Finite Group Databasebeta

← Group #14301472

Character table — Group #14301472

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222444444455888888888101010101012121212161616161616161620202020202020242424244040404040404040404040404048486060606060606060120120
order122344656101010121222412121520203030302446622442020606060606060444461212202020204881212121212122424242410102244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1-11111111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ61111111111111111-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ71111111111111111-1-1-111111111111-1-111-1-111-1-1-1-111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111-1-1-111111111111-1-111-1-111-1-1-1-1-1-1-1-11111111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111111111111-1-1111111111-1-1-1-1-1111111111111ii−i−i-1-1-11111-1i−i-1-1ii−i−iii−i−i11-1-1-1-1ii−i−ii−i
χ1011111111111111-1-1111111111-1-1-1-1-1111111111111−i−iii-1-1-11111-1−ii-1-1−i−iii−i−iii11-1-1-1-1−i−iii−ii
χ1111111111111111-1-1111111111-1-1-1-1-1-1-1-1-111111111ii−i−i-1-1-1-1-1-1-1-1i−i-1-1ii−i−iii−i−i-1-11111−i−iii−ii
χ1211111111111111-1-1111111111-1-1-1-1-1-1-1-1-111111111−i−iii-1-1-1-1-1-1-1-1−ii-1-1−i−iii−i−iii-1-11111ii−i−ii−i
χ1311111111111111-1-1-1-1-1111111-1-1-1-1-111-1-1-1-111-1-1-1-1ii−i−i-1-1-1-1-1-1-11−ii11ii−i−i−i−iii11-1-111ii−i−i−ii
χ1411111111111111-1-1-1-1-1111111-1-1-1-1-111-1-1-1-111-1-1-1-1−i−iii-1-1-1-1-1-1-11i−i11−i−iiiii−i−i11-1-111−i−iiii−i
χ1511111111111111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i-1-1-111111−ii11ii−i−i−i−iii-1-111-1-1−i−iiii−i
χ1611111111111111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-1−i−iii-1-1-111111i−i11−i−iiiii−i−i-1-111-1-1ii−i−i−ii
χ172222-2-2222222-2-2220002-2-22222-2-2222-20000-2-2000000002-2-2000000000000000002-22-200000000
χ182222-2-2222222-2-2220002-2-22222-2-222-220000-2-2000000002-2-200000000000000000-22-2200000000
χ192222-2-2222222-2-2-2-20002-2-2222-222-2-22-20000-2-200000000-222000000000000000002-2-2200000000
χ202222-2-2222222-2-2-2-20002-2-2222-222-2-2-220000-2-200000000-22200000000000000000-222-200000000
χ21222-122-12-1222-1-1222-1-1-122-1-1-1222-1-1000022-1-1-1-1-1-12222-1-1-10000222-1-1-1-1-1-1-1-1-1-1000000000000
χ22222-122-12-1222-1-1222-1-1-122-1-1-1222-1-1000022-1-1-1-1-1-1-2-2-2-2-1-1-100002-2-2-1-111111111000000000000
χ23222-122-12-1222-1-122-211-122-1-1-1222-1-10000-2-2-1-111112222-1-1-10000-2-2-211-1-1-1-11111000000000000
χ24222-122-12-1222-1-122-211-122-1-1-1222-1-10000-2-2-1-11111-2-2-2-2-1-1-10000-222111111-1-1-1-1000000000000
χ25222-122-12-1222-1-1-2-22-1-1-122-1-1-1-2-2-211000022-1-1-1-1-1-12i2i−2i−2i1110000-22i−2i11−i−iii−i−iii000000000000
χ26222-122-12-1222-1-1-2-22-1-1-122-1-1-1-2-2-211000022-1-1-1-1-1-1−2i−2i2i2i1110000-2−2i2i11ii−i−iii−i−i000000000000
