Finite Group Databasebeta

← Group #10624044

Character table — Group #10624044

Order 720.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size11222222224444444444666688881010101212121212121212121212121215151820202030303036366090
order123355661010361515151530303030441212151530302661220202020606060606060606044466621212202062
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-11111111111111-1-11-1-1-1-1-1-111-1-1
χ3111111111111111111111-1111111111-111-1-11111-1-1-1-111-1111-111-1-1-1-1
χ4111111111111111111111-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111
χ511111111111111111111-11-1-111111111-1-111-1-1-1-11111-1-1-11111-1-1-1-11-1
χ611111111111111111111-11-1-11111-1-1-11-1-111-1-1-1-1111111-1-1-1-1-111-1-1-11
χ711111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-11
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ92222−1−52−1+5222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222−1−52−1+52−1−52−1+520002−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52002000000−1−52−1+5200
χ102222−1−52−1+5222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-222−1−52−1+52−1−52−1+52000-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−5200-20000001+521−5200
χ112222−1−52−1+5222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-22-2-2−1−52−1+52−1−52−1+5200021+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200-20000001+521−5200
χ122222−1−52−1+5222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+52−1−52−1+52000-21+521−521+521−521+521+521−521−521+521+521−521−52002000000−1−52−1+5200
χ132222−1+52−1−5222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222−1+52−1−52−1+52−1−520002−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52002000000−1+52−1−5200
χ142222−1+52−1−5222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-222−1+52−1−52−1+52−1−52000-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+5200-20000001−521+5200
χ152222−1+52−1−5222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22-2-2−1+52−1−52−1+52−1−5200021−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200-20000001−521+5200
χ162222−1+52−1−5222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1−52000-21−521+521−521+521−521−521+521+521−521−521+521+52002000000−1+52−1−5200
χ17222-122-1222-1-12-12-12-12-10200-1-1-1-1222-100220000-1-1-1-1000-1-1-120000-10
χ18222-122-1222-1-12-12-12-12-10200-1-1-1-1-2-2-2-100220000-1-1-1-1000111-2000010
χ19222-122-1222-1-12-12-12-12-10-200-1-1-1-1222100-2-200001111000-1-1-1-2000010
χ20222-122-1222-1-12-12-12-12-10-200-1-1-1-1-2-2-2100-2-20000111100011120000-10
χ2122-12222-122-1-1-12-12-12-1220-1-1-1-1-1-12-1-102200-1-1-1-100002202-1-10-1-10000
χ2222-12222-122-1-1-12-12-12-1220-1-1-1-1-1-1-21102200-1-1-1-10000-2-20-2110110000
χ2322-12222-122-1-1-12-12-12-12-2011-1-1-1-12-1-10-2-20011110000-2-202-1-10110000
χ2422-12222-122-1-1-12-12-12-12-2011-1-1-1-1-2110-2-20011110000220-2110-1-10000
χ252-22222-2-2-2-22-22222-2-2-2-2000022-2-200000000000000002i−2i000002i−2i0000
χ262-22222-2-2-2-22-22222-2-2-2-2000022-2-20000000000000000−2i2i00000−2i2i0000
χ272-2-1222-21-2-2-11-12-121-21-2003−3-1-1110−i3i3000003−33−300002i−2i00−i3i30−ii0000
χ282-2-1222-21-2-2-11-12-121-21-2003−3-1-1110i3−i3000003−33−30000−2i2i00i3−i30i−i0000
χ292-2-1222-21-2-2-11-12-121-21-200−33-1-1110−i3i300000−33−330000−2i2i00−i3i30i−i0000
χ302-2-1222-21-2-2-11-12-121-21-200−33-1-1110i3−i300000−33−3300002i−2i00i3−i30−ii0000
χ31444-2−1−5−1+5-24−1−5−1+5-2-2−1−51+52−1+51−52−1−51+52−1+51−5204001+521−521+521−52000-200−1−5−1+500001+521+521−521−520000000000000
