Finite Group Databasebeta

← Group #14284112

Character table — Group #14284112

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222444444444444444888888888888888888881010101010101010101020202020202020242424242424242424244040404040404040404040406060606060606060120120
order122222344666456610101010101010121212121520202020303030303030306060606060606060444444121212124121212121212442020202020202020888824242424242424248888888844
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
χ91111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-1
χ101111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-1
χ111111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111i−ii−iii−i−iii−i−i−i−iii−i−iii-11
χ121111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-11111−ii−ii−i−iii−i−iiiii−i−iii−i−i-11
χ131111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111-11
χ141111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1111-11111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-11
χ151111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-11-1
χ161111-1-11-1-111111-1-11-1-1-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1-1-11111-111-1-1-11111-1-111-1-1-1-1111-1
χ172222222-2-2222-22222222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-22222-222-2-2-2-200000000000000000000000000000000
χ182222222-2-2222-22222222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22-2-2222200000000000000000000000000000000
χ19222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-100000000002222-1-1-1-1-1-1-1-10000000000
χ20222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-1-1-10000000000-2-2-2-2111111110000000000
χ21222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-211111100000000002i2i−2i−2i−i−i−i−iiiii0000000000
χ22222222-122-1-1-122-1-12222222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-21111110000000000−2i−2i2i2iiiii−i−i−i−i0000000000
χ23222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-2-1-1111100000000000000−i3i3−i3i3−i3i3−i3i30000000000
χ24222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-2-1-1111100000000000000i3−i3i3−i3i3−i3i3−i30000000000
χ25222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2221111211-1-1-1-1000000000000003−33−3−33−330000000000
χ26222222-1-2-2-1-1-1-22-1-122222221111-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2221111211-1-1-1-100000000000000−33−333−33−30000000000
χ272222-2-2222222-22-2-22-2-2-2-222-2-2222-2-22222-2-2-2-22-2-2-2-2222222-2-222-2-2-2-2-222-2-22200000000000000000000000000000000
χ282222-2-2222222-22-2-22-2-2-2-222-2-2222-2-22222-2-2-2-22-2-2-2-22222-2-222-2-222222-2-222-2-200000000000000000000000000000000
χ292222-2-2-122-1-1-1-22112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-122-2-2221111-2-1-111-1-1000000000000003−3−333−3−330000000000
χ302222-2-2-122-1-1-1-22112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-122-2-2221111-2-1-111-1-100000000000000−333−3−333−30000000000
χ312222-2-2-122-1-1-1-22112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-1-2-222-2-2-1-1-1-1211-1-11100000000000000−i3i3i3−i3i3−i3−i3i30000000000
χ322222-2-2-122-1-1-1-22112-2-2-2-22211-1-1-1-2-222-1-11111-11111-1-1-1-1-2-222-2-2-1-1-1-1211-1-11100000000000000i3−i3−i3i3−i3i3i3−i30000000000
χ332222-2-2-1-2-2-1-1-122112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-1111122-2-2-2-211112-1-1-1-11100000000002i−2i2i−2i−i−iii−i−iii0000000000
χ342222-2-2-1-2-2-1-1-122112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-1111122-2-2-2-211112-1-1-1-1110000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ352222-2-2-1-2-2-1-1-122112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-11111-2-22222-1-1-1-1-21111-1-100000000002-2-22-1-11111-1-10000000000
χ362222-2-2-1-2-2-1-1-122112-2-2-2-222-1-111-122-2-2-1-11111-1-1-1-1-11111-2-22222-1-1-1-1-21111-1-10000000000-222-211-1-1-1-1110000000000
