Finite Group Databasebeta

← Group #14302310

Character table — Group #14302310

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444444488888810101010101016161616161616162020202020202020202020202020202020202020202020202020202020202020202424242424244848120120120120120120
order122344644561010101212121212121520203030302244121220206060606060602266666688888888122424242424242424242424242424242448404040402020444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ511111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1i−i-1i−i
χ611111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11−ii1−ii
χ711111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1−ii-1−ii
χ811111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11i−i1i−i
χ91111111-1-11111111-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-111111-1-1-1
χ101111111-1-11111111-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1111
χ111111111-1-11111111-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111-1-1-1-11111-1-1-1-111111-1-1-1-1-1111-1-1-111
χ121111111-1-11111111-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111-1-1-1-11111-1-1-1-11111-111111-1-1-1111-1-1
χ131111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111ii−i−i−i−iii-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-1-111-1i−i1−ii
χ141111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111ii−i−i−i−iii-1iiii−i−i−i−i−i−i−i−iiiii-111111-1-11−ii-1i−i
χ151111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111−i−iiiii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-1-111-1−ii1i−i
χ161111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111−i−iiiii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i-111111-1-11i−i-1−ii
χ172222-2-220022222-2-200002-2-222222-2-2-2-200-2-2000000220000002i−2i002i−2i-200002i2i−2i−2i00002i2i−2i−2i00000000000000
χ182222-2-220022222-2-200002-2-222222-2-2-2-200-2-200000022000000−2i2i00−2i2i-20000−2i−2i2i2i0000−2i−2i2i2i00000000000000
χ192222-2-220022222-2-200002-2-2222-2-2222200-2-2000000-2-20000002-200-222000022-2-20000-2-22200000000000000
χ202222-2-220022222-2-200002-2-2222-2-2222200-2-2000000-2-2000000-22002-220000-2-222000022-2-200000000000000
χ21222-122-1222-1222-1-1-1-1-1-1-122-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222-122-1222-1222-1-1-1-1-1-1-122-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111111111111100000000000000
χ23222-122-1222-1222-1-1-1-1-1-1-122-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-21111112i2i2i2i−2i−2i−2i−2i1−i−i−i−i−i−i−i−iiiiiiiii00000000000000
χ24222-122-1222-1222-1-1-1-1-1-1-122-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-2111111−2i−2i−2i−2i2i2i2i2i1iiiiiiii−i−i−i−i−i−i−i−i00000000000000
χ25222-122-1-2-22-1222-1-11111-122-1-1-12222-1-1-2-2-1-11111-2-2-1-1111122-2-222-2-2-1-1-1-1-11111-1-1-1-1111100000000000000
χ26222-122-1-2-22-1222-1-11111-122-1-1-12222-1-1-2-2-1-11111-2-2-1-11111-2-222-2-222-11111-1-1-1-11111-1-1-1-100000000000000
χ27222-122-1-2-22-1222-1-11111-122-1-1-1-2-2-2-211-2-2-1-111112211-1-1-1-12i2i−2i−2i−2i−2i2i2i1−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ28222-122-1-2-22-1222-1-11111-122-1-1-1-2-2-2-211-2-2-1-111112211-1-1-1-1−2i−2i2i2i2i2i−2i−2i1iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ29222-1-2-2-1002-122211−i3−i3i3i3-1-2-2-1-1-122-2-2110011−i3−i3i3i300-1-1−i3−i3i3i3002i−2i002i−2i133−3−3−i−iii33−3−3−i−iii00000000000000
χ30222-1-2-2-1002-122211−i3−i3i3i3-1-2-2-1-1-122-2-2110011−i3−i3i3i300-1-1−i3−i3i3i300−2i2i00−2i2i1−3−333ii−i−i−3−333ii−i−i00000000000000
χ31222-1-2-2-1002-122211−i3−i3i3i3-1-2-2-1-1-1-2-222-1-10011−i3−i3i3i30011i3i3−i3−i3002-200-22-1−i3−i3i3i3-1-111i3i3−i3−i311-1-100000000000000
χ32222-1-2-2-1002-122211−i3−i3i3i3-1-2-2-1-1-1-2-222-1-10011−i3−i3i3i30011i3i3−i3−i300-22002-2-1i3i3−i3−i311-1-1−i3−i3i3i3-1-11100000000000000
