Finite Group Databasebeta

← Group #13104316

Character table — Group #13104316

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122444444444444444444444444888888888888101010101010101020202020202020202020202020202020202020202525252540404040404040405050100100100100
order12224455551010101010101010101010102020202020202020510101020202020202020202222444422441010101010101010202020202020202022221010101020202020444444
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
χ51111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1
χ61111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ71111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-1
χ911-1-1i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i1-1i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−ii−i1-1i−i
χ1011-1-1i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i-11−ii1111-1-1-1-1iiii−i−i−i−i1-11-1-1-111−i−iiii−i-11−ii
χ1111-1-1i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i-1-111−i−iii1-1i−i-1-1-1-11111−i−i−i−iiiii1-11-111-1-1ii−i−ii−i-11−ii
χ1211-1-1i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i-1-111−i−iii-11−ii-1-1-1-11111−i−i−i−iiiii1-11-1-1-111−i−iiii−i1-1i−i
χ1311-1-1−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii1-1−ii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii−ii1-1−ii
χ1411-1-1−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii-11i−i1111-1-1-1-1−i−i−i−iiiii1-11-1-1-111ii−i−i−ii-11i−i
χ1511-1-1−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii-1-111ii−i−i1-1−ii-1-1-1-11111iiii−i−i−i−i1-11-111-1-1−i−iii−ii-11i−i
χ1611-1-1−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii-1-111ii−i−i-11i−i-1-1-1-11111iiii−i−i−i−i1-11-1-1-111ii−i−i−ii1-1−ii
χ172222222222222222222222222222222222222222220000000000000000000000000000-2-2-2-200000000-2-20000
χ182222-2-22222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000-2-2-2-200000000220000
χ1922-2-22i−2i22222222-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22-2200000000−2i2i0000
χ2022-2-2−2i2i22222222-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-22-22000000002i−2i0000
χ212-22-2002222-2-2-2-222-2-222-2-2000000002-22-20000000000002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i22-2-200000000000000
χ222-22-2002222-2-2-2-222-2-222-2-2000000002-22-2000000000000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i22-2-200000000000000
χ232-22-2002222-2-2-2-222-2-222-2-2000000002-22-2000000002-22-20000000022-2-222-2-200000000-2-22200000000000000
χ242-22-2002222-2-2-2-222-2-222-2-2000000002-22-200000000-22-2200000000-2-222-2-22200000000-2-22200000000000000
χ252-2-22002222-2-2-2-2-2-222-2-222000000002-2-220000000000002-2-2200000000000022-2-2-2-2222-2-2200000000000000
χ262-2-22002222-2-2-2-2-2-222-2-222000000002-2-22000000000000-222-2000000000000-2-22222-2-22-2-2200000000000000
χ272-2-22002222-2-2-2-2-2-222-2-222000000002-2-22000000002-2-220000000022-2-2-2-22200000000-222-200000000000000
χ282-2-22002222-2-2-2-2-2-222-2-222000000002-2-2200000000-222-200000000-2-22222-2-200000000-222-200000000000000
χ29444444−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1+5−1−5−1−5-1-1-1-13−523+523−523+52-1-1-1-100000000222200000000000000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000
χ30444444−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1+5−1−5−1−5-1-1-1-13−523+523−523+52-1-1-1-100000000-2-2-2-2000000000000000000001−521+521−521+521−521+521−521+52000000
χ314444443−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+523−523−523+523+523−523−523+523+52-1-1-1-1−1−5−1+5−1−5−1+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
χ324444443−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+523−523−523+523+523−523−523+523+52-1-1-1-1−1−5−1+5−1−5−1+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+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−523+523+523−523−523+523+523−523−52-1-1-1-1−1+5−1−5−1+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+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−523+523+523−523−523+523+523−523−52-1-1-1-1−1+5−1−5−1+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
χ35444444−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1−5−1+5−1+5-1-1-1-13+523−523+523−52-1-1-1-100000000222200000000000000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000
χ36444444−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1−5−1+5−1+5-1-1-1-13+523−523+523−52-1-1-1-100000000-2-2-2-2000000000000000000001+521−521+521−521+521−521+521−52000000
χ374444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−51−51−51+51+51−51−51+51+5-1-1-1-1−3+52−3−52−3+52−3−5211110000000022-2-200000000000000000000−1+52−1−52−1+52−1−521−521+521−521+52000000
χ384444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−51−51−51+51+51−51−51+51+5-1-1-1-1−3+52−3−52−3+52−3−52111100000000-2-222000000000000000000001−521+521−521+52−1+52−1−52−1+52−1−52000000
χ394444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+52−3+52−3+52−3−52−3−52−3+52−3+52−3−52−3−52-1-1-1-11+51−51+51−511112222-2-2-2-20000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521+52000000000000000000
