Finite Group Databasebeta

← Group #14302816

Character table — Group #14302816

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222224444444448888888810101010101016161616161616162020202020242424242424404040404040404040404040404048486060606060606060120120
order12234462256101010121266152020303030224412121010303030306060446612442020202044441212121212121212121220208888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1111111ii−i−i-1-1iiii−i−i−i−i11iiii−i−i−i−i-1-1
χ6111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1111111−i−iii-1-1−i−i−i−iiiii11−i−i−i−iiiii-1-1
χ7111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii11
χ8111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i11
χ91111111-1-11111111-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-1-111-1-111-1-11111-1-111-1-11-1
χ101111111-1-11111111-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-111-1-1111-1
χ111111111-1-11111111-1-1111111111111-1-1-1-1-1-111-1-1111-1111111-11-1-1-111-1-111-1-1-1-1-1-111-1-111-11
χ121111111-1-11111111-1-1111111111111-1-1-1-1-1-111-1-1111-111111-11-11-1-1-1-111-1-111-1-111-1-111-1-1-11
χ131111111-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1i−i−ii11ii−i−i−i−iii11ii−i−i−i−iii-11
χ141111111-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1−iii−i11−i−iiiii−i−i11−i−iiiii−i−i-11
χ151111111-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111i−i−ii11ii−i−i−i−iii-1-1−i−iiiii−i−i1-1
χ161111111-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111−iii−i11−i−iiiii−i−i-1-1ii−i−i−i−iii1-1
χ172222-2-222-222222-2-22-22-2-222222-2-2-2-22-222-2-2-2-22-222-200000000002-200000000000000000000
χ182222-2-222-222222-2-22-22-2-2222-2-222222-222-2-2-2-2-22-2-220000000000-2200000000000000000000
χ192222-2-22-2222222-2-2-222-2-222222-2-2-2-2-22-2-222-2-2-2222-20000000000-2200000000000000000000
χ202222-2-22-2222222-2-2-222-2-2222-2-22222-22-2-222-2-22-2-2-2200000000002-200000000000000000000
χ21222-122-1222-1222-1-1-1-1-122-1-1-12222-1-122-1-1-1-1-1-122-1-1-10000002222-1-1-1-1-1-1-1-1-1-1000000000000
χ22222-122-1222-1222-1-1-1-1-122-1-1-12222-1-122-1-1-1-1-1-122-1-1-1000000-2-2-2-2-1-111111111000000000000
χ23222-122-1222-1222-1-1-1-1-122-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-21110000002i2i−2i−2i11−i−i−i−iiiii000000000000
χ24222-122-1222-1222-1-1-1-1-122-1-1-1-2-2-2-21122-1-1-1-1-1-1-2-2111000000−2i−2i2i2i11iiii−i−i−i−i000000000000
χ25222-122-1-2-22-1222-1-111-122-1-1-12222-1-1-2-21111-1-1-2-2-1-1-10000002-22-211-1-111-1-111000000000000
χ26222-122-1-2-22-1222-1-111-122-1-1-12222-1-1-2-21111-1-1-2-2-1-1-1000000-22-221111-1-111-1-1000000000000
χ27222-122-1-2-22-1222-1-111-122-1-1-1-2-2-2-211-2-21111-1-1221110000002i−2i−2i2i-1-1−i−iiiii−i−i000000000000
χ28222-122-1-2-22-1222-1-111-122-1-1-1-2-2-2-211-2-21111-1-122111000000−2i2i2i−2i-1-1ii−i−i−i−iii000000000000
χ29222-1-2-2-12-22-122211-11-1-2-2-1-1-122-2-2112-2-1-111112-2-1-110000000000-11−i3i3−i3i3−i3i3−i3i3000000000000
χ30222-1-2-2-12-22-122211-11-1-2-2-1-1-122-2-2112-2-1-111112-2-1-110000000000-11i3−i3i3−i3i3−i3i3−i3000000000000
χ31222-1-2-2-12-22-122211-11-1-2-2-1-1-1-2-222-1-12-2-1-11111-2211-100000000001-13−33−3−33−33000000000000
χ32222-1-2-2-12-22-122211-11-1-2-2-1-1-1-2-222-1-12-2-1-11111-2211-100000000001-1−33−333−33−3000000000000
χ33222-1-2-2-1-222-1222111-1-1-2-2-1-1-122-2-211-2211-1-111-22-1-1100000000001-1−i3i3i3−i3−i3i3i3−i3000000000000
χ34222-1-2-2-1-222-1222111-1-1-2-2-1-1-122-2-211-2211-1-111-22-1-1100000000001-1i3−i3−i3i3i3−i3−i3i3000000000000
χ35222-1-2-2-1-222-1222111-1-1-2-2-1-1-1-2-222-1-1-2211-1-1112-211-10000000000-113−3−33−333−3000000000000
χ36222-1-2-2-1-222-1222111-1-1-2-2-1-1-1-2-222-1-1-2211-1-1112-211-10000000000-11−333−33−3−33000000000000
χ3722-222-22002-2-2-222-20022-2-2-222-22-2220000002-2002-2-20000000000000000000000002i−2i002i−2i00
χ3822-222-22002-2-2-222-20022-2-2-222-22-2220000002-2002-2-2000000000000000000000000−2i2i00−2i2i00
