Finite Group Databasebeta

← Group #14285061

Character table — Group #14285061

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222444444444444444888888888888888888881010101010101010101020202020202020242424242424242424244040404040404040404040406060606060606060120120
order122222344666456610101012121212202020201010152020303030303030306060606060606060444444121212124121212121212241010101020202020888824242424242424248888888824
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
χ91111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i-11
χ101111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii-11
χ111111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111i−ii−iii−i−iii−i−i−i−iii−i−iii1-1
χ121111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111−ii−ii−i−iii−i−iiiii−i−iii−i−i1-1
χ131111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1111-1
χ141111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-11-1
χ151111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-1-11
χ161111-1-11-1-111111-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-11111-111-1-1-11111-1-111-1-1-1-111-11
χ172222222-2-2222-2222222-2-2-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2222-2-22-2-2-2-2-222-2-22200000000000000000000000000000000
χ182222222-2-2222-2222222-2-2-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-2-222-222222-2-222-2-200000000000000000000000000000000
χ19222222-122-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-100000000002222-1-1-1-1-1-1-1-10000000000
χ20222222-122-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-10000000000-2-2-2-2111111110000000000
χ21222222-122-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-211111100000000002i2i−2i−2i−i−i−i−iiiii0000000000
χ22222222-122-1-1-122-1-1222-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-21111110000000000−2i−2i2i2iiiii−i−i−i−i0000000000
χ23222222-1-2-2-1-1-1-22-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111222-2-221111-2-1-111-1-1000000000000003−33−33−33−30000000000
χ24222222-1-2-2-1-1-1-22-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111222-2-221111-2-1-111-1-100000000000000−33−33−33−330000000000
χ25222222-1-2-2-1-1-1-22-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-2-222-2-1-1-1-1211-1-11100000000000000−i3i3−i3i3i3−i3i3−i30000000000
χ26222222-1-2-2-1-1-1-22-1-12221111-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-2-222-2-1-1-1-1211-1-11100000000000000i3−i3i3−i3−i3i3−i3i30000000000
χ272222-2-2222222-22-2-2222-2-2222222-2-22-2-222-2-2-2-22-2-2-2-2222222-222-22222-222-2-2-2-200000000000000000000000000000000
χ282222-2-2222222-22-2-2222-2-2222222-2-22-2-222-2-2-2-22-2-2-2-22222-2-22-2-22-2-2-2-22-2-2222200000000000000000000000000000000
χ292222-2-2-122-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-122-222-2-1-1-1-1-2-1-1111100000000000000−i3i3i3−i3−i3i3i3−i30000000000
χ302222-2-2-122-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-122-222-2-1-1-1-1-2-1-1111100000000000000i3−i3−i3i3i3−i3−i3i30000000000
χ312222-2-2-122-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-1-2-22-2-221111211-1-1-1-1000000000000003−3−33−333−30000000000
χ322222-2-2-122-1-1-1-221122211-1-12222-2-2-1-2-2-1-11111-11111-1-1-1-1-2-22-2-221111211-1-1-1-100000000000000−333−33−3−330000000000
χ332222-2-2-1-2-2-1-1-12211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-1111122-2-2-2-211112-1-1-1-11100000000002i−2i2i−2i−i−iii−i−iii0000000000
χ342222-2-2-1-2-2-1-1-12211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-1111122-2-2-2-211112-1-1-1-1110000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ352222-2-2-1-2-2-1-1-12211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-11111-2-22222-1-1-1-1-21111-1-100000000002-2-22-1-11111-1-10000000000
χ362222-2-2-1-2-2-1-1-12211222-1-111-2-2-2-2-2-2-122-1-11111-1-1-1-1-11111-2-22222-1-1-1-1-21111-1-10000000000-222-211-1-1-1-1110000000000
χ3722-2-20022i−2i-22-202002-2-2002i−2i2i2i−2i−2i002002-20000-200002i2i−2i−2i2i−2i02-2022-2-202i−2i000000000000000000000000002−2−i2i2−i2i22−200
χ3822-2-20022i−2i-22-202002-2-2002i−2i2i2i−2i−2i002002-20000-200002i2i−2i−2i2i−2i02-2022-2-202i−2i00000000000000000000000000−22i2−i2i2−i2−2200
χ3922-2-20022i−2i-22-202002-2-2002i−2i2i2i−2i−2i002002-20000-200002i2i−2i−2i−2i2i0-220-2-2220−2i2i00000000000000000000000000−i2i2−222−2i2−i200
χ4022-2-20022i−2i-22-202002-2-2002i−2i2i2i−2i−2i002002-20000-200002i2i−2i−2i−2i2i0-220-2-2220−2i2i00000000000000000000000000i2−i22−2−22−i2i200
χ4122-2-2002−2i2i-22-202002-2-200−2i2i−2i−2i2i2i002002-20000-20000−2i−2i2i2i2i−2i0-220-2-22202i−2i00000000000000000000000000−i2i22−2−22i2−i200
