Finite Group Databasebeta

← Group #14299922

Character table — Group #14299922

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222444444455888888888101010101012121212161616161616161620202020202020242424244040404040404040404040404048486060606060606060120120
order12234465610121220204481015202424306060224121224443040406012012012012066888812202020204481212121224242424242410202444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111111-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1111-1-11111111111-1-11-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ61111111111111111-1111-1-11111111111-1-11-1-11-1-1-1-111-1-1-1-11-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111-1111-1-111111111-1-1111-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111-1111-1-111111111-1-1111-1-11-1-1-1-111-1-1-1-11111111-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ911111111111111-1-1111111111-1-1-1-1-1111111111111-1-1ii−i−i-11111i−i-1ii−i−i-1-1ii−i−i11-1-1-1-1ii−i−ii−i
χ1011111111111111-1-1111111111-1-1-1-1-1111111111111-1-1−i−iii-11111−ii-1−i−iii-1-1−i−iii11-1-1-1-1−i−iii−ii
χ1111111111111111-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i-1-1-1-1-1i−i-1ii−i−i-1-1ii−i−i-1-11111−i−iii−ii
χ1211111111111111-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1−i−iii-1-1-1-1-1−ii-1−i−iii-1-1−i−iii-1-11111ii−i−ii−i
χ1311111111111111-1-1-1111-1-1111-1-1-1-1-111-1-11-1-11-1-1-1-1-1-1ii−i−i-1-1-1-1-1−ii1−i−iii11ii−i−i11-1-111ii−i−i−ii
χ1411111111111111-1-1-1111-1-1111-1-1-1-1-111-1-11-1-11-1-1-1-1-1-1−i−iii-1-1-1-1-1i−i1ii−i−i11−i−iii11-1-111−i−iiii−i
χ1511111111111111-1-1-1111-1-1111-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1ii−i−i-11111−ii1−i−iii11ii−i−i-1-111-1-1−i−iiii−i
χ1611111111111111-1-1-1111-1-1111-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1−i−iii-11111i−i1ii−i−i11−i−iii-1-111-1-1ii−i−i−ii
χ172222-2-22222-2-2-2-222022-2002-2-2-2-22220000200-20000-2-22-22-2200000000000002-22-2000000000000
χ182222-2-22222-2-2-2-222022-2002-2-2-2-22220000200-20000-2-2-22-2220000000000000-22-22000000000000
χ192222-2-22222-2-2-2-2-2-2022-2002-2-222-2-2-20000200-20000222i−2i−2i2i-200000000000002i−2i−2i2i000000000000
χ202222-2-22222-2-2-2-2-2-2022-2002-2-222-2-2-20000200-2000022−2i2i2i−2i-20000000000000−2i2i2i−2i000000000000
χ21222-122-12-12-1-1222222-12-1-1-1-1-1222-1-10000-122-1-1-1-1-1-1-12222-10000222-1-1-1-1-1-1-1-1-1-1000000000000
χ22222-122-12-12-1-1222222-12-1-1-1-1-1222-1-10000-122-1-1-1-1-1-1-1-2-2-2-2-10000-2-221111-1-11111000000000000
χ23222-122-12-12-1-12222-22-1211-1-1-1222-1-10000-1-2-2-11111-1-12222-10000-2-2-2111111-1-1-1-1000000000000
χ24222-122-12-12-1-12222-22-1211-1-1-1222-1-10000-1-2-2-11111-1-1-2-2-2-2-1000022-2-1-1-1-1111111000000000000
χ25222-122-12-12-1-122-2-222-12-1-1-1-1-1-2-2-2110000-122-1-1-1-1-1112i2i−2i−2i100002i−2i-2−i−iii11−i−iii000000000000
χ26222-122-12-12-1-122-2-222-12-1-1-1-1-1-2-2-2110000-122-1-1-1-1-111−2i−2i2i2i10000−2i2i-2ii−i−i11ii−i−i000000000000
χ27222-122-12-12-1-122-2-2-22-1211-1-1-1-2-2-2110000-1-2-2-11111112i2i−2i−2i10000−2i2i2ii−i−i-1-1−i−iii000000000000
χ28222-122-12-12-1-122-2-2-22-1211-1-1-1-2-2-2110000-1-2-2-1111111−2i−2i2i2i100002i−2i2−i−iii-1-1ii−i−i000000000000
