Finite Group Databasebeta

← Group #13026288

Character table — Group #13026288

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1124444444444444558888888888888881016161616161616161620202020202020202040404040404040808080808080
order12222224444451010102244410101010202020202020202021010202020202020202222444444444444444488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−ii−i
χ41111111111111111-1-1111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−ii
χ511111111-1-1-1-1111111-11-11111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-11-11-111111-11-1-1-1
χ611111111-1-1-1-1111111-11-11111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-11-11-1-1-1-1-1-11-1111
χ711111111-1-1-1-11111-1-1-11-11111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111-11-11ii−i−ii−i−ii−ii
χ811111111-1-1-1-11111-1-1-11-11111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111-11-11−i−iii−iii−ii−i
χ911111-1-1111-1-1111111-1-11-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-11111-1-11-1-111111-11-11-1-1
χ1011111-1-1111-1-1111111-1-11-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-11111-1-11-1-11-1-1-1-11-11-111
χ1111111-1-1111-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111-111-1-1111-1-111-1-1-1-111-111-1ii−i−i−iii−i−ii
χ1211111-1-1111-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111-111-1-1111-1-111-1-1-1-111-111-1−i−iiii−i−iii−i
χ1311111-1-11-1-1111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-111-1-11111-1-11111-1-1-1-111
χ1411111-1-11-1-1111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-11111-1-1
χ1511111-1-11-1-1111111-1-11-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111111-1-111-1-1-1-111ii−i−i−i−iiii−i
χ1611111-1-11-1-1111111-1-11-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111111-1-111-1-1-1-111−i−iiiii−i−i−ii
χ172222-200-2220022222200-200000000222222-200-2-2-200002-22200-200-20000000000
χ182222-200-222002222-2-200-2000000002222-22-200-2-2-20000-22-2-20020020000000000
χ192222-200-2-2-20022222200200000000-2-2-2-222-20022-200002-2-2-200-20020000000000
χ202222-200-2-2-2002222-2-200200000000-2-2-2-2-22-20022-20000-222200200-20000000000
χ21222-2222-200002222220-202222000000002-22-2-200-20022-220000-20-200000000000
χ22222-2222-200002222-2-20-20222200000000-2-22-2-200-200-2-22-2000020200000000000
χ23222-22-2-2-20000222222020-2-2-2-2000000002-222200-200-2-2-220000-20200000000000
χ24222-22-2-2-200002222-2-2020-2-2-2-200000000-2-222200-200222-2000020-200000000000
χ25222-2-20020022222222-2000000222200002-2-200002-2-200-2-200222-2000000000000
χ26222-2-200200222222-2-2-200000022220000-2-2-200002-2-2002200-2-2-22000000000000
χ27222-2-200200-2-22222222000000-2-2-2-200002-2-2000022200-2-200-2-222000000000000
χ28222-2-200200-2-22222-2-22000000-2-2-2-20000-2-2-2000022200220022-2-2000000000000
χ29444444444444-1-1-1-100444-1-1-1-1-1-1-1-1-1-1-1-10-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-4-4-4-4-1-1-1-100-44-4-1-1-1-1111111110-1-1-1-111-1110000000000000000000000
χ3144444-4-4444-4-4-1-1-1-100-4-4411111111-1-1-1-10-1-111-1-1-1110000000000000000000000
χ3244444-4-44-4-444-1-1-1-1004-4-41111-1-1-1-111110-1-11111-1-1-10000000000000000000000
χ334444-400-44400-1-1-1-10000-455−5−555−5−5-1-1-1-10-115−51115−50000000000000000000000
χ344444-400-44400-1-1-1-10000-4−5−555−5−555-1-1-1-10-11−55111−550000000000000000000000
χ354444-400-4-4-400-1-1-1-10000455−5−5−5−55511110-115−5-1-11−550000000000000000000000
χ364444-400-4-4-400-1-1-1-100004−5−55555−5−511110-11−55-1-115−50000000000000000000000
χ37444-4444-40000-1-1-1-1000-40-1-1-1-155−5−555−5−501-1115−51−550000000000000000000000
χ38444-4444-40000-1-1-1-1000-40-1-1-1-1−5−555−5−55501-111−5515−50000000000000000000000
χ39444-44-4-4-40000-1-1-1-100040111155−5−5−5−55501-1-1-1−551−550000000000000000000000
χ40444-44-4-4-40000-1-1-1-1000401111−5−55555−5−501-1-1-15−515−50000000000000000000000
χ41444-4-40040044-1-1-1-100-40055−5−5-1-1-1-155−5−5011−55−55-1110000000000000000000000
χ42444-4-40040044-1-1-1-100-400−5−555-1-1-1-1−5−5550115−55−5-1110000000000000000000000
χ43444-4-400400-4-4-1-1-1-10040055−5−51111−5−555011−555−5-1-1-10000000000000000000000
χ44444-4-400400-4-4-1-1-1-100400−5−555111155−5−50115−5−55-1-1-10000000000000000000000
χ4544-40000000004-4-4444000000000000000-40000000000000000000002-22-2000000
χ4644-40000000004-4-4444000000000000000-4000000000000000000000-22-22000000
χ4744-40000000004-4-44-4-400000000000000040000000000000000000002i−2i−2i2i000000
χ4844-40000000004-4-44-4-40000000000000004000000000000000000000−2i2i2i−2i000000
χ494-40002-202i−2i2i−2i400-44-40002-22-22i−2i2i−2i2i−2i2i−2i00000000002-2002i−2i2i−2i00000000000000
χ504-40002-202i−2i2i−2i400-4-440002-22-22i−2i2i−2i2i−2i2i−2i0000000000-2200−2i2i−2i2i00000000000000
χ514-40002-20−2i2i−2i2i400-44-40002-22-2−2i2i−2i2i−2i2i−2i2i00000000002-200−2i2i−2i2i00000000000000
χ524-40002-20−2i2i−2i2i400-4-440002-22-2−2i2i−2i2i−2i2i−2i2i0000000000-22002i−2i2i−2i00000000000000
χ534-4000-2202i−2i−2i2i400-44-4000-22-22−2i2i−2i2i2i−2i2i−2i0000000000-22002i−2i−2i2i00000000000000
χ544-4000-2202i−2i−2i2i400-4-44000-22-22−2i2i−2i2i2i−2i2i−2i00000000002-200−2i2i2i−2i00000000000000
χ554-4000-220−2i2i2i−2i400-44-4000-22-222i−2i2i−2i−2i2i−2i2i0000000000-2200−2i2i2i−2i00000000000000
χ564-4000-220−2i2i2i−2i400-4-44000-22-222i−2i2i−2i−2i2i−2i2i00000000002-2002i−2i−2i2i00000000000000
χ578-80004-404i−4i4i−4i-225−25200000−1+51−5−1−51+5−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ588-80004-404i−4i4i−4i-2−2525200000−1−51+5−1+51−5−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ598-80004-40−4i4i−4i4i-225−25200000−1+51−5−1−51+52ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ608-80004-40−4i4i−4i4i-2−2525200000−1−51+5−1+51−52ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ618-8000-4404i−4i−4i4i-225−252000001−5−1+51+5−1−52ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ628-8000-4404i−4i−4i4i-2−25252000001+5−1−51−5−1+52ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ638-8000-440−4i4i4i−4i-225−252000001−5−1+51+5−1−5−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ648-8000-440−4i4i4i−4i-2−25252000001+5−1−51−5−1+5−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ651616-16000000000-444-40000000000000000000000000000000000000000000000000

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