χ4222-2-2002−2i2i-22-202002-2-200−2i2i−2i−2i2i2i002002-20000-20000−2i−2i2i2i2i−2i0-220-2-22202i−2i00000000000000000000000000i2−i2−222−2−i2i200
χ4322-2-2002−2i2i-22-202002-2-200−2i2i−2i−2i2i2i002002-20000-20000−2i−2i2i2i−2i2i02-2022-2-20−2i2i000000000000000000000000002−2i2−i2i2−i22−200
χ4422-2-2002−2i2i-22-202002-2-200−2i2i−2i−2i2i2i002002-20000-20000−2i−2i2i2i−2i2i02-2022-2-20−2i2i00000000000000000000000000−22−i2i2−i2i2−2200
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
χ474444444-4-4444-4-144-1-1-1-4-4-4-41111-1-1-111-1-1-1-1-1-1-1111111110000000000000000000−5−555−5−5550000000000000000000000
χ484444444-4-4444-4-144-1-1-1-4-4-4-41111-1-1-111-1-1-1-1-1-1-111111111000000000000000000055−5−555−5−50000000000000000000000
χ494444-4-4444444-4-1-4-4-1-1-1-4-444-1-1-1-111-111-1-11111-11111-1-1-1-10000000000000000000−5−55555−5−50000000000000000000000
χ504444-4-4444444-4-1-4-4-1-1-1-4-444-1-1-1-111-111-1-11111-11111-1-1-1-1000000000000000000055−5−5−5−5550000000000000000000000
χ514444-4-44-4-44444-1-4-4-1-1-144-4-4111111-1-1-1-1-11111-1-1-1-1-11111000000000000000004-4-1-1-1-111110000000000000000000000
χ524444-4-44-4-44444-1-4-4-1-1-144-4-4111111-1-1-1-1-11111-1-1-1-1-1111100000000000000000-441111-1-1-1-10000000000000000000000
χ5344-4-400-24i−4i2-2204004-4-400−2i2i4i4i−4i−4i00-200-22000020000−2i−2i2i2i4i−4i04-40-2-2220−2i2i000000000000000000000000000000000000
χ5444-4-400-24i−4i2-2204004-4-400−2i2i4i4i−4i−4i00-200-22000020000−2i−2i2i2i−4i4i0-44022-2-202i−2i000000000000000000000000000000000000
χ5544-4-400-2−4i4i2-2204004-4-4002i−2i−4i−4i4i4i00-200-220000200002i2i−2i−2i4i−4i0-44022-2-20−2i2i000000000000000000000000000000000000
χ5644-4-400-2−4i4i2-2204004-4-4002i−2i−4i−4i4i4i00-200-220000200002i2i−2i−2i−4i4i04-40-2-22202i−2i000000000000000000000000000000000000
χ574-44-400400-4-440400-44-40000000000400-440000-40000000000400-40000000004-400000000000000000000000000000000
χ584-44-400400-4-440400-44-40000000000400-440000-40000000000-4004000000000-4400000000000000000000000000000000
χ594-44-400-20022-20400-44-423−2300000000-2002-2000022323−23−23000000400-423−2323−2300000-2200000000000000000000000000000000
χ604-44-400-20022-20400-44-423−2300000000-2002-2000022323−23−23000000-4004−2323−2323000002-200000000000000000000000000000000
χ614-44-400-20022-20400-44-4−232300000000-2002-200002−23−232323000000400-4−2323−232300000-2200000000000000000000000000000000
χ624-44-400-20022-20400-44-4−232300000000-2002-200002−23−232323000000-400423−2323−23000002-200000000000000000000000000000000
χ634-4-444-44004-4-4044-4-4-44000000004-4400-4-444-4-44000000000000000000000000000000000000000000000000000000000
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χ654-4-444-44004-4-40-14-411-10000−55−55-11-1−5511-1-111-1−55−55−55−550000000000000000000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ1160000000000000000000000
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χ798888-8-8-488-4-4-4-8-244-2-2-244-4-4-2-2-2-22212211-1-1-1-11-1-1-1-111110000000000000000000000000000000000000000000000000
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χ8588-8-800-4−8i8i4-440-200-222004i−4i2i2i−2i−2i001001-1−i15i15−i15i15-115−15−1515−i−iii0000000000000000000000000000000000000000000000000
χ8688-8-800-4−8i8i4-440-200-222004i−4i2i2i−2i−2i001001-1i15−i15i15−i15-1−151515−15−i−iii0000000000000000000000000000000000000000000000000
χ878-88-800800-8-880-2002-220000−2i52i52i5−2i500-2002-2000020000−2i52i52i5−2i50000000000000000000000000000000000000000000000000
χ888-88-800800-8-880-2002-2200002i5−2i5−2i52i500-2002-20000200002i5−2i5−2i52i50000000000000000000000000000000000000000000000000
χ898-88-800-40044-40-2002-2243−4300−2i52i52i5−2i500100-11−i15i15i15−i15-1−3−333i5−i5−i5i50000000000000000000000000000000000000000000000000
χ908-88-800-40044-40-2002-2243−43002i5−2i5−2i52i500100-11i15−i15−i15i15-1−3−333−i5i5i5−i50000000000000000000000000000000000000000000000000
χ918-88-800-40044-40-2002-22−434300−2i52i52i5−2i500100-11i15−i15−i15i15-133−3−3i5−i5−i5i50000000000000000000000000000000000000000000000000
χ928-88-800-40044-40-2002-22−4343002i5−2i5−2i52i500100-11−i15i15i15−i15-133−3−3−i5i5i5−i50000000000000000000000000000000000000000000000000
χ938-8-888-8-400-4440-2-4422-20000−2525−2525-221−2525-1-111-1-115−55−55−55−50000000000000000000000000000000000000000000000000
χ948-8-888-8-400-4440-2-4422-2000025−2525−25-22125−25-1-111-1-11−55−55−55−550000000000000000000000000000000000000000000000000
χ958-8-88-88-400-4440-24-422-20000−2525−25252-2125−25-1-1-1-1111−55−555−55−50000000000000000000000000000000000000000000000000
χ968-8-88-88-400-4440-24-422-2000025−2525−252-21−2525-1-1-1-11115−55−5−55−550000000000000000000000000000000000000000000000000

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