χ33222-1-2-2-1002-122211i3i3−i3−i3-1-2-2-1-1-122-2-2110011i3i3−i3−i300-1-1i3i3−i3−i3002i−2i002i−2i1−3−333−i−iii−3−333−i−iii00000000000000
χ34222-1-2-2-1002-122211i3i3−i3−i3-1-2-2-1-1-122-2-2110011i3i3−i3−i300-1-1i3i3−i3−i300−2i2i00−2i2i133−3−3ii−i−i33−3−3ii−i−i00000000000000
χ35222-1-2-2-1002-122211i3i3−i3−i3-1-2-2-1-1-1-2-222-1-10011i3i3−i3−i30011−i3−i3i3i3002-200-22-1i3i3−i3−i3-1-111−i3−i3i3i311-1-100000000000000
χ36222-1-2-2-1002-122211i3i3−i3−i3-1-2-2-1-1-1-2-222-1-10011i3i3−i3−i30011−i3−i3i3i300-22002-2-1−i3−i3i3i311-1-1i3i3−i3−i3-1-11100000000000000
χ3722-222-22002-2-2-222-2000022-2-2-222-2-22-2-2002-20000002-200002i−2i002i−2i0022i−2i2i−2i00002i−2i2i−2i000000000000000000
χ3822-222-22002-2-2-222-2000022-2-2-222-2-22-2-2002-20000002-20000−2i2i00−2i2i002−2i2i−2i2i0000−2i2i−2i2i000000000000000000
χ3922-222-22002-2-2-222-2000022-2-2-22-222-222002-2000000-2200002-200-2200-22-22-20000-22-22000000000000000000
χ4022-222-22002-2-2-222-2000022-2-2-22-222-222002-2000000-220000-22002-200-2-22-2200002-22-2000000000000000000
χ4122-22-2222-22-2-2-22-222-22-22-22-2-222-22-2222-2-222-22-22-22-22-22-200000000-2000000000000000000000000000000
χ4222-22-2222-22-2-2-22-222-22-22-22-2-22-22-22-2-22-2-222-22-2-22-22-22-22000000002000000000000000000000000000000
χ4322-22-222-222-2-2-22-22-22-222-22-2-222-22-222-22-22-22-22-222-2-22-2200000000-2000000000000000000000000000000
χ4422-22-222-222-2-2-22-22-22-222-22-2-22-22-22-2-2-22-22-22-222-2-222-22-2000000002000000000000000000000000000000
χ4522-2-12-2-10021-2-22-11−i3i3i3−i3-12-211-12-2-221100-11−i3i3i3−i300-11−i3i3i3−i32i−2i002i−2i00-1−ii−ii3−33−3−ii−ii3−33−300000000000000
χ4622-2-12-2-10021-2-22-11−i3i3i3−i3-12-211-12-2-221100-11−i3i3i3−i300-11−i3i3i3−i3−2i2i00−2i2i00-1i−ii−i−33−33i−ii−i−33−3300000000000000
χ4722-2-12-2-10021-2-22-11−i3i3i3−i3-12-211-1-222-2-1-100-11−i3i3i3−i3001-1i3−i3−i3i32-200-22001-11-11−i3i3−i3i31-11-1i3−i3i3−i300000000000000
χ4822-2-12-2-10021-2-22-11−i3i3i3−i3-12-211-1-222-2-1-100-11−i3i3i3−i3001-1i3−i3−i3i3-22002-20011-11-1i3−i3i3−i3-11-11−i3i3−i3i300000000000000
χ4922-2-12-2-10021-2-22-11i3−i3−i3i3-12-211-12-2-221100-11i3−i3−i3i300-11i3−i3−i3i32i−2i002i−2i00-1−ii−ii−33−33−ii−ii−33−3300000000000000
χ5022-2-12-2-10021-2-22-11i3−i3−i3i3-12-211-12-2-221100-11i3−i3−i3i300-11i3−i3−i3i3−2i2i00−2i2i00-1i−ii−i3−33−3i−ii−i3−33−300000000000000
χ5122-2-12-2-10021-2-22-11i3−i3−i3i3-12-211-1-222-2-1-100-11i3−i3−i3i3001-1−i3i3i3−i32-200-22001-11-11i3−i3i3−i31-11-1−i3i3−i3i300000000000000
χ5222-2-12-2-10021-2-22-11i3−i3−i3i3-12-211-1-222-2-1-100-11i3−i3−i3i3001-1−i3i3i3−i3-22002-20011-11-1−i3i3−i3i3-11-11i3−i3i3−i300000000000000
χ5322-2-1-22-12-221-2-221-1-11-11-1-2211-12-22-2-1-12-21-1-11-112-2-11-11-11000000001−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000
χ5422-2-1-22-12-221-2-221-1-11-11-1-2211-12-22-2-1-12-21-1-11-112-2-11-11-11000000001i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000
χ5522-2-1-22-12-221-2-221-1-11-11-1-2211-1-22-22112-21-1-11-11-221-11-11-100000000-13−3−333−3−33−333−3−333−300000000000000
χ5622-2-1-22-12-221-2-221-1-11-11-1-2211-1-22-22112-21-1-11-11-221-11-11-100000000-1−333−3−333−33−3−333−3−3300000000000000
χ5722-2-1-22-1-2221-2-221-11-11-1-1-2211-12-22-2-1-1-221-11-11-1-22-111-11-1000000001−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000
χ5822-2-1-22-1-2221-2-221-11-11-1-1-2211-12-22-2-1-1-221-11-11-1-22-111-11-1000000001i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000
χ5922-2-1-22-1-2221-2-221-11-11-1-1-2211-1-22-2211-221-11-11-12-21-1-11-1100000000-13−3−33−333−3−333−33−3−3300000000000000
χ6022-2-1-22-1-2221-2-221-11-11-1-1-2211-1-22-2211-221-11-11-12-21-1-11-1100000000-1−333−33−3−333−3−33−333−300000000000000
χ61444444444-14-1-1-1444444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-100000000000000000000000000000000044-1-1-1-1-1-1000000
