Finite Group Databasebeta

← Group #14277124

Character table — Group #14277124

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222444444444444444888888888888888888881010101010101010101020202020202020242424242424242424244040404040404040404040406060606060606060120120
order12223444466625661010101212121220202020101015202030303030303030606060606060606022444412121212266661212884040404040404040888824242424242424248888888888
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
χ91111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-111-1-111i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-111-1-1i−i
χ101111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-111-1-111i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-1-111i−i
χ111111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-111-1-111−ii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-1-111−ii
χ121111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-111-1-111−ii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-111-1-1−ii
χ131111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111-1-111111-1-111-1-1i−iiiii−i−i−i−i1-1-1111-1-1-1-111−i−iiiii−i−i−ii
χ141111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111-1-111111-1-111-1-1i−iiiii−i−i−i−i-111-1-1-11111-1-1ii−i−i−i−iii−ii
χ151111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111-1-111111-1-111-1-1−ii−i−i−i−iiiii1-1-1111-1-1-1-111ii−i−i−i−iiii−i
χ161111111-1-1111-11-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111-1-111111-1-111-1-1−ii−i−i−i−iiiii-111-1-1-11111-1-1−i−iiiii−i−ii−i
χ1722222-2-222222-22-2-2222-2-2222222-2-22-2-222-2-2-2-22-2-2-2-222222222-2-22222-222-2-2-2-200000000000000000000000000000000
χ1822222-2-222222-22-2-2222-2-2222222-2-22-2-222-2-2-2-22-2-2-2-22222-2-2-2-222-2-2-2-22-2-2222200000000000000000000000000000000
χ1922222-2-2-2-22222222222-2-2-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222-2-200000000000000000000000000000000
χ2022222-2-2-2-22222222222-2-2-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-22200000000000000000000000000000000
χ212222-12222-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-100000000002222-1-1-1-1-1-1-1-10000000000
χ222222-12222-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-10000000000-2-2-2-2111111110000000000
χ232222-12222-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-211111100000000002i2i−2i−2i−i−i−i−iiiii0000000000
χ242222-12222-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-21111110000000000−2i−2i2i2iiiii−i−i−i−i0000000000
χ252222-122-2-2-1-1-1-2211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-1111122-2-2221111-2-1-111-1-100000000002i−2i2i−2i−i−iii−i−iii0000000000
χ262222-122-2-2-1-1-1-2211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-1111122-2-2221111-2-1-111-1-10000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ272222-122-2-2-1-1-1-2211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-11111-2-222-2-2-1-1-1-1211-1-11100000000002-2-22-1-11111-1-10000000000
χ282222-122-2-2-1-1-1-2211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-11111-2-222-2-2-1-1-1-1211-1-1110000000000-222-211-1-1-1-1110000000000
χ292222-1-2-222-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-12222-2-2-1-1-1-1-2-1-1111100000000000000−i3i3−i3i3−i3i3−i3i30000000000
χ302222-1-2-222-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-12222-2-2-1-1-1-1-2-1-1111100000000000000i3−i3i3−i3i3−i3i3−i30000000000
χ312222-1-2-222-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-1-2-2-2-2221111211-1-1-1-1000000000000003−33−3−33−330000000000
χ322222-1-2-222-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-1-2-2-2-2221111211-1-1-1-100000000000000−33−333−33−30000000000
χ332222-1-2-2-2-2-1-1-122-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-111000000000000003−3−333−3−330000000000
