Finite Group Databasebeta

← Group #14301414

Character table — Group #14301414

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222224444444445588888888101010101012121616161616161616202020202024242424244040404040404040404040404040484860606060606060606060120
order12234462256101010121244661520203030302241212441010303030306060446612420202020444412121212121212121212202044888888882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11
χ31111111111111111111111111111111-1-11111111111111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1
χ51111111111111111-1-111111111-1-1-1-1-11111111111-1-1-1-1-111111ii−i−i-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i-1
χ61111111111111111-1-111111111-1-1-1-1-11111111111-1-1-1-1-111111−i−iii-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii-1
χ71111111111111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-111−i−i−i−iiiii1
χ81111111111111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-111iiii−i−i−i−i1
χ91111111-1-1111111111-1-11111111111111-1-1-1-1-1-111-1-1111-111111-11-1-1-111-1-111-1-1-1-11111-1-111-1-1-1
χ101111111-1-1111111111-1-11111111111111-1-1-1-1-1-111-1-1111-11111-11-11-1-1-1-111-1-111-1-111-1-111-1-111-1
χ111111111-1-1111111111-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-1-1-111-1-111-1-111-1-1-1-111-1-1111
χ121111111-1-1111111111-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-1-1-111-1-11111-1-111-1-111-1-11
χ131111111-1-11111111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111i−i−ii11ii−i−i−i−iii-1-1-1-1ii−i−i−i−iii1
χ141111111-1-11111111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111−iii−i11−i−iiiii−i−i-1-1-1-1−i−iiiii−i−i1
χ151111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1i−i−ii11ii−i−i−i−iii1111−i−iiiii−i−i-1
χ161111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1−iii−i11−i−iiiii−i−i1111ii−i−i−i−iii-1
χ172222-2-222-222222-2-2222-22-2-2222-2-2222002-222-2-2-2-22-2-2-220000000002-2000000000000000000000
χ182222-2-222-222222-2-2-2-22-22-2-222222-2-2-2002-222-2-2-2-2-2222-2000000000-22000000000000000000000
χ192222-2-22-2222222-2-222-222-2-2222-2-222200-22-2-222-2-2-22-2-22000000000-22000000000000000000000
χ202222-2-22-2222222-2-2-2-2-222-2-222222-2-2-200-22-2-222-2-22-222-20000000002-2000000000000000000000
χ21222-122-1222-1222-1-122-1-1-122-1-1-1222-1-10022-1-1-1-1-1-122-1-1-1000002222-1-1-1-1-1-1-1-1-1-10000000000000
χ22222-122-1222-1222-1-122-1-1-122-1-1-1222-1-10022-1-1-1-1-1-122-1-1-100000-2-2-2-2-1-1111111110000000000000
χ23222-122-1222-1222-1-1-2-2-1-1-122-1-1-1-2-2-2110022-1-1-1-1-1-1-2-2111000002i2i−2i−2i11−i−i−i−iiiii0000000000000
χ24222-122-1222-1222-1-1-2-2-1-1-122-1-1-1-2-2-2110022-1-1-1-1-1-1-2-211100000−2i−2i2i2i11iiii−i−i−i−i0000000000000
χ25222-122-1-2-22-1222-1-12211-122-1-1-1222-1-100-2-21111-1-1-2-2-1-1-1000002-22-211-1-111-1-1110000000000000
χ26222-122-1-2-22-1222-1-12211-122-1-1-1222-1-100-2-21111-1-1-2-2-1-1-100000-22-221111-1-111-1-10000000000000
χ27222-122-1-2-22-1222-1-1-2-211-122-1-1-1-2-2-21100-2-21111-1-122111000002i−2i−2i2i-1-1−i−iiiii−i−i0000000000000
χ28222-122-1-2-22-1222-1-1-2-211-122-1-1-1-2-2-21100-2-21111-1-12211100000−2i2i2i−2i-1-1ii−i−i−i−iii0000000000000
χ29222-1-2-2-12-22-12221122-11-1-2-2-1-1-1-2-22-1-1002-2-1-111112-211-1000000000-113−33−33−33−30000000000000
χ30222-1-2-2-12-22-12221122-11-1-2-2-1-1-1-2-22-1-1002-2-1-111112-211-1000000000-11−33−33−33−330000000000000
χ31222-1-2-2-12-22-122211-2-2-11-1-2-2-1-1-122-211002-2-1-11111-22-1-110000000001-1−i3i3−i3i3i3−i3i3−i30000000000000
χ32222-1-2-2-12-22-122211-2-2-11-1-2-2-1-1-122-211002-2-1-11111-22-1-110000000001-1i3−i3i3−i3−i3i3−i3i30000000000000
χ33222-1-2-2-1-222-122211221-1-1-2-2-1-1-1-2-22-1-100-2211-1-111-2211-10000000001-13−3−333−3−330000000000000
χ34222-1-2-2-1-222-122211221-1-1-2-2-1-1-1-2-22-1-100-2211-1-111-2211-10000000001-1−333−3−333−30000000000000
χ35222-1-2-2-1-222-122211-2-21-1-1-2-2-1-1-122-21100-2211-1-1112-2-1-11000000000-11−i3i3i3−i3i3−i3−i3i30000000000000
χ36222-1-2-2-1-222-122211-2-21-1-1-2-2-1-1-122-21100-2211-1-1112-2-1-11000000000-11i3−i3−i3i3−i3i3i3−i30000000000000
χ3722-222-22002-2-2-222-2220022-2-2-222-2-222000000002-2002-2-200000000000000000000000002-2002-20
χ3822-222-22002-2-2-222-2220022-2-2-222-2-222000000002-2002-2-20000000000000000000000000-2200-220
