Finite Group Databasebeta

← Group #13104217

Character table — Group #13104217

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122444444444444444444444444888888888888101010101010101020202020202020202020202020202020202020202525252540404040404040405050100100100100
order12442455551010101010101010202020202020202020202020510101010102020202020204444444422442020202020202020202020202020202022441010101020202020248888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ51111-1-1111111-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-111-1-1iiii−i−i−i−i1-11-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-1-111-1-111ii−i−i
χ61111-1-1111111-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-111-1-1iiii−i−i−i−i-11-11iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-111-1-11111−i−iii
χ71111-1-1111111-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-111-1-1−i−i−i−iiiii1-11-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-1-111-1-111−i−iii
χ81111-1-1111111-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-111-1-1−i−i−i−iiiii-11-11−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-111-1-11111ii−i−i
χ911-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-111-11-1
χ1011-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-111-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-11-11-11
χ1111-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-11-11-11
χ1211-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-111-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-111-11-1
χ1311-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1111-1-111ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-11111-1-1-1-1-11i−i−ii
χ1411-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1111-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-11111-11−iii−i
χ1511-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1111-1-111−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-11111-1-1-1-1-11−iii−i
χ1611-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1111-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-11111-11i−i−ii
χ172222222222222222222222222222222222222222220000000000000000000000000000-2-2-2-200000000-2-20000
χ182222-2-2222222-2-2-2-2222222-2-2-2-222222-2-2-2-22-2-222-2-20000000000000000000000000000222200000000-2-20000
χ1922-2-22-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000022-2-2000000002-20000
χ2022-2-2-22222222-2-2-2-222-2-2-2-22222-2-2-2-22-2-2-2-2222-2-2220000000000000000000000000000-2-222000000002-20000
χ212-22i−2i002222-2-20000-2-22i2i−2i−2i00002i2i−2i−2i20000-2002i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2-22i−2i00000000000000
χ222-22i−2i002222-2-20000-2-22i2i−2i−2i00002i2i−2i−2i20000-2002i−2i001−i−1+i−1−i1+i1+i−1−i−1+i1−i00001−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i-22−2i2i00000000000000
χ232-22i−2i002222-2-20000-2-22i2i−2i−2i00002i2i−2i−2i20000-2002i−2i00−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i-22−2i2i00000000000000
χ242-22i−2i002222-2-20000-2-22i2i−2i−2i00002i2i−2i−2i20000-2002i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-22i−2i00000000000000
χ252-2−2i2i002222-2-20000-2-2−2i−2i2i2i0000−2i−2i2i2i20000-200−2i2i001+i−1−i−1+i1−i1−i−1+i−1−i1+i00001+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i-222i−2i00000000000000
χ262-2−2i2i002222-2-20000-2-2−2i−2i2i2i0000−2i−2i2i2i20000-200−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2-2−2i2i00000000000000
χ272-2−2i2i002222-2-20000-2-2−2i−2i2i2i0000−2i−2i2i2i20000-200−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-2−2i2i00000000000000