χ342222-1-2-2-2-2-1-1-122-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-2-2-211112-1-1-1-11100000000000000−333−3−333−30000000000
χ352222-1-2-2-2-2-1-1-122-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-100000000000000−i3i3i3−i3i3−i3−i3i30000000000
χ362222-1-2-2-2-2-1-1-122-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-21111-1-100000000000000i3−i3−i3i3−i3i3i3−i30000000000
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χ4222-2-2200−2i2i2-2-202002-2-200−2i2i−2i−2i2i2i002002-20000-20000−2i−2i2i2i2-2−2i2i00−2i−2i2i2i02-200000000000000000000000000−22−i2i2−22−i2i200
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χ4422-2-2200−2i2i2-2-202002-2-200−2i2i−2i−2i2i2i002002-20000-20000−2i−2i2i2i-222i−2i002i2i−2i−2i0-2200000000000000000000000000i2−i2−22−i2i22−200
χ454444444444444-144-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000044-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444444-144-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-4-4111111110000000000000000000000
χ474444444-4-4444-4-1-4-4-1-1-144-4-4111111-1-1-1-1-11111-1-1-1-1-11111000000000000000004i−4i−i−i−i−iiiii0000000000000000000000
χ484444444-4-4444-4-1-4-4-1-1-144-4-4111111-1-1-1-1-11111-1-1-1-1-1111100000000000000000−4i4iiiii−i−i−i−i0000000000000000000000
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χ798888-4-8-888-4-4-4-8-244-2-2-244-4-4-2-2-2-22212211-1-1-1-11-1-1-1-111110000000000000000000000000000000000000000000000000
χ808888-4-8-8-8-8-4-4-48-2-4-4-2-2-244442222-2-21221111111-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000
χ8188-8-88008i−8i8-8-80-200-222008i−8i−2i−2i2i2i00-200-22000020000−2i−2i2i2i0000000000000000000000000000000000000000000000000
χ8288-8-8800−8i8i8-8-80-200-22200−8i8i2i2i−2i−2i00-200-220000200002i2i−2i−2i0000000000000000000000000000000000000000000000000
χ8388-8-8-4008i−8i-4440-200-22200−4i4i−2i−2i2i2i001001-1−i15i15i15−i15-1−1515−1515ii−i−i0000000000000000000000000000000000000000000000000
χ8488-8-8-4008i−8i-4440-200-22200−4i4i−2i−2i2i2i001001-1i15−i15−i15i15-115−1515−15ii−i−i0000000000000000000000000000000000000000000000000
χ8588-8-8-400−8i8i-4440-200-222004i−4i2i2i−2i−2i001001-1−i15i15i15−i15-115−1515−15−i−iii0000000000000000000000000000000000000000000000000
χ8688-8-8-400−8i8i-4440-200-222004i−4i2i2i−2i−2i001001-1i15−i15−i15i15-1−1515−1515−i−iii0000000000000000000000000000000000000000000000000
χ878-88-8-48i−8i004-440-2002-22−4i4i00−2i52i5−2i52i5−25251−2i2i-1155−5−5-1ii−i−ii5−i5i5−i50000000000000000000000000000000000000000000000000
χ888-88-8-48i−8i004-440-2002-22−4i4i002i5−2i52i5−2i525−251−2i2i-11−5−555-1ii−i−i−i5i5−i5i50000000000000000000000000000000000000000000000000
χ898-88-8-4−8i8i004-440-2002-224i−4i00−2i52i5−2i52i525−2512i−2i-11−5−555-1−i−iiii5−i5i5−i50000000000000000000000000000000000000000000000000
χ908-88-8-4−8i8i004-440-2002-224i−4i002i5−2i52i5−2i5−252512i−2i-1155−5−5-1−i−iii−i5i5−i5i50000000000000000000000000000000000000000000000000
χ918-8-8880000-8-880-20022-20000−252525−2500-200220000-20000−252525−250000000000000000000000000000000000000000000000000
χ928-8-8880000-8-880-20022-2000025−25−252500-200220000-2000025−25−25250000000000000000000000000000000000000000000000000
χ938-8-88-4000044-40-2−4i34i322-20000−252525−2500100-1-1i3−i3i3−i31−i15i15i15−i155−5−550000000000000000000000000000000000000000000000000
χ948-8-88-4000044-40-2−4i34i322-2000025−25−252500100-1-1i3−i3i3−i31i15−i15−i15i15−555−50000000000000000000000000000000000000000000000000
χ958-8-88-4000044-40-24i3−4i322-20000−252525−2500100-1-1−i3i3−i3i31i15−i15−i15i155−5−550000000000000000000000000000000000000000000000000
χ968-8-88-4000044-40-24i3−4i322-2000025−25−252500100-1-1−i3i3−i3i31−i15i15i15−i15−555−50000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.