χ3922-222-22002-2-2-222-2-2-20022-2-2-22-222-2-2000000002-200-22200000000000000000000000002i−2i00−2i2i0
χ4022-222-22002-2-2-222-2-2-20022-2-2-22-222-2-2000000002-200-2220000000000000000000000000−2i2i002i−2i0
χ4122-22-222002-2-2-22-2222002-22-2-22-22-22200000000-2200-22-2000000000000000000000002-2002-2000
χ4222-22-222002-2-2-22-2222002-22-2-22-22-22200000000-2200-22-200000000000000000000000-2200-22000
χ4322-22-222002-2-2-22-22-2-2002-22-2-222-22-2-200000000-22002-22000000000000000000000002i−2i00−2i2i000
χ4422-22-222002-2-2-22-22-2-2002-22-2-222-22-2-200000000-22002-2200000000000000000000000−2i2i002i−2i000
χ45444444444-14-1-1-1440044-1-1-1-1-1-10000044-1-1-1-1-1-1-1-1000004-1-1-1-100000000000000-1-100000000000
χ46444444444-14-1-1-1440044-1-1-1-1-1-100000-4-4-1-1-1-1-1-1-1-100000-41111000000000000001100000000000
χ474444444-4-4-14-1-1-14400-4-4-1-1-1-1-1-10000044111111-1-100000-4-1-1-1-1000000000000001100000000000
χ484444444-4-4-14-1-1-14400-4-4-1-1-1-1-1-100000-4-4111111-1-1000004111100000000000000-1-100000000000
χ494444-4-444-4-14-1-1-1-4-4004-4-111-1-1-10000000-11-1-11111000000−5−55500000000000000−5500000000000
χ504444-4-444-4-14-1-1-1-4-4004-4-111-1-1-10000000-11-1-1111100000055−5−5000000000000005−500000000000
χ514444-4-44-44-14-1-1-1-4-400-44-111-1-1-100000001-111-1-111000000−5−555000000000000005−500000000000
χ524444-4-44-44-14-1-1-1-4-400-44-111-1-1-100000001-111-1-11100000055−5−500000000000000−5500000000000
χ5344-4-24-4-20042-4-44-224400-24-422-24-4-4-2-200000000-2200-22200000000000000000000000000000000
χ5444-4-24-4-20042-4-44-22-4-400-24-422-2-4442200000000-22002-2-200000000000000000000000000000000
χ5544-4-2-44-20042-4-442-24400-2-4422-2-44-4-2-2000000002-2002-2200000000000000000000000000000000
χ5644-4-2-44-20042-4-442-2-4-400-2-4422-24-4422000000002-200-22-200000000000000000000000000000000
χ574-40400-4004000-4004i−4i0040000-40004i−4i2i−2i000000000000002i−2i2i−2i00000000000000002-2000000000
χ584-40400-4004000-4004i−4i0040000-40004i−4i−2i2i00000000000000−2i2i−2i2i0000000000000000-22000000000
χ594-40400-4004000-400−4i4i0040000-4000−4i4i2i−2i000000000000002i−2i2i−2i0000000000000000-22000000000
χ604-40400-4004000-400−4i4i0040000-4000−4i4i−2i2i00000000000000−2i2i−2i2i00000000000000002-2000000000
χ61888-488-488-2-4-2-2-2-4-400-4-41-2-21110000000-2-21111110000000000000000000000000000000000000
χ62888-488-4-8-8-2-4-2-2-2-4-400441-2-2111000000022-1-1-1-1110000000000000000000000000000000000000
χ63888-4-8-8-48-8-2-4-2-2-24400-441221110000000-2211-1-1-1-10000000000000000000000000000000000000
χ64888-4-8-8-4-88-2-4-2-2-244004-412211100000002-2-1-111-1-10000000000000000000000000000000000000
χ6588-888-8800-2-822-28-80000-2-2222-20000000000000-220000000000000000000000000000000000000
χ6688-88-88800-2-822-2-880000-22-222-200000000000002-20000000000000000000000000000000000000
χ6788-8-48-8-400-2422-2-4400001-22-1-11000000000−i15i15−i15i151-10000000000000000000000000000000000000
χ6888-8-48-8-400-2422-2-4400001-22-1-11000000000i15−i15i15−i151-10000000000000000000000000000000000000
χ6988-8-4-88-400-2422-24-4000012-2-1-11000000000−i15i15i15−i15-110000000000000000000000000000000000000
χ7088-8-4-88-400-2422-24-4000012-2-1-11000000000i15−i15−i15i15-110000000000000000000000000000000000000
χ718-80800-800-20−25252000000-200−25252000004i−4i00000000000000−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47000000000000000000000000000
χ728-80800-800-20−25252000000-200−2525200000−4i4i000000000000002ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ592ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ47000000000000000000000000000
χ738-80800-800-2025−252000000-20025−252000004i−4i00000000000000−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59000000000000000000000000000
χ748-80800-800-2025−252000000-20025−25200000−4i4i000000000000002ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ472ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ59000000000000000000000000000
χ758-80-4004008000-8008i−8i00-400004000−4i4i00000000000000000000000000000000000000000000000
χ768-80-4004008000-800−8i8i00-4000040004i−4i00000000000000000000000000000000000000000000000
χ7716-160-800800-40−4545400000020025−25-20000000000000000000000000000000000000000000000000000
χ7816-160-800800-4045−454000000200−2525-20000000000000000000000000000000000000000000000000000

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