Finite Group Databasebeta

← Group #14302817

Character table — Group #14302817

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444444488888810101010101016161616161616162020202020202020202020202020202020202020202020202020202020202020202424242424244848120120120120120120
order122344622566666101010121215202030303022441212101030303030606044668888888812121212122424242424242424242424242424242444202020202020444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1ii−i−i
χ611111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111−i−iii
χ711111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1−i−iii
χ811111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111ii−i−i
χ91111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1111-11-11-1
χ101111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-1-11-11-11
χ111111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1111-1-11-11
χ121111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-111111-1-1-111-11-1
χ131111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-1-111-11i−i−ii
χ141111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii-11111iiii−i−i−i−i−i−i−i−iiiii-111111-1-11-1−iii−i
χ151111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-1-111-11−iii−i
χ161111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i-11111−i−i−i−iiiiiiiii−i−i−i−i-111111-1-11-1i−i−ii
χ172222-2-222-22222-2-2222-2-22-2-222222-2-2-2-22-222-2-2-2-22-22200000000-222-2-2000000000000000000000000000000
χ182222-2-222-22222-2-2222-2-22-2-2222-2-222222-222-2-2-2-2-22-2-2000000002-2-222000000000000000000000000000000
χ192222-2-22-2222-2-222222-2-22-2-222222-2-2-2-2-22-2-222-2-2-222200000000-2-2-222000000000000000000000000000000
χ202222-2-22-2222-2-222222-2-22-2-2222-2-22222-22-2-222-2-22-2-2-200000000222-2-2000000000000000000000000000000
χ21222-122-1222-1-1-1-1-1222-1-1-122-1-1-12222-1-122-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222-122-1222-1-1-1-1-1222-1-1-122-1-1-12222-1-122-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1111111111111111100000000000000
χ23222-122-1222-1-1-1-1-1222-1-1-122-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-2112i2i2i2i−2i−2i−2i−2i11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000
χ24222-122-1222-1-1-1-1-1222-1-1-122-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-211−2i−2i−2i−2i2i2i2i2i11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000
χ25222-122-1-2-22-11111222-1-1-122-1-1-12222-1-1-2-21111-1-1-2-2-1-122-2-222-2-2-11111-1-1-1-11111-1-1-1-1111100000000000000
χ26222-122-1-2-22-11111222-1-1-122-1-1-12222-1-1-2-21111-1-1-2-2-1-1-2-222-2-222-111111111-1-1-1-11111-1-1-1-100000000000000
χ27222-122-1-2-22-11111222-1-1-122-1-1-1-2-2-2-211-2-21111-1-122112i2i−2i−2i−2i−2i2i2i1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ28222-122-1-2-22-11111222-1-1-122-1-1-1-2-2-2-211-2-21111-1-12211−2i−2i2i2i2i2i−2i−2i1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ29222-1-2-2-12-22-1-1-11122211-1-2-2-1-1-122-2-2112-2-1-111112-2-1-1000000001-1-11133−3−333−3−333−3−333−3−300000000000000
χ30222-1-2-2-12-22-1-1-11122211-1-2-2-1-1-122-2-2112-2-1-111112-2-1-1000000001-1-111−3−333−3−333−3−333−3−33300000000000000
χ31222-1-2-2-12-22-1-1-11122211-1-2-2-1-1-1-2-222-1-12-2-1-11111-221100000000-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ32222-1-2-2-12-22-1-1-11122211-1-2-2-1-1-1-2-222-1-12-2-1-11111-221100000000-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ33222-1-2-2-1-222-111-1-122211-1-2-2-1-1-122-2-211-2211-1-111-22-1-100000000111-1-133−3−3−3−33333−3−3−3−33300000000000000