χ29222-1-2-2-12-1211-2-22202-1-23−3-111-2-22-1-10000-100133−3−3112-22-2-100000003−33−33−3-11-11000000000000
χ30222-1-2-2-12-1211-2-22202-1-23−3-111-2-22-1-10000-100133−3−311-22-22-10000000−33−333−31-11-1000000000000
χ31222-1-2-2-12-1211-2-22202-1-2−33-111-2-22-1-10000-1001−3−333112-22-2-10000000−33−33−33-11-11000000000000
χ32222-1-2-2-12-1211-2-22202-1-2−33-111-2-22-1-10000-1001−3−33311-22-22-100000003−33−3−331-11-1000000000000
χ33222-1-2-2-12-1211-2-2-2-202-1-23−3-11122-2110000-100133−3−3-1-12i−2i−2i2i10000000i3−i3−i3i3−33−iii−i000000000000
χ34222-1-2-2-12-1211-2-2-2-202-1-23−3-11122-2110000-100133−3−3-1-1−2i2i2i−2i10000000−i3i3i3−i3−33i−i−ii000000000000
χ35222-1-2-2-12-1211-2-2-2-202-1-2−33-11122-2110000-1001−3−333-1-12i−2i−2i2i10000000−i3i3i3−i33−3−iii−i000000000000
χ36222-1-2-2-12-1211-2-2-2-202-1-2−33-11122-2110000-1001−3−333-1-1−2i2i2i−2i10000000i3−i3−i3i33−3i−i−ii000000000000
χ3722-222-222-222-2-2-2220-222002-2-2-22-2222-200-20020000-220000-2000000000000000002-2-2200000000
χ3822-222-222-222-2-2-2220-222002-2-2-22-222-2200-20020000-220000-200000000000000000-222-200000000
χ3922-222-222-222-2-2-2-2-20-222002-2-22-22-2-22-200-200200002-200002000000000000000002-22-200000000
χ4022-222-222-222-2-2-2-2-20-222002-2-22-22-2-2-2200-200200002-20000200000000000000000-22-2200000000
χ4122-22-2222-22-2222220-22-2002222-2-2220000-200-200002-20000-2000000000000000000000002-22-200
χ4222-22-2222-22-2222220-22-2002222-2-2220000-200-200002-20000-200000000000000000000000-22-2200
χ4322-22-2222-22-2222-2-20-22-200222-222-2-20000-200-20000-2200002000000000000000000000002i−2i−2i2i00
χ4422-22-2222-22-2222-2-20-22-200222-222-2-20000-200-20000-220000200000000000000000000000−2i2i2i−2i00
χ454444444-14-144-1-1004-1-1-144-1-1-1000004444-1-1-1-1-1-1-1-10000000-1-1-1-10000000000000-1-10000000000
χ464444444-14-144-1-1004-1-1-144-1-1-100000-4-4-4-4-1-1-1-1-1-1-1-1000000011110000000000000110000000000
χ474444444-14-144-1-100-4-1-1-1-4-4-1-1-10000044-4-4-111-11111000000011110000000000000-1-10000000000
χ484444444-14-144-1-100-4-1-1-1-4-4-1-1-100000-4-444-111-111110000000-1-1-1-10000000000000110000000000
χ4944-444-44-1-4-14-4110001-1-100-111000004-4001−i5i5-1−i5i5−i5i50000000−i5−i5i5i50000000000000-110000000000
χ5044-444-44-1-4-14-4110001-1-100-111000004-4001i5−i5-1i5−i5i5−i50000000i5i5−i5−i50000000000000-110000000000
χ5144-444-44-1-4-14-4110001-1-100-11100000-44001−i5i5-1−i5i5−i5i50000000i5i5−i5−i500000000000001-10000000000
χ5244-444-44-1-4-14-4110001-1-100-11100000-44001i5−i5-1i5−i5i5−i50000000−i5−i5i5i500000000000001-10000000000
χ5344-4-24-4-2424-22-4-4440-4-2400-222-44-4-2-20000200-200002-20000200000000000000000000000000000
χ5444-4-24-4-2424-22-4-4-4-40-4-2400-2224-44220000200-20000-220000-200000000000000000000000000000
χ5544-4-2-44-24242-244440-4-2-400-2-2-24-4-4-2-2000020020000-220000200000000000000000000000000000
χ5644-4-2-44-24242-244-4-40-4-2-400-2-2-2-444220000200200002-20000-200000000000000000000000000000
χ574-40400-440-400004i−4i004000-4000004i−4i002i−2i0000000000000002i−2i2i−2i000000000000000002-2000000
χ584-40400-440-400004i−4i004000-4000004i−4i00−2i2i000000000000000−2i2i−2i2i00000000000000000-22000000
