Finite Group Databasebeta

← Group #12019652

Character table — Group #12019652

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222224448888888101016161616161616161616161616161620202032323232323232323232404040408080808080
order1225510104101022488202044444441010101020204040404024420202020202020202020448844444
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111-1-1111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111-1-11-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-11111-111-1-1111111-1-1-1-1111-1-11111-1-1-1-111-1-1-111-1-1
χ61111111111111-1-11111-1-1-111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-111
χ71111111111111-1-111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111
χ81111111111111-1-111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1
χ91111111111-1-11111111-1i−ii−i-1-1-1-1111111111-1-1ii−i−iii−i−i-1-111-1i−ii−i
χ101111111111-1-11111111-1−ii−ii-1-1-1-1111111111-1-1−i−iii−i−iii-1-111-1−ii−ii
χ111111111111-1-111111-1-1-1i−ii−i-1-1-1-1111111-1-1-1-1-1ii−i−iii−i−i11-1-11−ii−ii
χ121111111111-1-111111-1-1-1−ii−ii-1-1-1-1111111-1-1-1-1-1−i−iii−i−iii11-1-11i−ii−i
χ131111111111-1-11-1-111111i−i−ii-1-1-1-111-1-1-1-111111ii−i−i−i−iii-1-1-1-11i−i−ii
χ141111111111-1-11-1-111111−iii−i-1-1-1-111-1-1-1-111111−i−iiiii−i−i-1-1-1-11−iii−i
χ151111111111-1-11-1-111-1-11i−i−ii-1-1-1-111-1-1-1-1-1-1-111ii−i−i−i−iii1111-1−iii−i
χ161111111111-1-11-1-111-1-11−iii−i-1-1-1-111-1-1-1-1-1-1-111−i−iiiii−i−i1111-1i−i−ii
χ1722222222222-2-20022220000022-2-2-2-200002-2-200000000002-20000000
χ1822222222222-2-20022-2-20000022-2-2-2-20000-2220000000000-220000000
χ192222222222-22-200222200000-2-222-2-200002-2-20000000000-220000000
χ202222222222-22-20022-2-200000-2-222-2-20000-22200000000002-20000000
χ21222−1+52−1−52−1+52−1−522−1+52−1−5222222−1+52−1−520022222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000
χ22222−1+52−1−52−1+52−1−522−1+52−1−5222222−1+52−1−52002-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52000−1+52−1−521−521+521−521+521−521+521−521+52000000000
χ23222−1+52−1−52−1+52−1−522−1+52−1−52222-2-2−1+52−1−5200-222-2-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+520001−521+52−1+52−1−52−1+52−1−521−521+521−521+52000000000
χ24222−1+52−1−52−1+52−1−522−1+52−1−52222-2-2−1+52−1−5200-2-2-222−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+520001−521+521−521+521−521+52−1+52−1−52−1+52−1−52000000000
χ25222−1+52−1−52−1+52−1−522−1+52−1−52-2-2222−1+52−1−5200-22i−2i2i−2i1−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−520001−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000
χ26222−1+52−1−52−1+52−1−522−1+52−1−52-2-2222−1+52−1−5200-2−2i2i−2i2i1−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−520001−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000
χ27222−1+52−1−52−1+52−1−522−1+52−1−52-2-22-2-2−1+52−1−520022i−2i−2i2i1−521+521−521+52−1+52−1−521−521−521+521+52000−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000
χ28222−1+52−1−52−1+52−1−522−1+52−1−52-2-22-2-2−1+52−1−52002−2i2i2i−2i1−521+521−521+52−1+52−1−521−521−521+521+52000−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000
χ29222−1−52−1+52−1−52−1+522−1−52−1+5222222−1−52−1+520022222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000
χ30222−1−52−1+52−1−52−1+522−1−52−1+5222222−1−52−1+52002-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52000−1−52−1+521+521−521+521−521+521−521+521−52000000000
χ31222−1−52−1+52−1−52−1+522−1−52−1+52222-2-2−1−52−1+5200-222-2-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−520001+521−52−1−52−1+52−1−52−1+521+521−521+521−52000000000
χ32222−1−52−1+52−1−52−1+522−1−52−1+52222-2-2−1−52−1+5200-2-2-222−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−520001+521−521+521−521+521−52−1−52−1+52−1−52−1+52000000000
χ33222−1−52−1+52−1−52−1+522−1−52−1+52-2-2222−1−52−1+5200-22i−2i2i−2i1+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+520001+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000
χ34222−1−52−1+52−1−52−1+522−1−52−1+52-2-2222−1−52−1+5200-2−2i2i−2i2i1+521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+520001+521−52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000
χ35222−1−52−1+52−1−52−1+522−1−52−1+52-2-22-2-2−1−52−1+520022i−2i−2i2i1+521−521+521−52−1−52−1+521+521+521−521−52000−1−52−1+52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000
χ36222−1−52−1+52−1−52−1+522−1−52−1+52-2-22-2-2−1−52−1+52002−2i2i2i−2i1+521−521+521−52−1−52−1+521+521+521−521−52000−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000
χ374444444-44400000-4-444000000000000000-4000000000000000000000
χ384444444-44400000-4-4-4-40000000000000004000000000000000000000
χ39444−1+5−1−5−1+5−1−54−1+5−1−54-4-400−1+5−1−50000000−1+5−1−51−51+51−51+500000000000000000000000000
χ40444−1+5−1−5−1+5−1−54−1+5−1−5-44-400−1+5−1−500000001−51+5−1+5−1−51−51+500000000000000000000000000
χ41444−1−5−1+5−1−5−1+54−1−5−1+54-4-400−1−5−1+50000000−1−5−1+51+51−51+51−500000000000000000000000000
χ42444−1−5−1+5−1−5−1+54−1−5−1+5-44-400−1−5−1+500000001+51−5−1−5−1+51+51−500000000000000000000000000
χ4344-444440-4-40002i−2i004-4000000000002i−2i2i−2i0000000000000002i−2i00000
χ4444-444440-4-40002i−2i00-44000000000002i−2i2i−2i000000000000000−2i2i00000
χ4544-444440-4-4000−2i2i004-400000000000−2i2i−2i2i000000000000000−2i2i00000
χ4644-444440-4-4000−2i2i00-4400000000000−2i2i−2i2i0000000000000002i−2i00000
χ47888−2+25−2−25−2+25−2−25-8−2+25−2−25000002−252+25000000000000000000000000000000000000000
χ48888−2−25−2+25−2−25−2+25-8−2−25−2+25000002+252−25000000000000000000000000000000000000000
χ4988-8−2+25−2−25−2+25−2−2502−252+250004i−4i000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000
χ5088-8−2+25−2−25−2+25−2−2502−252+25000−4i4i0000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000
χ5188-8−2−25−2+25−2−25−2+2502+252−250004i−4i000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000
χ5288-8−2−25−2+25−2−25−2+2502+252−25000−4i4i0000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000
χ538-8088-8-800000000000000000000000000004i−4i0000000000000000000
χ548-8088-8-80000000000000000000000000000−4i4i0000000000000000000
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.