χ282-2−2i2i002222-2-20000-2-2−2i−2i2i2i0000−2i−2i2i2i20000-200−2i2i00−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i-222i−2i00000000000000
χ29444444−1+5−1−53−523+52−1+5−1−5−1+5−1+5−1−5−1−53−523+52−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−53−523+523−523+52-13−523+52-1-1-13−523+52-1-1-1-100000000222200000000000000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000
χ30444444−1+5−1−53−523+52−1+5−1−5−1+5−1+5−1−5−1−53−523+52−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−53−523+523−523+52-13−523+52-1-1-13−523+52-1-1-1-100000000-2-2-2-2000000000000000000001−521+521−521+521−521+521−521+52000000
χ314444443−523+52−1−5−1+53−523+523−523−523+523+52−1−5−1+53−523+523−523+523−523−523+523+52−1−5−1+5−1−5−1+5-1−1−5−1+5-1-1-1−1−5−1+5-1-1-1-1222222220000−1+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+52−1−52000000000000000000
χ324444443−523+52−1−5−1+53−523+523−523−523+523+52−1−5−1+53−523+523−523+523−523−523+523+52−1−5−1+5−1−5−1+5-1−1−5−1+5-1-1-1−1−5−1+5-1-1-1-1-2-2-2-2-2-2-2-200001−521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+52000000000000000000
χ334444443+523−52−1+5−1−53+523−523+523+523−523−52−1+5−1−53+523−523+523−523+523+523−523−52−1+5−1−5−1+5−1−5-1−1+5−1−5-1-1-1−1+5−1−5-1-1-1-1222222220000−1−52−1+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+52000000000000000000
χ344444443+523−52−1+5−1−53+523−523+523+523−523−52−1+5−1−53+523−523+523−523+523+523−523−52−1+5−1−5−1+5−1−5-1−1+5−1−5-1-1-1−1+5−1−5-1-1-1-1-2-2-2-2-2-2-2-200001+521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−52000000000000000000
χ35444444−1−5−1+53+523−52−1−5−1+5−1−5−1−5−1+5−1+53+523−52−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+53+523−523+523−52-13+523−52-1-1-13+523−52-1-1-1-100000000222200000000000000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000
χ36444444−1−5−1+53+523−52−1−5−1+5−1−5−1−5−1+5−1+53+523−52−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+53+523−523+523−52-13+523−52-1-1-13+523−52-1-1-1-100000000-2-2-2-2000000000000000000001+521−521+521−521+521−521+521−52000000
χ374444-4-4−1+5−1−53−523+52−1+5−1−51−51−51+51+53−523+52−1+5−1−5−1+5−1−51−51−51+51+53−523+523−523+52-1−3+52−3−5211-1−3+52−3−52-1-111000000002-22-200000000000000000000−1+52−1−521−521+52−1+52−1−521−521+52000000
χ384444-4-4−1+5−1−53−523+52−1+5−1−51−51−51+51+53−523+52−1+5−1−5−1+5−1−51−51−51+51+53−523+523−523+52-1−3+52−3−5211-1−3+52−3−52-1-11100000000-22-22000000000000000000001−521+52−1+52−1−521−521+52−1+52−1−52000000
χ394444-4-43−523+52−1−5−1+53−523+52−3+52−3+52−3−52−3−52−1−5−1+53−523+523−523+52−3+52−3+52−3−52−3−52−1−5−1+5−1−5−1+5-11+51−511-11+51−5-1-1112i2i2i2i−2i−2i−2i−2i0000−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ404444-4-43−523+52−1−5−1+53−523+52−3+52−3+52−3−52−3−52−1−5−1+53−523+523−523+52−3+52−3+52−3−52−3−52−1−5−1+5−1−5−1+5-11+51−511-11+51−5-1-111−2i−2i−2i−2i2i2i2i2i0000ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ414444-4-43+523−52−1+5−1−53+523−52−3−52−3−52−3+52−3+52−1+5−1−53+523−523+523−52−3−52−3−52−3+52−3+52−1+5−1−5−1+5−1−5-11−51+511-11−51+5-1-1112i2i2i2i−2i−2i−2i−2i0000−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ424444-4-43+523−52−1+5−1−53+523−52−3−52−3−52−3+52−3+52−1+5−1−53+523−523+523−52−3−52−3−52−3+52−3+52−1+5−1−5−1+5−1−5-11−51+511-11−51+5-1-111−2i−2i−2i−2i2i2i2i2i0000ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ434444-4-4−1−5−1+53+523−52−1−5−1+51+51+51−51−53+523−52−1−5−1+5−1−5−1+51+51+51−51−53+523−523+523−52-1−3−52−3+5211-1−3−52−3+52-1-111000000002-22-200000000000000000000−1−52−1+521+521−52−1−52−1+521+521−52000000