χ594-40400-440-40000−4i4i004000-400000−4i4i002i−2i0000000000000002i−2i2i−2i00000000000000000-22000000
χ604-40400-440-40000−4i4i004000-400000−4i4i00−2i2i000000000000000−2i2i−2i2i000000000000000002-2000000
χ618888-8-88-28-2-8-822000-2-2200-222000000000-20020000000000000000000000000000000000000000
χ62888-488-4-2-4-2-4-4-2-2008-21-2-4-41110000000001-2-211111000000000000000000000000000000000000
χ63888-488-4-2-4-2-4-4-2-200-8-21-2441110000000001221-1-1-1-1000000000000000000000000000000000000
χ64888-4-8-8-4-2-4-24422000-21243−431-1-1000000000100-1−3−333000000000000000000000000000000000000
χ65888-4-8-8-4-2-4-24422000-212−43431-1-1000000000100-133−3−3000000000000000000000000000000000000
χ6688-88-888-2-8-2-88-2-20002-2200-2-2-200000000020020000000000000000000000000000000000000000
χ6788-8-48-8-4-24-2-442200021-2001-1-1000000000-1−2i52i51i5−i5i5−i5000000000000000000000000000000000000
χ6888-8-48-8-4-24-2-442200021-2001-1-1000000000-12i5−2i51−i5i5−i5i5000000000000000000000000000000000000
χ6988-8-4-88-4-24-24-4-2-200021200111000000000-100-1−i15i15i15−i15000000000000000000000000000000000000
χ7088-8-4-88-4-24-24-4-2-200021200111000000000-100-1i15−i15−i15i15000000000000000000000000000000000000
χ718-80800-8-20200−2i52i50000-20002−2i52i500000004i−4i000000000000000ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47+ζ58−ζ59−ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47−ζ58+ζ59−ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47−ζ58−ζ59ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47+ζ58+ζ590000000000000000000000000
χ728-80800-8-20200−2i52i50000-20002−2i52i50000000−4i4i000000000000000−ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47−ζ58+ζ59ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47+ζ58−ζ59ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47+ζ58+ζ59−ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47−ζ58−ζ590000000000000000000000000
χ738-80800-8-202002i5−2i50000-200022i5−2i500000004i−4i000000000000000−ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47−ζ58−ζ59ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47+ζ58+ζ59ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47+ζ58−ζ59−ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47−ζ58+ζ590000000000000000000000000
χ748-80800-8-202002i5−2i50000-200022i5−2i50000000−4i4i000000000000000ζ2+ζ7+ζ11−ζ14+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34+ζ38+ζ43−ζ46+ζ47+ζ58+ζ59−ζ2−ζ7−ζ11+ζ14−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34−ζ38−ζ43+ζ46−ζ47−ζ58−ζ59−ζ2+ζ7+ζ11+ζ14+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34−ζ38+ζ43+ζ46+ζ47−ζ58+ζ59ζ2−ζ7−ζ11−ζ14−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34+ζ38−ζ43−ζ46−ζ47+ζ58−ζ590000000000000000000000000
χ758-80-400480-800008i−8i00-4000400000−4i4i000000000000000000000000000000000000000000000000
χ768-80-400480-80000−8i8i00-40004000004i−4i000000000000000000000000000000000000000000000000
χ7716-160-8008-40400−4i54i500002000-22i5−2i500000000000000000000000000000000000000000000000000000
χ7816-160-8008-404004i5−4i500002000-2−2i52i500000000000000000000000000000000000000000000000000000

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