χ34222-1-2-2-1-222-111-1-122211-1-2-2-1-1-122-2-211-2211-1-111-22-1-100000000111-1-1−3−33333−3−3−3−33333−3−300000000000000
χ35222-1-2-2-1-222-111-1-122211-1-2-2-1-1-1-2-222-1-1-2211-1-1112-21100000000-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ36222-1-2-2-1-222-111-1-122211-1-2-2-1-1-1-2-222-1-1-2211-1-1112-21100000000-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ3722-222-22002-20000-2-222-222-2-2-222-22-2-2-20000002-2002-2002i−2i002i−2i2000000002i−2i2i−2i00002i−2i2i−2i00000000000000
χ3822-222-22002-20000-2-222-222-2-2-222-22-2-2-20000002-2002-200−2i2i00−2i2i200000000−2i2i−2i2i0000−2i2i−2i2i00000000000000
χ3922-222-22002-20000-2-222-222-2-2-22-22-22220000002-200-22002-200-22-2000000002-22-20000-22-2200000000000000
χ4022-222-22002-20000-2-222-222-2-2-22-22-22220000002-200-2200-22002-2-200000000-22-2200002-22-200000000000000
χ4122-22-222002-20000-2-22-222-22-2-222-2-2222000000-22002-22-2002-200-200002-22-200002-22-2000000000000000000
χ4222-22-222002-20000-2-22-222-22-2-222-2-2222000000-22002-2-2200-2200-20000-22-220000-22-22000000000000000000
χ4322-22-222002-20000-2-22-222-22-2-22-222-2-2-2000000-2200-222i−2i00−2i2i00200002i−2i2i−2i0000−2i2i−2i2i000000000000000000
χ4422-22-222002-20000-2-22-222-22-2-22-222-2-2-2000000-2200-22−2i2i002i−2i0020000−2i2i−2i2i00002i−2i2i−2i000000000000000000
χ4522-2-12-2-10021−i3i3−i3i3-2-22-11-12-211-12-22-21100−i3i3−i3i3-1100-11002i−2i002i−2i-1−i3i3−i3i33−3−33−ii−ii3−3−33−ii−ii00000000000000
χ4622-2-12-2-10021−i3i3−i3i3-2-22-11-12-211-12-22-21100−i3i3−i3i3-1100-1100−2i2i00−2i2i-1−i3i3−i3i3−333−3i−ii−i−333−3i−ii−i00000000000000
χ4722-2-12-2-10021−i3i3−i3i3-2-22-11-12-211-1-22-22-1-100−i3i3−i3i3-11001-1002-200-221i3−i3i3−i3−i3i3i3−i3-11-11i3−i3−i3i31-11-100000000000000
χ4822-2-12-2-10021−i3i3−i3i3-2-22-11-12-211-1-22-22-1-100−i3i3−i3i3-11001-100-22002-21i3−i3i3−i3i3−i3−i3i31-11-1−i3i3i3−i3-11-1100000000000000
χ4922-2-12-2-10021i3−i3i3−i3-2-22-11-12-211-12-22-21100i3−i3i3−i3-1100-11002i−2i002i−2i-1i3−i3i3−i3−333−3−ii−ii−333−3−ii−ii00000000000000
χ5022-2-12-2-10021i3−i3i3−i3-2-22-11-12-211-12-22-21100i3−i3i3−i3-1100-1100−2i2i00−2i2i-1i3−i3i3−i33−3−33i−ii−i3−3−33i−ii−i00000000000000
χ5122-2-12-2-10021i3−i3i3−i3-2-22-11-12-211-1-22-22-1-100i3−i3i3−i3-11001-1002-200-221−i3i3−i3i3i3−i3−i3i3-11-11−i3i3i3−i31-11-100000000000000
χ5222-2-12-2-10021i3−i3i3−i3-2-22-11-12-211-1-22-22-1-100i3−i3i3−i3-11001-100-22002-21−i3i3−i3i3−i3i3i3−i31-11-1i3−i3−i3i3-11-1100000000000000
χ5322-2-1-22-10021−i3i3i3−i3-2-221-1-1-2211-12-2-22-1-100−i3i3i3−i31-100-112-2002-2001−i3i3i3−i3-11-11−i3i3i3−i3-11-11−i3i3i3−i300000000000000
χ5422-2-1-22-10021−i3i3i3−i3-2-221-1-1-2211-12-2-22-1-100−i3i3i3−i31-100-11-2200-22001−i3i3i3−i31-11-1i3−i3−i3i31-11-1i3−i3−i3i300000000000000
χ5522-2-1-22-10021−i3i3i3−i3-2-221-1-1-2211-1-222-21100−i3i3i3−i31-1001-12i−2i00−2i2i00-1i3−i3−i3i3−ii−ii3−3−33i−ii−i−333−300000000000000
χ5622-2-1-22-10021−i3i3i3−i3-2-221-1-1-2211-1-222-21100−i3i3i3−i31-1001-1−2i2i002i−2i00-1i3−i3−i3i3i−ii−i−333−3−ii−ii3−3−3300000000000000
χ5722-2-1-22-10021i3−i3−i3i3-2-221-1-1-2211-12-2-22-1-100i3−i3−i3i31-100-112-2002-2001i3−i3−i3i3-11-11i3−i3−i3i3-11-11i3−i3−i3i300000000000000
χ5822-2-1-22-10021i3−i3−i3i3-2-221-1-1-2211-12-2-22-1-100i3−i3−i3i31-100-11-2200-22001i3−i3−i3i31-11-1−i3i3i3−i31-11-1−i3i3i3−i300000000000000
