Finite Group Databasebeta

← Group #12019646

Character table — Group #12019646

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size112222244455888888810161616161616161616161616161616203232323232323232323240404040408080808080
order1225510104101044224882020444444101010102020404040402202020202020202020204448844444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111-1-1111-111-1-1111111-1-1-1-11-1-11111-1-1-1-1111-1-1-111-1-1
χ4111111111111111-1-1111-1-1-111111111-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-111
χ5111111111111-1-1111111-1i−ii−i-1-1-1-11111111-1-1ii−i−iii−i−i-1-1111-1i−ii−i
χ6111111111111-1-1111111-1−ii−ii-1-1-1-11111111-1-1−i−iii−i−iii-1-1111-1−ii−ii
χ7111111111111-1-11-1-11111i−i−ii-1-1-1-111-1-1-1-1111ii−i−i−i−iii-1-11-1-11i−i−ii
χ8111111111111-1-11-1-11111−iii−i-1-1-1-111-1-1-1-1111−i−iiiii−i−i-1-11-1-11−iii−i
χ91111111111-1-11111111-1111111111111111-11111111111-1-1-1-1-1-1-1-1-1-1
χ101111111111-1-11111111-11-1-1-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111-1-1111-1-111-1-111-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111-1-111
χ121111111111-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1
χ131111111111-1-1-1-111111-1-1i−ii−i-1-1-1-1111111-1-1-1ii−i−iii−i−i11-1-1-11−ii−ii
χ141111111111-1-1-1-111111-1-1−ii−ii-1-1-1-1111111-1-1-1−i−iii−i−iii11-1-1-11i−ii−i
χ151111111111-1-1-1-11-1-111-11i−i−ii-1-1-1-111-1-1-1-1-111ii−i−i−i−iii11-111-1−iii−i
χ161111111111-1-1-1-11-1-111-11−iii−i-1-1-1-111-1-1-1-1-111−i−iiiii−i−i11-111-1i−i−ii
χ172222222222222-2-2002220000022-2-2-2-20000200000000002-2-20000000
χ18222222222222-22-20022200000-2-222-2-2000020000000000-22-20000000
χ192222222222-2-22-2-20022-20000022-2-2-2-20000-20000000000-2220000000
χ202222222222-2-2-22-20022-200000-2-222-2-20000-200000000002-220000000
χ21222−1+52−1−52−1+52−1−522−1+52−1−520022222−1+52−1−52022222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−520−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ22222−1+52−1−52−1+52−1−522−1+52−1−520022222−1+52−1−5202-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−520−1+52−1−521−521+521−521+521−521+521−521+520000000000
χ23222−1+52−1−52−1+52−1−522−1+52−1−5200222-2-2−1+52−1−520-222-2-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+5201−521+52−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ24222−1+52−1−52−1+52−1−522−1+52−1−5200222-2-2−1+52−1−520-2-2-222−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+5201−521+521−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ25222−1+52−1−52−1+52−1−522−1+52−1−5200-2-2222−1+52−1−520-22i−2i2i−2i1−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−5201−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ26222−1+52−1−52−1+52−1−522−1+52−1−5200-2-2222−1+52−1−520-2−2i2i−2i2i1−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−5201−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ27222−1+52−1−52−1+52−1−522−1+52−1−5200-2-22-2-2−1+52−1−52022i−2i−2i2i1−521+521−521+52−1+52−1−521−521−521+521+520−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ28222−1+52−1−52−1+52−1−522−1+52−1−5200-2-22-2-2−1+52−1−5202−2i2i2i−2i1−521+521−521+52−1+52−1−521−521−521+521+520−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ29222−1−52−1+52−1−52−1+522−1−52−1+520022222−1−52−1+52022222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+520−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ30222−1−52−1+52−1−52−1+522−1−52−1+520022222−1−52−1+5202-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+520−1−52−1+521+521−521+521−521+521−521+521−520000000000
χ31222−1−52−1+52−1−52−1+522−1−52−1+5200222-2-2−1−52−1+520-222-2-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−5201+521−52−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ32222−1−52−1+52−1−52−1+522−1−52−1+5200222-2-2−1−52−1+520-2-2-222−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−5201+521−521+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ33222−1−52−1+52−1−52−1+522−1−52−1+5200-2-2222−1−52−1+520-22i−2i2i−2i1+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+5201+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ34222−1−52−1+52−1−52−1+522−1−52−1+5200-2-2222−1−52−1+520-2−2i2i−2i2i1+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+5201+521−52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ35222−1−52−1+52−1−52−1+522−1−52−1+5200-2-22-2-2−1−52−1+52022i−2i−2i2i1+521−521+521−52−1−52−1+521+521+521−521−520−1−52−1+52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ36222−1−52−1+52−1−52−1+522−1−52−1+5200-2-22-2-2−1−52−1+5202−2i2i2i−2i1+521−521+521−52−1−52−1+521+521+521−521−520−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ374444444-4444400000-4-44000000000000000-400000000000000000000
χ384444444-444-4-400000-4-4-4000000000000000400000000000000000000
χ39444−1+5−1−5−1+5−1−54−1+5−1−5004-4-400−1+5−1−5000000−1+5−1−51−51+51−51+50000000000000000000000000
χ40444−1+5−1−5−1+5−1−54−1+5−1−500-44-400−1+5−1−50000001−51+5−1+5−1−51−51+50000000000000000000000000
χ41444−1−5−1+5−1−5−1+54−1−5−1+5004-4-400−1−5−1+5000000−1−5−1+51+51−51+51−50000000000000000000000000
χ42444−1−5−1+5−1−5−1+54−1−5−1+500-44-400−1−5−1+50000001+51−5−1−5−1+51+51−50000000000000000000000000
χ4344-444440-4-4440002i−2i00-4000000000002i−2i2i−2i000000000000002i−2i00000
χ4444-444440-4-444000−2i2i00-400000000000−2i2i−2i2i00000000000000−2i2i00000
χ4544-444440-4-4-4-40002i−2i004000000000002i−2i2i−2i00000000000000−2i2i00000
χ4644-444440-4-4-4-4000−2i2i00400000000000−2i2i−2i2i000000000000002i−2i00000
χ47888−2+25−2−25−2+25−2−25-8−2+25−2−2500000002−252+250000000000000000000000000000000000000
χ48888−2−25−2+25−2−25−2+25-8−2−25−2+2500000002+252−250000000000000000000000000000000000000
χ4988-8−2+25−2−25−2+25−2−2502−252+25000004i−4i00000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000
χ5088-8−2+25−2−25−2+25−2−2502−252+2500000−4i4i000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000
χ5188-8−2−25−2+25−2−25−2+2502+252−25000004i−4i00000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000
χ5288-8−2−25−2+25−2−25−2+2502+252−2500000−4i4i000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000
χ538-8088-8-80008i−8i00000000000000000000000000000000000000000000
χ548-8088-8-8000−8i8i00000000000000000000000000000000000000000000
χ5516-160−4+45−4−454−454+450000000000000000000000000000000000000000000000000
χ5616-160−4−45−4+454+454−450000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.