Finite Group Databasebeta

← Group #14299700

Character table — Group #14299700

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444445588888881010101010161616161616161620202020202020202020202020202020202020202020202020202020202020202024244848484860606060120120120120
order122344622566666101212441015202030303022412121010303030306060446688888888121212121224242424242424242424242424242424884040404088888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111ii−i−i-1-1i−i
χ6111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1−i−iii11−ii
χ7111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111−i−iii-1-1−ii
χ8111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1ii−i−i11i−i
χ91111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111111-1-1-1
χ101111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-1-1111
χ111111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-11-111
χ121111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111111-11-1-1
χ131111111-1-111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii-11111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1ii−i−i-11−ii
χ141111111-1-111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii-11111iiii−i−i−i−i−i−i−i−iiiii-11-1-111−i−iii1-1i−i
χ151111111-1-111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i-11111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1−i−iii-11i−i
χ161111111-1-111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111ii−i−i1-1−ii
χ172222-2-222-22222-2-22-2-22222-2-2222-2-22222-222-2-2-2-22-2-2-200000000222-2-2000000000000000000000000000000
χ182222-2-222-22222-2-22-2-2-2-222-2-222222-2-2-22-222-2-2-2-2-222200000000-2-2-222000000000000000000000000000000
χ192222-2-22-2222-2-2222-2-22222-2-2222-2-2222-22-2-222-2-2-22-2-2000000002-2-222000000000000000000000000000000
χ202222-2-22-2222-2-2222-2-2-2-222-2-222222-2-2-2-22-2-222-2-22-22200000000-222-2-2000000000000000000000000000000
χ21222-122-1222-1-1-1-1-12-1-1222-122-1-1-1222-1-122-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222-122-1222-1-1-1-1-12-1-1222-122-1-1-1222-1-122-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1111111111111111100000000000000
χ23222-122-1222-1-1-1-1-12-1-1-2-22-122-1-1-1-2-2-21122-1-1-1-1-1-1-2-2112i2i2i2i−2i−2i−2i−2i11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000
χ24222-122-1222-1-1-1-1-12-1-1-2-22-122-1-1-1-2-2-21122-1-1-1-1-1-1-2-211−2i−2i−2i−2i2i2i2i2i11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000
χ25222-122-1-2-22-111112-1-1222-122-1-1-1222-1-1-2-21111-1-1-2-2-1-122-2-222-2-2-11111-1-1-1-11111-1-1-1-1111100000000000000
χ26222-122-1-2-22-111112-1-1222-122-1-1-1222-1-1-2-21111-1-1-2-2-1-1-2-222-2-222-111111111-1-1-1-11111-1-1-1-100000000000000
χ27222-122-1-2-22-111112-1-1-2-22-122-1-1-1-2-2-211-2-21111-1-122112i2i−2i−2i−2i−2i2i2i1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ28222-122-1-2-22-111112-1-1-2-22-122-1-1-1-2-2-211-2-21111-1-12211−2i−2i2i2i2i2i−2i−2i1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ29222-1-2-2-12-22-1-1-111211222-1-2-2-1-1-1-2-22-1-12-2-1-111112-21100000000-1-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ30222-1-2-2-12-22-1-1-111211222-1-2-2-1-1-1-2-22-1-12-2-1-111112-21100000000-1-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ31222-1-2-2-12-22-1-1-111211-2-22-1-2-2-1-1-122-2112-2-1-11111-22-1-100000000111-1-133−3−333−3−3−3−333−3−33300000000000000