χ62444444444-14-1-1-1444444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000000000000-4-4111111000000
χ634444444-4-4-14-1-1-144-4-4-4-4-1-1-1-1-1-100000011-1-111110000000000000000000000000000000004-41111-1-1000000
χ644444444-4-4-14-1-1-144-4-4-4-4-1-1-1-1-1-100000011-1-11111000000000000000000000000000000000-44-1-1-1-111000000
χ6544-44-4444-4-1-411-1-444-44-4-11-111-1000000-111-1-11-1100000000000000000000000000000000000−5−555−55000000
χ6644-44-4444-4-1-411-1-444-44-4-11-111-1000000-111-1-11-110000000000000000000000000000000000055−5−55−5000000
χ6744-44-444-44-1-411-1-44-44-44-11-111-10000001-11-11-11-100000000000000000000000000000000000−5−5555−5000000
χ6844-44-444-44-1-411-1-44-44-44-11-111-10000001-11-11-11-10000000000000000000000000000000000055−5−5−55000000
χ698888-8-8800-28-2-2-2-8-80000-222-2-2-20000000022000000000000000000000000000000000000000000000000000
χ70888-488-488-2-4-2-2-2-4-4-4-4-4-41-2-2111000000-2-211111100000000000000000000000000000000000000000000000
χ71888-488-4-8-8-2-4-2-2-2-4-444441-2-21110000002211-1-1-1-100000000000000000000000000000000000000000000000
χ72888-4-8-8-400-2-4-2-2-244−4i3−4i34i34i312211100000000-1-1i3i3−i3−i300000000000000000000000000000000000000000000000
χ73888-4-8-8-400-2-4-2-2-2444i34i3−4i3−4i312211100000000-1-1−i3−i3i3i300000000000000000000000000000000000000000000000
χ7488-888-8800-2-822-28-80000-2-2222-200000000-22000000000000000000000000000000000000000000000000000
χ7588-8-48-8-400-2422-2-44−4i34i34i3−4i31-22-1-11000000001-1i3−i3−i3i300000000000000000000000000000000000000000000000
χ7688-8-48-8-400-2422-2-444i3−4i3−4i34i31-22-1-11000000001-1−i3i3i3−i300000000000000000000000000000000000000000000000
χ7788-8-4-88-48-8-2422-24-4-44-4412-2-1-11000000-22-111-11-100000000000000000000000000000000000000000000000
χ7888-8-4-88-4-88-2422-24-44-44-412-2-1-110000002-2-11-11-1100000000000000000000000000000000000000000000000
χ798-80800-8008000-800000080000-80000000000000000000000000000000000000000000000000000000000000
χ808-80800-800-20−25252000000-200−252520000000000000000000000000000000000000000000000000−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ119ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ119−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ119ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ11900000000
χ818-80800-800-20−25252000000-200−252520000000000000000000000000000000000000000000000000ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ119−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ119ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ119−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ11900000000
χ828-80800-800-2025−252000000-20025−2520000000000000000000000000000000000000000000000000−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ119ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ119ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ119−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ11900000000
χ838-80800-800-2025−252000000-20025−2520000000000000000000000000000000000000000000000000ζ7+ζ13−ζ23+ζ29+ζ31−ζ37+ζ47+ζ53−ζ61+ζ71−ζ77−ζ79−ζ101−ζ103+ζ109−ζ119−ζ7−ζ13+ζ23−ζ29−ζ31+ζ37−ζ47−ζ53+ζ61−ζ71+ζ77+ζ79+ζ101+ζ103−ζ109+ζ119−ζ7−ζ13+ζ23+ζ29+ζ31+ζ37−ζ47−ζ53−ζ61+ζ71+ζ77−ζ79−ζ101+ζ103+ζ109−ζ119ζ7+ζ13−ζ23−ζ29−ζ31−ζ37+ζ47+ζ53+ζ61−ζ71−ζ77+ζ79+ζ101−ζ103−ζ109+ζ11900000000
χ848-80-4004008000-8000000-400004000043−430000000000000000000000000000000000000000000000000000000
χ858-80-4004008000-8000000-4000040000−43430000000000000000000000000000000000000000000000000000000
χ8616-160-800800-40−4545400000020025−25-20000000000000000000000000000000000000000000000000000000000000
χ8716-160-800800-4045−454000000200−2525-20000000000000000000000000000000000000000000000000000000000000

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