001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i325001-1−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5+5i3200−1+i321−i325001-1
χ3633333-1-1-1-1-10000000000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i320000000000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i320000000000
χ3793−3523+352-30-3−1+52−1−52100000000000−9+9i32−3ζ2−3ζ8−3ζ11−3ζ143−3i3203−3i32ζ2+ζ8ζ11+ζ14−1+i3200000000000−9−9i32−3ζ7−3ζ13−3ζ−3ζ43+3i3203+3i32ζ7+ζ13ζ+ζ4−1−i3200000000000
χ3893+3523−352-30-3−1−52−1+52100000000000−9+9i32−3ζ11−3ζ14−3ζ2−3ζ83−3i3203−3i32ζ11+ζ14ζ2+ζ8−1+i3200000000000−9−9i32−3ζ−3ζ4−3ζ7−3ζ133+3i3203+3i32ζ+ζ4ζ7+ζ13−1−i3200000000000
χ3912-3-303-4110-10000000000−6+6i33−3i323−3i320−3+3i322−2i3−1+i32−1+i3201−i320000000000−6−6i33+3i323+3i320−3−3i322+2i3−1−i32−1−i3201+i320000000000
χ4015003-3-500-110000000000−15+15i3200−3+3i323−3i325−5i32001−i32−1+i320000000000−15−15i3200−3−3i323+3i325+5i32001+i32−1−i320000000000
χ4111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4231−521+52-1031−521+52-1031−521+52-1031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320
χ4331+521−52-1031+521−52-1031+521−52-1031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320
χ444-1-1014-1-1014-1-1014-1-101−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32
χ455001-15001-15001-15001-1−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32
χ461111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111
χ4731−521+52-1031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i32031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i32031−521+52-10
χ4831+521−52-1031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i32031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i32031+521−52-10
χ494-1-1014-1-101−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i324-1-101−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i324-1-101
χ505001-15001-1−5+5i3200−1+i321−i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i325001-1−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5+5i3200−1+i321−i32−5−5i3200−1−i321+i325001-1
χ511111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32
χ5231−521+52-1031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3−3i32−ζ7−ζ13−ζ−ζ41+i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i32031−521+52-10−3+3i32−ζ2−ζ8−ζ11−ζ141−i320−3+3i32−ζ2−ζ8−ζ11−ζ141−i32031−521+52-10−3−3i32−ζ7−ζ13−ζ−ζ41+i320
χ5331+521−52-1031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3−3i32−ζ−ζ4−ζ7−ζ131+i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i32031+521−52-10−3+3i32−ζ11−ζ14−ζ2−ζ81−i320−3+3i32−ζ11−ζ14−ζ2−ζ81−i32031+521−52-10−3−3i32−ζ−ζ4−ζ7−ζ131+i320
χ544-1-1014-1-101−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i32−2−2i31+i321+i320−1−i32−2−2i31+i321+i320−1−i32−2+2i31−i321−i320−1+i324-1-101−2+2i31−i321−i320−1+i32−2+2i31−i321−i320−1+i324-1-101−2−2i31+i321+i320−1−i32
χ555001-15001-1−5−5i3200−1−i321+i32−5+5i3200−1+i321−i32−5−5i3200−1−i321+i32−5−5i3200−1−i321+i32−5+5i3200−1+i321−i325001-1−5+5i3200−1+i321−i32−5+5i3200−1+i321−i325001-1−5−5i3200−1−i321+i32
χ5633333-1-1-1-1-10000000000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i320000000000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i320000000000
χ5793−3523+352-30-3−1+52−1−52100000000000−9−9i32−3ζ7−3ζ13−3ζ−3ζ43+3i3203+3i32ζ7+ζ13ζ+ζ4−1−i3200000000000−9+9i32−3ζ2−3ζ8−3ζ11−3ζ143−3i3203−3i32ζ2+ζ8ζ11+ζ14−1+i3200000000000
χ5893+3523−352-30-3−1−52−1+52100000000000−9−9i32−3ζ−3ζ4−3ζ7−3ζ133+3i3203+3i32ζ+ζ4ζ7+ζ13−1−i3200000000000−9+9i32−3ζ11−3ζ14−3ζ2−3ζ83−3i3203−3i32ζ11+ζ14ζ2+ζ8−1+i3200000000000
χ5912-3-303-4110-10000000000−6−6i33+3i323+3i320−3−3i322+2i3−1−i32−1−i3201+i320000000000−6+6i33−3i323−3i320−3+3i322−2i3−1+i32−1+i3201−i320000000000
χ6015003-3-500-110000000000−15−15i3200−3−3i323+3i325+5i32001+i32−1−i320000000000−15+15i3200−3+3i323−3i325−5i32001−i32−1+i320000000000

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