χ27222-122-12-1222-1-1-2-2-211-122-1-1-1-2-2-2110000-2-2-1-111112i2i−2i−2i11100002−2i2i-1-1−i−iiiii−i−i000000000000
χ28222-122-12-1222-1-1-2-2-211-122-1-1-1-2-2-2110000-2-2-1-11111−2i−2i2i2i111000022i−2i-1-1ii−i−i−i−iii000000000000
χ2922-222-222-22-2-22-22200022-2-2-22-22-2220000002-200002-22-2-2-220000000002-22-20000000000000000
χ3022-222-222-22-2-22-22200022-2-2-22-22-2220000002-20000-22-22-2-22000000000-22-220000000000000000
χ3122-222-222-22-2-22-2-2-200022-2-2-222-22-2-20000002-200002i−2i−2i2i22-20000000002i−2i−2i2i0000000000000000
χ3222-222-222-22-2-22-2-2-200022-2-2-222-22-2-20000002-20000−2i2i2i−2i22-2000000000−2i2i2i−2i0000000000000000
χ3322-22-2222-22-2-2-22220002-22-2-22-2-2222000000-2200000000-22-2000000000000000000000002-22-200
χ3422-22-2222-22-2-2-22220002-22-2-22-2-2222000000-2200000000-22-200000000000000000000000-22-2200
χ3522-22-2222-22-2-2-22-2-20002-22-2-2222-2-2-2000000-22000000002-22000000000000000000000002i−2i−2i2i00
χ3622-22-2222-22-2-2-22-2-20002-22-2-2222-2-2-2000000-22000000002-2200000000000000000000000−2i2i2i−2i00
χ3722-2-12-2-1212-2-2-11220−i3i3-12-211-1-22-2-1-1000000-11−i3−i3i3i32-22-211-10000000−i3i3-11-11−i3i3−i3i3000000000000
χ3822-2-12-2-1212-2-2-11220−i3i3-12-211-1-22-2-1-1000000-11−i3−i3i3i3-22-2211-10000000−i3i31-11-1i3−i3i3−i3000000000000
χ3922-2-12-2-1212-2-2-11220i3−i3-12-211-1-22-2-1-1000000-11i3i3−i3−i32-22-211-10000000i3−i3-11-11i3−i3i3−i3000000000000
χ4022-2-12-2-1212-2-2-11220i3−i3-12-211-1-22-2-1-1000000-11i3i3−i3−i3-22-2211-10000000i3−i31-11-1−i3i3−i3i3000000000000
χ4122-2-12-2-1212-2-2-11-2-20−i3i3-12-211-12-2211000000-11−i3−i3i3i32i−2i−2i2i-1-110000000i3−i3−iii−i3−3−33000000000000
χ4222-2-12-2-1212-2-2-11-2-20−i3i3-12-211-12-2211000000-11−i3−i3i3i3−2i2i2i−2i-1-110000000i3−i3i−i−ii−333−3000000000000
χ4322-2-12-2-1212-2-2-11-2-20i3−i3-12-211-12-2211000000-11i3i3−i3−i32i−2i−2i2i-1-110000000−i3i3−iii−i−333−3000000000000
χ4422-2-12-2-1212-2-2-11-2-20i3−i3-12-211-12-2211000000-11i3i3−i3−i3−2i2i2i−2i-1-110000000−i3i3i−i−ii3−3−33000000000000
χ454444444-14-1-1-14400444-1-1-1-1-1-1000004444-1-1-1-1-1-1-1-10000000-1-1-1-10000000000000-1-10000000000
χ464444444-14-1-1-14400444-1-1-1-1-1-100000-4-4-4-4-1-1-1-1-1-1-1-1000000011110000000000000110000000000
χ474444444-14-1-1-14400-4-4-4-1-1-1-1-1-10000044-4-411-1-11111000000011110000000000000-1-10000000000
χ484444444-14-1-1-14400-4-4-4-1-1-1-1-1-100000-4-44411-1-111110000000-1-1-1-10000000000000110000000000
χ494444-4-44-14-1-1-1-4-400000-111-1-1-1000004-400−5511−55−550000000−5−5550000000000000-110000000000
χ504444-4-44-14-1-1-1-4-400000-111-1-1-1000004-4005−5115−55−5000000055−5−50000000000000-110000000000
χ514444-4-44-14-1-1-1-4-400000-111-1-1-100000-4400−5511−55−55000000055−5−500000000000001-10000000000
χ524444-4-44-14-1-1-1-4-400000-111-1-1-100000-44005−5115−55−50000000−5−55500000000000001-10000000000
χ53444-2-4-4-24-24442244000-2-4-4-2-2-24-4-4-2-20000002200000000-22200000000000000000000000000000