χ32444-2−1−5−1+5-24−1−5−1+5-2-2−1−51+52−1+51−52−1−51+52−1+51−520-4001+521−521+521−520002001+51−50000−1−52−1−52−1+52−1+520000000000000
χ33444-2−1+5−1−5-24−1+5−1−5-2-2−1+51−52−1−51+52−1+51−52−1−51+5204001−521+521−521+52000-200−1+5−1−500001−521−521+521+520000000000000
χ34444-2−1+5−1−5-24−1+5−1−5-2-2−1+51−52−1−51+52−1+51−52−1−51+520-4001−521+521−521+520002001−51+50000−1+52−1+52−1−52−1−520000000000000
χ3544-24−1−5−1+54-2−1−5−1+5-2-21+52−1−51−52−1+51+52−1−51−52−1+540-2-21+521−521+521−520000−1−5−1+5001+521+521−521−5200000000000000000
χ3644-24−1−5−1+54-2−1−5−1+5-2-21+52−1−51−52−1+51+52−1−51−52−1+5-40221+521−521+521−5200001+51−500−1−52−1−52−1+52−1+5200000000000000000
χ3744-24−1+5−1−54-2−1+5−1−5-2-21−52−1+51+52−1−51−52−1+51+52−1−540-2-21−521+521−521+520000−1+5−1−5001−521−521+521+5200000000000000000
χ3844-24−1+5−1−54-2−1+5−1−5-2-21−52−1+51+52−1−51−52−1+51+52−1−5-40221−521+521−521+5200001−51+500−1+52−1+52−1−52−1−5200000000000000000
χ3944-2-244-2-24411-2-2-2-2-2-2-2-2000011114-2-20000000000000000-2110000000
χ4044-2-244-2-24411-2-2-2-2-2-2-2-200001111-42200000000000000002-1-10000000
χ414-444−1−5−1+5-4-41+51−54-4−1−5−1−5−1+5−1+51+51+51−51−50000−1−5−1+51+51−500000000000000000000000000000
χ424-444−1+5−1−5-4-41−51+54-4−1+5−1+5−1−5−1−51−51−51+51+50000−1+5−1−51−51+500000000000000000000000000000
χ434-44-2442-4-4-4-224-24-2-42-420000-2-22200000000000000000000000000000
χ444-44-2−1−5−1+52-41+51−5-22−1−51+52−1+51−521+5−1−521−5−1+5200001+521−52−1−52−1+52000000000000ζ11+ζ19−ζ31−ζ59−ζ11−ζ19+ζ31+ζ59−ζ7−ζ23+ζ43+ζ47ζ7+ζ23−ζ43−ζ470000000000000
χ454-44-2−1−5−1+52-41+51−5-22−1−51+52−1+51−521+5−1−521−5−1+5200001+521−52−1−52−1+52000000000000−ζ11−ζ19+ζ31+ζ59ζ11+ζ19−ζ31−ζ59ζ7+ζ23−ζ43−ζ47−ζ7−ζ23+ζ43+ζ470000000000000
χ464-44-2−1+5−1−52-41−51+5-22−1+51−52−1−51+521−5−1+521+5−1−5200001−521+52−1+52−1−52000000000000−ζ7−ζ23+ζ43+ζ47ζ7+ζ23−ζ43−ζ47−ζ11−ζ19+ζ31+ζ59ζ11+ζ19−ζ31−ζ590000000000000
χ474-44-2−1+5−1−52-41−51+5-22−1+51−52−1−51+521−5−1+521+5−1−5200001−521+52−1+52−1−52000000000000ζ7+ζ23−ζ43−ζ47−ζ7−ζ23+ζ43+ζ47ζ11+ζ19−ζ31−ζ59−ζ11−ζ19+ζ31+ζ590000000000000
χ484-4-24−1−5−1+5-421+51−5-221+52−1−51−52−1+5−1−521+5−1+521−50023−231+521−52−1−52−1+5200000000−ζ11+ζ19+ζ31−ζ59ζ11−ζ19−ζ31+ζ59ζ7−ζ23+ζ43−ζ47−ζ7+ζ23−ζ43+ζ4700000000000000000
χ494-4-24−1−5−1+5-421+51−5-221+52−1−51−52−1+5−1−521+5−1+521−500−23231+521−52−1−52−1+5200000000ζ11−ζ19−ζ31+ζ59−ζ11+ζ19+ζ31−ζ59−ζ7+ζ23−ζ43+ζ47ζ7−ζ23+ζ43−ζ4700000000000000000
χ504-4-24−1+5−1−5-421−51+5-221−52−1+51+52−1−5−1+521−5−1−521+50023−231−521+52−1+52−1−5200000000ζ7−ζ23+ζ43−ζ47−ζ7+ζ23−ζ43+ζ47−ζ11+ζ19+ζ31−ζ59ζ11−ζ19−ζ31+ζ5900000000000000000
χ514-4-24−1+5−1−5-421−51+5-221−52−1+51+52−1−5−1+521−5−1−521+500−23231−521+52−1+52−1−5200000000−ζ7+ζ23−ζ43+ζ47ζ7−ζ23+ζ43−ζ47ζ11−ζ19−ζ31+ζ59−ζ11+ζ19+ζ31−ζ5900000000000000000
χ524-4-2-24422-4-41-1-2-2-2-22222000011-1-10−2i32i300000000000000000i3−i30000000
χ534-4-2-24422-4-41-1-2-2-2-22222000011-1-102i3−2i300000000000000000−i3i30000000
χ5488-4-4−2−25−2+25-4-4−2−25−2+25221+51+51−51−51+51+51−51−50000−1−52−1+52−1−52−1+5200000000000000000000000000000
χ5588-4-4−2+25−2−25-4-4−2+25−2−25221−51−51+51+51−51−51+51+50000−1+52−1−52−1+52−1−5200000000000000000000000000000
χ568-8-4-4−2−25−2+25442+252−252-21+51+51−51−5−1−5−1−5−1+5−1+50000−1−52−1+521+521−5200000000000000000000000000000
χ578-8-4-4−2+25−2−25442−252+252-21−51−51+51+5−1+5−1+5−1−5−1−50000−1+52−1−521−521+5200000000000000000000000000000

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