χ32222-1-2-2-12-22-1-1-111211-2-22-1-2-2-1-1-122-2112-2-1-11111-22-1-100000000111-1-1−3−333−3−33333−3−333−3−300000000000000
χ33222-1-2-2-1-222-111-1-1211222-1-2-2-1-1-1-2-22-1-1-2211-1-111-221100000000-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ34222-1-2-2-1-222-111-1-1211222-1-2-2-1-1-1-2-22-1-1-2211-1-111-221100000000-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ35222-1-2-2-1-222-111-1-1211-2-22-1-2-2-1-1-122-211-2211-1-1112-2-1-1000000001-1-11133−3−3−3−333−3−33333−3−300000000000000
χ36222-1-2-2-1-222-111-1-1211-2-22-1-2-2-1-1-122-211-2211-1-1112-2-1-1000000001-1-111−3−33333−3−333−3−3−3−33300000000000000
χ3722-222-22002-2000022-222-222-2-2-222-2-2220000002-2002-2002-2002-2-2000000002-22-200002-22-200000000000000
χ3822-222-22002-2000022-222-222-2-2-222-2-2220000002-2002-200-2200-22-200000000-22-220000-22-2200000000000000
χ3922-222-22002-2000022-2-2-2-222-2-2-22-222-2-20000002-200-22002i−2i00−2i2i2000000002i−2i2i−2i0000−2i2i−2i2i00000000000000
χ4022-222-22002-2000022-2-2-2-222-2-2-22-222-2-20000002-200-2200−2i2i002i−2i200000000−2i2i−2i2i00002i−2i2i−2i00000000000000
χ4122-22-222002-200002-2222-22-22-2-22-22-222000000-2200-222-2002-200-200002-22-200002-22-2000000000000000000
χ4222-22-222002-200002-2222-22-22-2-22-22-222000000-2200-22-2200-2200-20000-22-220000-22-22000000000000000000
χ4322-22-222002-200002-22-2-2-22-22-2-222-22-2-2000000-22002-22i−2i00−2i2i00200002i−2i2i−2i0000−2i2i−2i2i000000000000000000
χ4422-22-222002-200002-22-2-2-22-22-2-222-22-2-2000000-22002-2−2i2i002i−2i0020000−2i2i−2i2i00002i−2i2i−2i000000000000000000
χ4522-2-12-2-10021−i3i3−i3i32-1122-2-12-211-12-2-2-1-100−i3i3−i3i3-1100-11002-2002-21−i3i3−i3i3−i3i3i3−i3-11-11−i3i3i3−i3-11-1100000000000000
χ4622-2-12-2-10021−i3i3−i3i32-1122-2-12-211-12-2-2-1-100−i3i3−i3i3-1100-1100-2200-221−i3i3−i3i3i3−i3−i3i31-11-1i3−i3−i3i31-11-100000000000000
χ4722-2-12-2-10021−i3i3−i3i32-11-2-2-2-12-211-1-2221100−i3i3−i3i3-11001-1002i−2i00−2i2i-1i3−i3i3−i33−3−33−ii−ii−333−3i−ii−i00000000000000
χ4822-2-12-2-10021−i3i3−i3i32-11-2-2-2-12-211-1-2221100−i3i3−i3i3-11001-100−2i2i002i−2i-1i3−i3i3−i3−333−3i−ii−i3−3−33−ii−ii00000000000000
χ4922-2-12-2-10021i3−i3i3−i32-1122-2-12-211-12-2-2-1-100i3−i3i3−i3-1100-11002-2002-21i3−i3i3−i3i3−i3−i3i3-11-11i3−i3−i3i3-11-1100000000000000
χ5022-2-12-2-10021i3−i3i3−i32-1122-2-12-211-12-2-2-1-100i3−i3i3−i3-1100-1100-2200-221i3−i3i3−i3−i3i3i3−i31-11-1−i3i3i3−i31-11-100000000000000
χ5122-2-12-2-10021i3−i3i3−i32-11-2-2-2-12-211-1-2221100i3−i3i3−i3-11001-1002i−2i00−2i2i-1−i3i3−i3i3−333−3−ii−ii3−3−33i−ii−i00000000000000
χ5222-2-12-2-10021i3−i3i3−i32-11-2-2-2-12-211-1-2221100i3−i3i3−i3-11001-100−2i2i002i−2i-1−i3i3−i3i33−3−33i−ii−i−333−3−ii−ii00000000000000
χ5322-2-1-22-10021−i3i3i3−i321-122-2-1-2211-1-22-2-1-100−i3i3i3−i31-1001-12-2002-2001−i3i3i3−i3-11-11−i3i3i3−i3-11-11−i3i3i3−i300000000000000
χ5422-2-1-22-10021−i3i3i3−i321-122-2-1-2211-1-22-2-1-100−i3i3i3−i31-1001-1-2200-22001−i3i3i3−i31-11-1i3−i3−i3i31-11-1i3−i3−i3i300000000000000
χ5522-2-1-22-10021−i3i3i3−i321-1-2-2-2-1-2211-12-221100−i3i3i3−i31-100-112i−2i00−2i2i00-1i3−i3−i3i3−ii−ii3−3−33i−ii−i−333−300000000000000
χ5622-2-1-22-10021−i3i3i3−i321-1-2-2-2-1-2211-12-221100−i3i3i3−i31-100-11−2i2i002i−2i00-1i3−i3−i3i3i−ii−i−333−3−ii−ii3−3−3300000000000000
χ5722-2-1-22-10021i3−i3−i3i321-122-2-1-2211-1-22-2-1-100i3−i3−i3i31-1001-12-2002-2001i3−i3−i3i3-11-11i3−i3−i3i3-11-11i3−i3−i3i300000000000000