χ372-2-222-2200-22-2022-2222-2-2-2-20000200002-222-2-2-2000000002i−2i2i−2i002i2i−2i−2i02i−2i000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00
χ382-2-222-2200-22-2022-2222-2-2-2-20000200002-222-2-2-2000000002i−2i2i−2i002i2i−2i−2i02i−2i00000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00
χ392-2-222-2200-22-2022-2222-2-2-2-20000200002-222-2-2-200000000−2i2i−2i2i00−2i−2i2i2i0−2i2i000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00
χ402-2-222-2200-22-2022-2222-2-2-2-20000200002-222-2-2-200000000−2i2i−2i2i00−2i−2i2i2i0−2i2i00000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00
χ412-2-22-22200-22-202-222-2-222-2-20000200002-2-2-222-2000000002i−2i−2i2i00−2i−2i2i2i02i−2i000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00
χ422-2-22-22200-22-202-222-2-222-2-20000200002-2-2-222-2000000002i−2i−2i2i00−2i−2i2i2i02i−2i00000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00
χ432-2-22-22200-22-202-222-2-222-2-20000200002-2-2-222-200000000−2i2i2i−2i002i2i−2i−2i0−2i2i000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00
χ442-2-22-22200-22-202-222-2-222-2-20000200002-2-2-222-200000000−2i2i2i−2i002i2i−2i−2i0−2i2i00000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00
χ454444444444444-144-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000044-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444444-144-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-4-4111111110000000000000000000000
χ474444444-4-4444-4-144-1-1-1-1-1-1-1-4-4-4-4-11111-1-1-1-1-1-1-1111111110000000000000000000−5−555−5−5550000000000000000000000
χ484444444-4-4444-4-144-1-1-1-1-1-1-1-4-4-4-4-11111-1-1-1-1-1-1-111111111000000000000000000055−5−555−5−50000000000000000000000
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χ514444-4-44-4-44444-1-4-4-11111-1-144-4-4-1-1-111-1-11111-1-1-1-1-11111000000000000000004-4-1-1-1-111110000000000000000000000
χ524444-4-44-4-44444-1-4-4-11111-1-144-4-4-1-1-111-1-11111-1-1-1-1-1111100000000000000000-441111-1-1-1-10000000000000000000000
χ5344-4-40044-44-4-40400-400004-4004-44004-4-4-400004000044-4-40000000000000000000000000000000000000000000000000
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χ858-88-800800-8-880-2002−252525−252-20000-200002-2−252525−252000000000000000000000000000000000000000000000000000000000
χ868-88-800800-8-880-200225−25−25252-20000-200002-225−25−25252000000000000000000000000000000000000000000000000000000000
χ878-88-800-40044-40-2002−252525−252-243−430010000-115−5−55-1−33−33−1515−15150000000000000000000000000000000000000000000000000
χ888-88-800-40044-40-2002−252525−252-2−43430010000-115−5−55-13−33−315−1515−150000000000000000000000000000000000000000000000000
χ898-88-800-40044-40-200225−25−25252-243−430010000-11−555−5-1−33−3315−1515−150000000000000000000000000000000000000000000000000
χ908-88-800-40044-40-200225−25−25252-2−43430010000-11−555−5-13−33−3−1515−15150000000000000000000000000000000000000000000000000
χ918-8-888-8800-88-80-28-8-2-2-222220000-20000-22-2-2222000000000000000000000000000000000000000000000000000000000
χ928-8-888-8-4004-440-2-44-2-2-222220000100001-111-1-1-1−151515−15−151515−150000000000000000000000000000000000000000000000000
χ938-8-888-8-4004-440-2-44-2-2-222220000100001-111-1-1-115−15−151515−15−15150000000000000000000000000000000000000000000000000
χ948-8-88-88800-88-80-2-88-222-2-2220000-20000-2222-2-22000000000000000000000000000000000000000000000000000000000
χ958-8-88-88-4004-440-24-4-222-2-2220000100001-1-1-111-1−151515−1515−15−15150000000000000000000000000000000000000000000000000
χ968-8-88-88-4004-440-24-4-222-2-2220000100001-1-1-111-115−15−1515−151515−150000000000000000000000000000000000000000000000000

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