Finite Group Databasebeta

← Group #14302076

Character table — Group #14302076

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222444444444444444888888888888888888881010101010101010101020202020202020242424242424242424244040404040404040404040406060606060606060120120
order1222222236662566666610101010101010101010101530303030303030303030303030303022222266662666666241010101020202020444412121212121212124444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii11
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-1
χ10111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-1
χ11111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111i−ii−iii−i−iii−i−i−i−iii−i−iii-11
χ12111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111−ii−ii−i−iii−i−iiiii−i−iii−i−i-11
χ13111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111-11
χ14111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-11
χ15111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-11-1
χ16111111-1-11111-1111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-11111-111-1-1-11111-1-111-1-1-1-1111-1
χ1722222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-100000000002222-1-1-1-1-1-1-1-10000000000
χ1822222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-10000000000-2-2-2-2111111110000000000
χ1922222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-211111100000000002i2i−2i−2i−i−i−i−iiiii0000000000
χ2022222222-1-1-1-122-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-21111110000000000−2i−2i2i2iiiii−i−i−i−i0000000000
χ21222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-11100000000002i−2i2i−2i−i−iii−i−iii0000000000
χ22222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-1110000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ23222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-100000000002-2-22-1-11111-1-10000000000
χ24222222-2-2-1-1-1-1-22-1-111112222222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-10000000000-222-211-1-1-1-1110000000000
χ252222-2-2222222-22-2-222-2-222-2-2-2-2222-2-22222-2-2-2-22222-2-2-2-2222-2-22-2-2-2-2-222-2-22200000000000000000000000000000000
χ262222-2-2222222-22-2-222-2-222-2-2-2-2222-2-22222-2-2-2-22222-2-2-2-2-2-2-222-222222-2-222-2-200000000000000000000000000000000
χ272222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-11111222-2-221111-2-1-111-1-1000000000000003−33−33−33−30000000000
χ282222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-11111222-2-221111-2-1-111-1-100000000000000−33−33−33−330000000000
χ292222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-11111-2-2-222-2-1-1-1-1211-1-11100000000000000−i3i3−i3i3i3−i3i3−i30000000000
χ302222-2-222-1-1-1-1-2211-1-11122-2-2-2-2222-2-2-1-1-1-11111-1-1-1-11111-2-2-222-2-1-1-1-1211-1-11100000000000000i3−i3i3−i3−i3i3−i3i30000000000
χ312222-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-2222222-2-2-2-2-2-2-2-2222222-222-22222-222-2-2-2-200000000000000000000000000000000
χ322222-2-2-2-2222222-2-2-2-22222-2-2-2-22-2-2222222-2-2-2-2-2-2-2-22222-2-22-2-22-2-2-2-22-2-2222200000000000000000000000000000000
χ332222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-122-222-2-1-1-1-1-2-1-1111100000000000000−i3i3i3−i3−i3i3i3−i30000000000
χ342222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-122-222-2-1-1-1-1-2-1-1111100000000000000i3−i3−i3i3i3−i3−i3i30000000000
χ352222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-1-2-22-2-221111211-1-1-1-1000000000000003−3−33−333−30000000000
χ362222-2-2-2-2-1-1-1-1221111-1-122-2-2-2-22-2-222-1-1-1-111111111-1-1-1-1-2-22-2-221111211-1-1-1-100000000000000−333−33−3−330000000000
χ372-22-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-2000000000022-2-222-2-2000002-20000000000000000000000002i−2i2i−2i0000
χ382-22-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-2000000000022-2-222-2-2000002-2000000000000000000000000−2i2i−2i2i0000
χ392-22-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-20000000000-2-222-2-22200000-220000000000000000000000002-2-220000
χ402-22-22-20022-2-2022-200002-222-2-2-2000022-2-222-2-20000000000-2-222-2-22200000-22000000000000000000000000-222-20000
χ412-22-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-22200000000002-22-2-2-222000002-200000000000000000000002i−2i00002i−2i00
χ422-22-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-22200000000002-22-2-2-222000002-20000000000000000000000−2i2i0000−2i2i00
χ432-22-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-2220000000000-22-2222-2-200000-2200000000000000000000002-20000-2200
χ442-22-2-220022-2-202-2200002-2-2-222-2000022-2-2-2-2220000000000-22-2222-2-200000-220000000000000000000000-2200002-200
χ454444444444444-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000044-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444444-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-4-4111111110000000000000000000000
χ47444444-4-44444-4-144-4-4-4-4-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000000004-4-1-1-1-111110000000000000000000000
χ48444444-4-44444-4-144-4-4-4-4-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000-441111-1-1-1-10000000000000000000000
χ494444-4-4444444-4-1-4-444-4-4-1-11111-1-1-111-1-1-1-11111-1-1-1-111110000000000000000000−5−555−5−5550000000000000000000000
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χ514444-4-4-4-444444-1-4-4-4-444-1-11111-111-1-1-1-1-1-111111111-1-1-1-10000000000000000000−5−55555−5−50000000000000000000000
χ524444-4-4-4-444444-1-4-4-4-444-1-11111-111-1-1-1-1-1-111111111-1-1-1-1000000000000000000055−5−5−5−5550000000000000000000000
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χ918-8-8800008-8-880-20000002-2−252525−2520000-222-2−252525−25000000000000000000000000000000000000000000000000000000000
χ928-8-8800008-8-880-20000002-225−25−252520000-222-225−25−2525000000000000000000000000000000000000000000000000000000000
χ938-8-880000-444-40-20000−4i34i32-2−252525−25200001-1-115−5−55i15−i15−i15i15i3−i3i3−i30000000000000000000000000000000000000000000000000
χ948-8-880000-444-40-20000−4i34i32-225−25−2525200001-1-11−555−5−i15i15i15−i15i3−i3i3−i30000000000000000000000000000000000000000000000000
χ958-8-880000-444-40-200004i3−4i32-2−252525−25200001-1-115−5−55−i15i15i15−i15−i3i3−i3i30000000000000000000000000000000000000000000000000
χ968-8-880000-444-40-200004i3−4i32-225−25−2525200001-1-11−555−5i15−i15−i15i15−i3i3−i3i30000000000000000000000000000000000000000000000000

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