χ5822-2-1-22-10021i3−i3−i3i321-122-2-1-2211-1-22-2-1-100i3−i3−i3i31-1001-1-2200-22001i3−i3−i3i31-11-1−i3i3i3−i31-11-1−i3i3i3−i300000000000000
χ5922-2-1-22-10021i3−i3−i3i321-1-2-2-2-1-2211-12-221100i3−i3−i3i31-100-112i−2i00−2i2i00-1−i3i3i3−i3−ii−ii−333−3i−ii−i3−3−3300000000000000
χ6022-2-1-22-10021i3−i3−i3i321-1-2-2-2-1-2211-12-221100i3−i3−i3i31-100-11−2i2i002i−2i00-1−i3i3i3−i3i−ii−i3−3−33−ii−ii−333−300000000000000
χ61444444444-144444-14400-1-1-1-1-1-1-100000-1-1-1-1-1-1-1-100000000000000000000000000000000044-1-1-1-100000000
χ62444444444-144444-14400-1-1-1-1-1-1-100000-1-1-1-1-1-1-1-1000000000000000000000000000000000-4-4111100000000
χ634444444-4-4-14-4-4-4-4-14400-1-1-1-1-1-1-100000111111-1-10000000000000000000000000000000004-4-1-11100000000
χ644444444-4-4-14-4-4-4-4-14400-1-1-1-1-1-1-100000111111-1-1000000000000000000000000000000000-4411-1-100000000
χ654444-4-444-4-1444-4-4-1-4-400-1-111-1-1-100000-11-1-1111100000000000000000000000000000000000−i5i5−i5i500000000
χ664444-4-444-4-1444-4-4-1-4-400-1-111-1-1-100000-11-1-1111100000000000000000000000000000000000i5−i5i5−i500000000
χ674444-4-44-44-14-4-444-1-4-400-1-111-1-1-1000001-111-1-11100000000000000000000000000000000000−i5i5i5−i500000000
χ684444-4-44-44-14-4-444-1-4-400-1-111-1-1-1000001-111-1-11100000000000000000000000000000000000i5−i5−i5i500000000
χ694-40400-400400000-4004i−4i040000-40004i−4i000000000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000
χ704-40400-400400000-4004i−4i040000-40004i−4i00000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ714-40400-400400000-400−4i4i040000-4000−4i4i00000000000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ724-40400-400400000-400−4i4i040000-4000−4i4i000000000000000000000000000000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1190000
χ73888-488-488-2-4-4-4-4-4-2-4-400-21-2-211100000-2-211111100000000000000000000000000000000000000000000000
χ74888-488-4-8-8-2-44444-2-4-400-21-2-21110000022-1-1-1-11100000000000000000000000000000000000000000000000
χ75888-4-8-8-48-8-2-4-4-444-24400-212211100000-2211-1-1-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-4-88-2-444-4-4-24400-2122111000002-2-1-111-1-100000000000000000000000000000000000000000000000
χ7788-888-8800-2-80000-28-8002-2-2222-200000000000-2200000000000000000000000000000000000000000000000
χ7888-88-88800-2-80000-2-88002-22-222-2000000000002-200000000000000000000000000000000000000000000000
χ7988-8-48-8-400-24−4i34i3−4i34i3-2-440021-22-1-110000000i3−i3i3−i31-100000000000000000000000000000000000000000000000
χ8088-8-48-8-400-244i3−4i34i3−4i3-2-440021-22-1-110000000−i3i3−i3i31-100000000000000000000000000000000000000000000000
χ8188-8-4-88-400-24−4i34i34i3−4i3-24-400212-2-1-110000000i3−i3−i3i3-1100000000000000000000000000000000000000000000000
χ8288-8-4-88-400-244i3−4i3−4i34i3-24-400212-2-1-110000000−i3i3i3−i3-1100000000000000000000000000000000000000000000000
χ838-80-400400800000-8008i−8i0-400004000−4i4i0000000000000000000000000000000000000000000000000000000
χ848-80-400400800000-800−8i8i0-4000040004i−4i0000000000000000000000000000000000000000000000000000000
χ8516-1601600-1600-400000400000-400004000000000000000000000000000000000000000000000000000000000000
χ8616-160-800800-400000400000200−2i152i15-2000000000000000000000000000000000000000000000000000000000000
χ8716-160-800800-4000004000002002i15−2i15-2000000000000000000000000000000000000000000000000000000000000

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