χ5922-2-1-22-10021i3−i3−i3i3-2-221-1-1-2211-1-222-21100i3−i3−i3i31-1001-12i−2i00−2i2i00-1−i3i3i3−i3−ii−ii−333−3i−ii−i3−3−3300000000000000
χ6022-2-1-22-10021i3−i3−i3i3-2-221-1-1-2211-1-222-21100i3−i3−i3i31-1001-1−2i2i002i−2i00-1−i3i3i3−i3i−ii−i3−3−33−ii−ii−333−300000000000000
χ61444444444-144444-1-1-144-1-1-1-1-1-1000000-1-1-1-1-1-1-1-100000000000000000000000000000000044-1-1-1-1-1-1000000
χ62444444444-144444-1-1-144-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000000000000-4-4111111000000
χ634444444-4-4-14-4-4-4-4-1-1-144-1-1-1-1-1-1000000111111-1-10000000000000000000000000000000004-41111-1-1000000
χ644444444-4-4-14-4-4-4-4-1-1-144-1-1-1-1-1-1000000111111-1-1000000000000000000000000000000000-44-1-1-1-111000000
χ654444-4-444-4-1444-4-4-1-1-1-4-4-111-1-1-1000000-11-1-1111100000000000000000000000000000000000−5−555−55000000
χ664444-4-444-4-1444-4-4-1-1-1-4-4-111-1-1-1000000-11-1-111110000000000000000000000000000000000055−5−55−5000000
χ674444-4-44-44-14-4-444-1-1-1-4-4-111-1-1-10000001-111-1-11100000000000000000000000000000000000−5−5555−5000000
χ684444-4-44-44-14-4-444-1-1-1-4-4-111-1-1-10000001-111-1-1110000000000000000000000000000000000055−5−5−55000000
χ69888-488-488-2-4-4-4-4-4-2-2-2-4-41-2-2111000000-2-211111100000000000000000000000000000000000000000000000
χ70888-488-4-8-8-2-44444-2-2-2-4-41-2-211100000022-1-1-1-11100000000000000000000000000000000000000000000000
χ71888-4-8-8-48-8-2-4-4-444-2-2-244122111000000-2211-1-1-1-100000000000000000000000000000000000000000000000
χ72888-4-8-8-4-88-2-444-4-4-2-2-2441221110000002-2-1-111-1-100000000000000000000000000000000000000000000000
χ7388-888-8800-2-8000022-28-8-2-2222-2000000000000-2200000000000000000000000000000000000000000000000
χ7488-88-88800-2-8000022-2-88-22-222-20000000000002-200000000000000000000000000000000000000000000000
χ7588-8-48-8-400-24−4i34i3−4i34i322-2-441-22-1-1100000000i3−i3i3−i31-100000000000000000000000000000000000000000000000
χ7688-8-48-8-400-244i3−4i34i3−4i322-2-441-22-1-1100000000−i3i3−i3i31-100000000000000000000000000000000000000000000000
χ7788-8-4-88-400-24−4i34i34i3−4i322-24-412-2-1-1100000000i3−i3−i3i3-1100000000000000000000000000000000000000000000000
χ7888-8-4-88-400-244i3−4i3−4i34i322-24-412-2-1-1100000000−i3i3i3−i3-1100000000000000000000000000000000000000000000000
χ798-80800-80080000000-80080000-80000000000000000000000000000000000000000000000000000000000000
χ808-80800-800-200000−2525200-200−252520000000000000000000000000000000000000000000000000−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ4700000000
χ818-80800-800-200000−2525200-200−2525200000000000000000000000000000000000000000000000002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ4700000000
χ828-80800-800-20000025−25200-20025−25200000000000000000000000000000000000000000000000002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ5900000000
χ838-80800-800-20000025−25200-20025−2520000000000000000000000000000000000000000000000000−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ5900000000
χ848-80-40040080000000-800-400004000043−430000000000000000000000000000000000000000000000000000000
χ858-80-40040080000000-800-4000040000−43430000000000000000000000000000000000000000000000000000000
χ8616-160-800800-400000−454540020025−25-20000000000000000000000000000000000000000000000000000000000000
χ8716-160-800800-40000045−45400200−2525-20000000000000000000000000000000000000000000000000000000000000

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