χ54444-2-4-4-24-244422-4-4000-2-4-4-2-2-2-4442200000022000000002-2-200000000000000000000000000000
χ5544-4-2-44-2424-4-42-244000-2-4422-2-4-44-2-20000002-2000000002-2200000000000000000000000000000
χ5644-4-2-44-2424-4-42-2-4-4000-2-4422-244-4220000002-200000000-22-200000000000000000000000000000
χ574-40400-440-400004-400040000-40004-4002i−2i0000000000000002i−2i2i−2i000000000000000002i−2i000000
χ584-40400-440-400004-400040000-40004-400−2i2i000000000000000−2i2i−2i2i00000000000000000−2i2i000000
χ594-40400-440-40000-4400040000-4000-44002i−2i0000000000000002i−2i2i−2i00000000000000000−2i2i000000
χ604-40400-440-40000-4400040000-4000-4400−2i2i000000000000000−2i2i−2i2i000000000000000002i−2i000000
χ61888-488-4-2-4-2-2-2-4-4008-4-41-2-2111000000000-2-2111111000000000000000000000000000000000000
χ62888-488-4-2-4-2-2-2-4-400-8441-2-21110000000002211-1-1-1-1000000000000000000000000000000000000
χ63888-4-8-8-4-2-4-2-2-24400000122111000000000−2525-1-15−55−5000000000000000000000000000000000000
χ64888-4-8-8-4-2-4-2-2-2440000012211100000000025−25-1-1−55−55000000000000000000000000000000000000
χ6588-888-88-2-8-2228-800000-2-2222-200000000000-220000000000000000000000000000000000000000
χ6688-88-888-2-8-222-8800000-22-222-2000000000002-20000000000000000000000000000000000000000
χ6788-8-48-8-4-24-222-44000−4i34i31-22-1-11000000000001-1i3i3−i3−i3000000000000000000000000000000000000
χ6888-8-48-8-4-24-222-440004i3−4i31-22-1-11000000000001-1−i3−i3i3i3000000000000000000000000000000000000
χ6988-8-4-88-4-24-2224-40000012-2-1-1100000000000-11−i15i15i15−i15000000000000000000000000000000000000
χ7088-8-4-88-4-24-2224-40000012-2-1-1100000000000-11i15−i15−i15i15000000000000000000000000000000000000
χ718-80800-8-202−25250000000-200−2525200000004i−4i000000000000000−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ470000000000000000000000000
χ728-80800-8-202−25250000000-200−252520000000−4i4i0000000000000002ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ592ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ470000000000000000000000000
χ738-80800-8-20225−250000000-20025−25200000004i−4i000000000000000−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ590000000000000000000000000
χ748-80800-8-20225−250000000-20025−2520000000−4i4i0000000000000002ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ472ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ590000000000000000000000000
χ758-80-400480-800008-8000-400004000-44000000000000000000000000000000000000000000000000
χ768-80-400480-80000-88000-4000040004-4000000000000000000000000000000000000000000000000
χ7716-160-8008-404−4545000000020025−25-200000000000000000000000000000000000000000000000000000
χ7816-160-8008-40445−450000000200−2525-200000000000000000000000000000000000000000000000000000

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