Finite Group Databasebeta

← Group #12019643

Character table — Group #12019643

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size112488888161616161622481616161616323232323222481616161616323232323255102040404040408080808080
order1224224884444451010201010204040202020202051010201010204040202020202022242248844444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1
χ31111111-1-1-111-1-11111111-1-1-111-1-11111111-1-1-111-1-11111111-1-1-111-1-1
χ41111111-1-1-1-1-1111111111-1-1-1-1-1111111111-1-1-1-1-1111111111-1-1-1-1-111
χ51111-1-1111-1i−ii−i1111-1-1111-1i−ii−i1111-1-1111-1i−ii−i1111-1-1111-1i−ii−i
χ61111-1-1111-1−ii−ii1111-1-1111-1−ii−ii1111-1-1111-1−ii−ii1111-1-1111-1−ii−ii
χ71111-1-11-1-11i−i−ii1111-1-11-1-11i−i−ii1111-1-11-1-11i−i−ii1111-1-11-1-11i−i−ii
χ81111-1-11-1-11−iii−i1111-1-11-1-11−iii−i1111-1-11-1-11−iii−i1111-1-11-1-11−iii−i
χ922222-2-2000000022222-2-2000000022222-2-2000000022222-2-20000000
χ102222-22-200000002222-22-200000002222-22-200000002222-22-20000000
χ11444-40000000000444-40000000000444-40000000000444-40000000000
χ1244-400002i−2i0000044-400002i−2i0000044-400002i−2i0000044-400002i−2i00000
χ1344-40000−2i2i0000044-40000−2i2i0000044-40000−2i2i0000044-40000−2i2i00000
χ148-80000000000008-80000000000008-80000000000008-8000000000000
χ15111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ171111111-1-1-111-1-11111111-1-1-111-1-11111111-1-1-111-1-1-1-1-1-1-1-1-1111-1-111
χ181111111-1-1-1-1-1111111111-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-111111-1-1
χ191111-1-1111-1i−ii−i1111-1-1111-1i−ii−i1111-1-1111-1i−ii−i-1-1-1-111-1-1-11−ii−ii
χ201111-1-1111-1−ii−ii1111-1-1111-1−ii−ii1111-1-1111-1−ii−ii-1-1-1-111-1-1-11i−ii−i
χ211111-1-11-1-11i−i−ii1111-1-11-1-11i−i−ii1111-1-11-1-11i−i−ii-1-1-1-111-111-1−iii−i
χ221111-1-11-1-11−iii−i1111-1-11-1-11−iii−i1111-1-11-1-11−iii−i-1-1-1-111-111-1i−i−ii
χ2322222-2-2000000022222-2-2000000022222-2-20000000-2-2-2-2-2220000000
χ242222-22-200000002222-22-200000002222-22-20000000-2-2-2-22-220000000
χ25444-40000000000444-40000000000444-40000000000-4-4-440000000000
χ2644-400002i−2i0000044-400002i−2i0000044-400002i−2i00000-4-440000−2i2i00000
χ2744-40000−2i2i0000044-40000−2i2i0000044-40000−2i2i00000-4-4400002i−2i00000
χ288-80000000000008-80000000000008-8000000000000-88000000000000
χ2922222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000000
χ302222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+5200000000000000
χ312222222-2-2-222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−1−52−1−521+521+5200000000000000
χ322222222-2-2-2-2-222−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+52−1−52−1−5200000000000000
χ332222-2-2222-22i−2i2i−2i−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ19−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ700000000000000
χ342222-2-2222-2−2i2i−2i2i−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ19−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ700000000000000
χ352222-2-22-2-222i−2i−2i2i−1+52−1+52−1+52−1+521−521−52−1+521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ19−1−52−1−52−1−52−1−521+521+52−1−521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ700000000000000
χ362222-2-22-2-22−2i2i2i−2i−1+52−1+52−1+52−1+521−521−52−1+521−521−52−1+52ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ19−1−52−1−52−1−52−1−521+521+52−1−521+521+52−1−52ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ700000000000000
χ3744444-4-40000000−1+5−1+5−1+5−1+5−1+51−51−50000000−1−5−1−5−1−5−1−5−1−51+51+5000000000000000000000
χ384444-44-40000000−1+5−1+5−1+5−1+51−5−1+51−50000000−1−5−1−5−1−5−1−51+5−1−51+5000000000000000000000
χ39888-80000000000−2+25−2+25−2+252−250000000000−2−25−2−25−2−252+25000000000000000000000000
χ4088-800004i−4i00000−2+25−2+252−250000−2ζ11−2ζ192ζ11+2ζ1900000−2−25−2−252+250000−2ζ3−2ζ72ζ3+2ζ70000000000000000000
χ4188-80000−4i4i00000−2+25−2+252−2500002ζ11+2ζ19−2ζ11−2ζ1900000−2−25−2−252+2500002ζ3+2ζ7−2ζ3−2ζ70000000000000000000
χ4216-16000000000000−4+454−45000000000000−4−454+4500000000000000000000000000
χ4322222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+5200000000000000
χ442222222222-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−5200000000000000
χ452222222-2-2-222-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−1+52−1+521−521−5200000000000000
χ462222222-2-2-2-2-222−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−52−1+52−1+5200000000000000
χ472222-2-2222-22i−2i2i−2i−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ1900000000000000
χ482222-2-2222-2−2i2i−2i2i−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ1900000000000000
χ492222-2-22-2-222i−2i−2i2i−1−52−1−52−1−52−1−521+521+52−1−521+521+52−1−52−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ3−ζ7−1+52−1+52−1+52−1+521−521−52−1+521−521−52−1+52−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ11−ζ1900000000000000
χ502222-2-22-2-22−2i2i2i−2i−1−52−1−52−1−52−1−521+521+52−1−521+521+52−1−52ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ3+ζ7−1+52−1+52−1+52−1+521−521−52−1+521−521−52−1+52ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ11+ζ1900000000000000
χ5144444-4-40000000−1−5−1−5−1−5−1−5−1−51+51+50000000−1+5−1+5−1+5−1+5−1+51−51−5000000000000000000000
χ524444-44-40000000−1−5−1−5−1−5−1−51+5−1−51+50000000−1+5−1+5−1+5−1+51−5−1+51−5000000000000000000000
χ53888-80000000000−2−25−2−25−2−252+250000000000−2+25−2+25−2+252−25000000000000000000000000
χ5488-800004i−4i00000−2−25−2−252+250000−2ζ3−2ζ72ζ3+2ζ700000−2+25−2+252−250000−2ζ11−2ζ192ζ11+2ζ190000000000000000000
χ5588-80000−4i4i00000−2−25−2−252+2500002ζ3+2ζ7−2ζ3−2ζ700000−2+25−2+252−2500002ζ11+2ζ19−2ζ11−2ζ190000000000000000000
χ5616-16000000000000−4−454+45000000000000−4+454−4500000000000000000000000000

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