χ404444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+52−3+52−3+52−3−52−3−52−3+52−3+52−3−52−3−52-1-1-1-11+51−51+51−51111-2-2-2-2222200001−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ414444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−52−3−52−3−52−3+52−3+52−3−52−3−52−3+52−3+52-1-1-1-11−51+51−51+511112222-2-2-2-20000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521−52000000000000000000
χ424444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−52−3−52−3−52−3+52−3+52−3−52−3−52−3+52−3+52-1-1-1-11−51+51−51+51111-2-2-2-2222200001+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000000000
χ434444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+51+51+51−51−51+51+51−51−5-1-1-1-1−3−52−3+52−3−52−3+5211110000000022-2-200000000000000000000−1−52−1+52−1−52−1+521+521−521+521−52000000
χ444444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+51+51+51−51−51+51+51−51−5-1-1-1-1−3−52−3+52−3−52−3+52111100000000-2-222000000000000000000001+521−521+521−52−1−52−1+52−1−52−1+52000000
χ4544-4-44i−4i−1+53−523+52−1−5−1+53−523+52−1−51−51+5−3+52−3−52−3+52−3−521−51+5−2ζ11−2ζ19−2ζ11−2ζ19−2ζ3−2ζ7−2ζ3−2ζ72ζ11+2ζ192ζ11+2ζ192ζ3+2ζ72ζ3+2ζ7-1-111ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−i−iii000000002-22i−2i00000000000000000000−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000
χ4644-4-44i−4i−1+53−523+52−1−5−1+53−523+52−1−51−51+5−3+52−3−52−3+52−3−521−51+5−2ζ11−2ζ19−2ζ11−2ζ19−2ζ3−2ζ7−2ζ3−2ζ72ζ11+2ζ192ζ11+2ζ192ζ3+2ζ72ζ3+2ζ7-1-111ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−i−iii00000000-22−2i2i000000000000000000001−521+52−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000
χ4744-4-44i−4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+52−3−521+51−51+51−5−3+52−3−52ζ3+ζ7+2ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ3−2ζ7−ζ11−ζ19-1-111−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−i−iii22-2-22i2i−2i−2i0000−1+52−1−52−1+52−1−521−521+521−521+52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ4844-4-44i−4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+52−3−521+51−51+51−5−3+52−3−52ζ3+ζ7+2ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ3−2ζ7−ζ11−ζ19-1-111−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−i−iii-2-222−2i−2i2i2i00001−521+521−521+52−1+52−1−52−1+52−1−52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ4944-4-44i−4i3+52−1+5−1−53−523+52−1+5−1−53−52−3−52−3+521−51+51−51+5−3−52−3+522ζ3+2ζ7+ζ11+ζ192ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19-1-111−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7−i−iii22-2-22i2i−2i−2i0000−1−52−1+52−1−52−1+521+521−521+521−52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ5044-4-44i−4i3+52−1+5−1−53−523+52−1+5−1−53−52−3−52−3+521−51+51−51+5−3−52−3+522ζ3+2ζ7+ζ11+ζ192ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19-1-111−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7−i−iii-2-222−2i−2i2i2i00001+521−521+521−52−1−52−1+52−1−52−1+52ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ5144-4-44i−4i−1−53+523−52−1+5−1−53+523−52−1+51+51−5−3−52−3+52−3−52−3+521+51−5−2ζ3−2ζ7−2ζ3−2ζ7−2ζ11−2ζ19−2ζ11−2ζ192ζ3+2ζ72ζ3+2ζ72ζ11+2ζ192ζ11+2ζ19-1-1112ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−i−iii000000002-22i−2i00000000000000000000−1−52−1+521+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000
χ5244-4-44i−4i−1−53+523−52−1+5−1−53+523−52−1+51+51−5−3−52−3+52−3−52−3+521+51−5−2ζ3−2ζ7−2ζ3−2ζ7−2ζ11−2ζ19−2ζ11−2ζ192ζ3+2ζ72ζ3+2ζ72ζ11+2ζ192ζ11+2ζ19-1-1112ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−i−iii00000000-22−2i2i000000000000000000001+521−52−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000
χ5344-4-4−4i4i−1+53−523+52−1−5−1+53−523+52−1−51−51+5−3+52−3−52−3+52−3−521−51+52ζ11+2ζ192ζ11+2ζ192ζ3+2ζ72ζ3+2ζ7−2ζ11−2ζ19−2ζ11−2ζ19−2ζ3−2ζ7−2ζ3−2ζ7-1-111−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19ii−i−i000000002-2−2i2i00000000000000000000−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000
χ5444-4-4−4i4i−1+53−523+52−1−5−1+53−523+52−1−51−51+5−3+52−3−52−3+52−3−521−51+52ζ11+2ζ192ζ11+2ζ192ζ3+2ζ72ζ3+2ζ7−2ζ11−2ζ19−2ζ11−2ζ19−2ζ3−2ζ7−2ζ3−2ζ7-1-111−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19ii−i−i00000000-222i−2i000000000000000000001−521+52−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000
χ5544-4-4−4i4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+52−3−521+51−51+51−5−3+52−3−52−ζ3−ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ192ζ3+2ζ7+ζ11+ζ19-1-1112ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19ii−i−i22-2-2−2i−2i2i2i0000−1+52−1−52−1+52−1−521−521+521−521+52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ5644-4-4−4i4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+52−3−521+51−51+51−5−3+52−3−52−ζ3−ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ192ζ3+2ζ7+ζ11+ζ19-1-1112ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19ii−i−i-2-2222i2i−2i−2i00001−521+521−521+52−1+52−1−52−1+52−1−52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
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χ888-8-8800−2−253+53−5−2+252+25−3−5−3+52−252+252−253+53−5−3−5−3+5−2−25−2+2500000000-222-2000000000000000000000000000000000000000000000000000000

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