χ444444-4-4−1−5−1+53+523−52−1−5−1+51+51+51−51−53+523−52−1−5−1+5−1−5−1+51+51+51−51−53+523−523+523−52-1−3−52−3+5211-1−3−52−3+52-1-11100000000-22-22000000000000000000001+521−52−1−52−1+521+521−52−1−52−1+52000000
χ4544-4-44-4−1+5−1−53−523+52−1+5−1−5−1+5−1+5−1−5−1−53−523+521−51+51−51+51−51−51+51+5−3+52−3−52−3+52−3−52-13−523+52-1-1-1−3+52−3−521111000000002-2-2200000000000000000000−1+52−1−521−521+521−521+52−1+52−1−52000000
χ4644-4-44-4−1+5−1−53−523+52−1+5−1−5−1+5−1+5−1−5−1−53−523+521−51+51−51+51−51−51+51+5−3+52−3−52−3+52−3−52-13−523+52-1-1-1−3+52−3−52111100000000-222-2000000000000000000001−521+52−1+52−1−52−1+52−1−521−521+52000000
χ4744-4-44-43−523+52−1−5−1+53−523+523−523−523+523+52−1−5−1+5−3+52−3−52−3+52−3−52−3+52−3+52−3−52−3−521+51−51+51−5-1−1−5−1+5-1-1-11+51−5111122-2-222-2-20000−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+52000000000000000000
χ4844-4-44-43−523+52−1−5−1+53−523+523−523−523+523+52−1−5−1+5−3+52−3−52−3+52−3−52−3+52−3+52−3−52−3−521+51−51+51−5-1−1−5−1+5-1-1-11+51−51111-2-222-2-22200001−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−52000000000000000000
χ4944-4-44-43+523−52−1+5−1−53+523−523+523+523−523−52−1+5−1−5−3−52−3+52−3−52−3+52−3−52−3−52−3+52−3+521−51+51−51+5-1−1+5−1−5-1-1-11−51+5111122-2-222-2-20000−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−52000000000000000000
χ5044-4-44-43+523−52−1+5−1−53+523−523+523+523−523−52−1+5−1−5−3−52−3+52−3−52−3+52−3−52−3−52−3+52−3+521−51+51−51+5-1−1+5−1−5-1-1-11−51+51111-2-222-2-22200001+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+52000000000000000000
χ5144-4-44-4−1−5−1+53+523−52−1−5−1+5−1−5−1−5−1+5−1+53+523−521+51−51+51−51+51+51−51−5−3−52−3+52−3−52−3+52-13+523−52-1-1-1−3−52−3+521111000000002-2-2200000000000000000000−1−52−1+521+521−521+521−52−1−52−1+52000000
χ5244-4-44-4−1−5−1+53+523−52−1−5−1+5−1−5−1−5−1+5−1+53+523−521+51−51+51−51+51+51−51−5−3−52−3+52−3−52−3+52-13+523−52-1-1-1−3−52−3+52111100000000-222-2000000000000000000001+521−52−1−52−1+52−1−52−1+521+521−52000000
χ5344-4-4-44−1+5−1−53−523+52−1+5−1−51−51−51+51+53−523+521−51+51−51+5−1+5−1+5−1−5−1−5−3+52−3−52−3+52−3−52-1−3+52−3−5211-13−523+5211-1-10000000022-2-200000000000000000000−1+52−1−52−1+52−1−521−521+521−521+52000000
χ5444-4-4-44−1+5−1−53−523+52−1+5−1−51−51−51+51+53−523+521−51+51−51+5−1+5−1+5−1−5−1−5−3+52−3−52−3+52−3−52-1−3+52−3−5211-13−523+5211-1-100000000-2-222000000000000000000001−521+521−521+52−1+52−1−52−1+52−1−52000000
χ5544-4-4-443−523+52−1−5−1+53−523+52−3+52−3+52−3−52−3−52−1−5−1+5−3+52−3−52−3+52−3−523−523−523+523+521+51−51+51−5-11+51−511-1−1−5−1+511-1-12i2i−2i−2i−2i−2i2i2i0000−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ5644-4-4-443−523+52−1−5−1+53−523+52−3+52−3+52−3−52−3−52−1−5−1+5−3+52−3−52−3+52−3−523−523−523+523+521+51−51+51−5-11+51−511-1−1−5−1+511-1-1−2i−2i2i2i2i2i−2i−2i0000ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ5744-4-4-443+523−52−1+5−1−53+523−52−3−52−3−52−3+52−3+52−1+5−1−5−3−52−3+52−3−52−3+523+523+523−523−521−51+51−51+5-11−51+511-1−1+5−1−511-1-12i2i−2i−2i−2i−2i2i2i0000−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ5844-4-4-443+523−52−1+5−1−53+523−52−3−52−3−52−3+52−3+52−1+5−1−5−3−52−3+52−3−52−3+523+523+523−523−521−51+51−51+5-11−51+511-1−1+5−1−511-1-1−2i−2i2i2i2i2i−2i−2i0000ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ5944-4-4-44−1−5−1+53+523−52−1−5−1+51+51+51−51−53+523−521+51−51+51−5−1−5−1−5−1+5−1+5−3−52−3+52−3−52−3+52-1−3−52−3+5211-13+523−5211-1-10000000022-2-200000000000000000000−1−52−1+52−1−52−1+521+521−521+521−52000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.