χ3922-222-22002-2-2-222-20022-2-2-22-22-22-2-20000002-200-2220000000000000000000000002-200-2200
χ4022-222-22002-2-2-222-20022-2-2-22-22-22-2-20000002-200-222000000000000000000000000-22002-200
χ4122-22-222002-2-2-22-22002-22-2-222-2-22-2-2000000-22002-2200000000000000000000002-2002-20000
χ4222-22-222002-2-2-22-22002-22-2-222-2-22-2-2000000-22002-220000000000000000000000-2200-220000
χ4322-22-222002-2-2-22-22002-22-2-22-222-222000000-2200-22-200000000000000000000002i−2i00−2i2i0000
χ4422-22-222002-2-2-22-22002-22-2-22-222-222000000-2200-22-20000000000000000000000−2i2i002i−2i0000
χ45444444444-14-1-1-14444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-10000044-1-1-1-100000000000000-1-10000000000
χ46444444444-14-1-1-14444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-100000-4-4111100000000000000110000000000
χ474444444-4-4-14-1-1-144-4-4-1-1-1-1-1-1000000111111-1-1000004-4111100000000000000-1-10000000000
χ484444444-4-4-14-1-1-144-4-4-1-1-1-1-1-1000000111111-1-100000-44-1-1-1-100000000000000110000000000
χ494444-4-444-4-14-1-1-1-4-44-4-111-1-1-1000000-11-1-111110000000−5−55500000000000000−550000000000
χ504444-4-444-4-14-1-1-1-4-44-4-111-1-1-1000000-11-1-11111000000055−5−5000000000000005−50000000000
χ514444-4-44-44-14-1-1-1-4-4-44-111-1-1-10000001-111-1-1110000000−5−555000000000000005−50000000000
χ524444-4-44-44-14-1-1-1-4-4-44-111-1-1-10000001-111-1-111000000055−5−500000000000000−550000000000
χ5344-4-24-4-20042-4-44-2200-24-422-24-44-4-2-2000000-2200-22200000000000000000000000000000000
χ5444-4-24-4-20042-4-44-2200-24-422-2-44-4422000000-22002-2-200000000000000000000000000000000
χ5544-4-2-44-20042-4-442-200-2-4422-24-4-44220000002-200-22-200000000000000000000000000000000
χ5644-4-2-44-20042-4-442-200-2-4422-2-444-4-2-20000002-2002-2200000000000000000000000000000000
χ57888-488-488-2-4-2-2-2-4-4-4-41-2-2111000000-2-21111110000000000000000000000000000000000000
χ58888-488-4-8-8-2-4-2-2-2-4-4441-2-211100000022-1-1-1-1110000000000000000000000000000000000000
χ59888-4-8-8-48-8-2-4-2-2-244-44122111000000-2211-1-1-1-10000000000000000000000000000000000000
χ60888-4-8-8-4-88-2-4-2-2-2444-41221110000002-2-1-111-1-10000000000000000000000000000000000000
χ6188-888-8800-2-822-28-800-2-2222-2000000000000-220000000000000000000000000000000000000
χ6288-88-88800-2-822-2-8800-22-222-20000000000002-20000000000000000000000000000000000000
χ6388-8-48-8-400-2422-2-44001-22-1-1100000000−i15i15−i15i151-10000000000000000000000000000000000000
χ6488-8-48-8-400-2422-2-44001-22-1-1100000000i15−i15i15−i151-10000000000000000000000000000000000000
χ6588-8-4-88-400-2422-24-40012-2-1-1100000000−i15i15i15−i15-110000000000000000000000000000000000000
χ6688-8-4-88-400-2422-24-40012-2-1-1100000000i15−i15−i15i15-110000000000000000000000000000000000000
χ678-80800-8008000-8000080000-8000000000000000000000000000000000000000000000000000
χ688-80800-800-20−252520000-200−25252000000000000000000000−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ4700000000000000000000000000
χ698-80800-800-20−252520000-200−252520000000000000000000002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ4700000000000000000000000000
χ708-80800-800-2025−2520000-20025−2520000000000000000000002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ5900000000000000000000000000
χ718-80800-800-2025−2520000-20025−252000000000000000000000−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ5900000000000000000000000000
χ728-80-4004008000-80000-400004000043−43000000000000000000000000000000000000000000000
χ738-80-4004008000-80000-4000040000−4343000000000000000000000000000000000000000000000
χ7416-160-800800-40−45454000020025−25-2000000000000000000000000000000000000000000000000000
χ7516-160-800800-4045−4540000200−2525-2000000000000000000000000000000000000000000000000000

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