Finite Group Databasebeta

← Group #13107605

Character table — Group #13107605

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size112222222222244444444558888888888888888881010101010101010101010101010101010101010101010202020202020202020202020202020202020202040404040505050505050505050505050
order12244551010202020205101010202020204455101010101010102020202020202020202222444888888881010101020202020101020204040404040404040404040404040404010102020224488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-11-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-1111111111111111111-1-111-111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111-1-1111111111111111111-1-111-111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ8111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111-1-11111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ10111-1-11111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-1-111
χ11111-1-11111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ12111-1-11111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-111-1-1
χ13111-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111-1-11-1ii−i−i−i−iii1111-1-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii1-11-1-11-11ii−i−i−i−iii
χ14111-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111-1-11-1−i−iiiii−i−i1111-1-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-11-1-11-11−i−iiiii−i−i
χ15111-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-11-1-11ii−i−i−i−iii1111-1-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-111-11-1−i−iiiii−i−i
χ16111-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-11-1-11−i−iiiii−i−i1111-1-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-111-11-1ii−i−i−i−iii
χ1711-11-1111111111-1-11-1-1-1-11111-1-1-1-1-11111111-1-1-1-11-111-1-1-11-11-11-11-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1-1-1111-11-11-11-1
χ1811-11-1111111111-1-11-1-1-1-11111-1-1-1-1-11111111-1-1-1-11-111-1-1-1-11-11-11-1111111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-11-11-11-11
χ1911-11-1111111111-1-11-1-1-1-11111-1-1-1-1-11111111-1-1-1-11-1-1-1-1111-11-11-11-111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-11-11-11-11
χ2011-11-1111111111-1-11-1-1-1-11111-1-1-1-1-11111111-1-1-1-11-1-1-1-111-11-11-11-1111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-11-11-11-11-1
χ2111-11-1111111111-1-11-1-1-1-1-1-111-1-1-1-1-11111111-1-1-1-1-11111-1-1i−ii−i−ii−ii-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1i−ii−i−ii−ii
χ2211-11-1111111111-1-11-1-1-1-1-1-111-1-1-1-1-11111111-1-1-1-1-11111-1-1−ii−iii−ii−i-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1−ii−iii−ii−i
χ2311-11-1111111111-1-11-1-1-1-1-1-111-1-1-1-1-11111111-1-1-1-1-11-1-1111i−ii−i−ii−ii-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111−ii−iii−ii−i
χ2411-11-1111111111-1-11-1-1-1-1-1-111-1-1-1-1-11111111-1-1-1-1-11-1-1111−ii−iii−ii−i-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111i−ii−i−ii−ii
χ2511-1-111111-1-1-1-11-1-1111111111-1-1-1-1-111-1-1-1-1-11111-111-1-1-111-1-111-1-11-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1111-1-11-111-11-1-111-1-11
χ2611-1-111111-1-1-1-11-1-1111111111-1-1-1-1-111-1-1-1-1-11111-111-1-1-11-111-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-11-1-11-111-1-111-1-111-1
χ2711-1-111111-1-1-1-11-1-1111111111-1-1-1-1-111-1-1-1-1-11111-11-11-11-11-1-111-1-11-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-111-11-1-11-111-1-111-1
χ2811-1-111111-1-1-1-11-1-1111111111-1-1-1-1-111-1-1-1-1-11111-11-11-11-1-111-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-111-11-1-111-1-111-1-11
χ2911-1-111111-1-1-1-11-1-111111-1-111-1-1-1-1-111-1-1-1-1-111111-11-11-11i−i−ii−iii−i1111-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11i−i−ii−iii−i
χ3011-1-111111-1-1-1-11-1-111111-1-111-1-1-1-1-111-1-1-1-1-111111-11-11-11−iii−ii−i−ii1111-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11−iii−ii−i−ii
χ3111-1-111111-1-1-1-11-1-111111-1-111-1-1-1-1-111-1-1-1-1-111111-1-1111-1i−i−ii−iii−i1111-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1-111-1−iii−ii−i−ii
χ3211-1-111111-1-1-1-11-1-111111-1-111-1-1-1-1-111-1-1-1-1-111111-1-1111-1−iii−ii−i−ii1111-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii-111-1-111-1i−i−ii−iii−i
χ3322222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−522222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52220020022222222−1+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+52−1−520000000000000000
χ3422222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−522222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522200200-2-2-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+520000000000000000
χ3522222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−5222-2-2−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-200-2002i2i2i2i−2i−2i−2i−2i1−521−521+521+521−521−521+521+521−521+521−521+52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ70000000000000000
χ3622222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−5222-2-2−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-200-200−2i−2i−2i−2i2i2i2i2i1−521−521+521+521−521−521+521+521−521+521−521+52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ70000000000000000
χ3722222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+522222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52220020022222222−1−52−1−52−1+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+520000000000000000
χ3822222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+522222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522200200-2-2-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−520000000000000000
χ3922222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+5222-2-2−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-200-2002i2i2i2i−2i−2i−2i−2i1+521+521−521−521+521+521−521−521+521−521+521−52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ190000000000000000
χ4022222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+5222-2-2−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-200-200−2i−2i−2i−2i2i2i2i2i1+521+521−521−521+521+521−521−521+521−521+521−52ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ190000000000000000
χ41222-2-2−1+52−1−52−1+52−1−521−521−521+521+522−1+52−1−5221−521+52-2-222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52-21−521−521+521+521−521−521+521+52-2-20020022-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+520000000000000000
χ42222-2-2−1+52−1−52−1+52−1−521−521−521+521+522−1+52−1−5221−521+52-2-222−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52-21−521−521+521+521−521−521+521+52-2-200200-2-222-2-2221−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−520000000000000000
χ43222-2-2−1+52−1−52−1+52−1−521−521−521+521+522−1+52−1−5221−521+52-2-2-2-2−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52-21−521−521+521+521−521−521+521+522200-2002i2i−2i−2i−2i−2i2i2i−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ70000000000000000
χ44222-2-2−1+52−1−52−1+52−1−521−521−521+521+522−1+52−1−5221−521+52-2-2-2-2−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1−52-21−521−521+521+521−521−521+521+522200-200−2i−2i2i2i2i2i−2i−2i−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ70000000000000000
χ45222-2-2−1−52−1+52−1−52−1+521+521+521−521−522−1−52−1+5221+521−52-2-222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52-21+521+521−521−521+521+521−521−52-2-20020022-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−520000000000000000
χ46222-2-2−1−52−1+52−1−52−1+521+521+521−521−522−1−52−1+5221+521−52-2-222−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52-21+521+521−521−521+521+521−521−52-2-200200-2-222-2-2221+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+520000000000000000
χ47222-2-2−1−52−1+52−1−52−1+521+521+521−521−522−1−52−1+5221+521−52-2-2-2-2−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52-21+521+521−521−521+521+521−521−522200-2002i2i−2i−2i−2i−2i2i2i−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ190000000000000000
χ48222-2-2−1−52−1+52−1−52−1+521+521+521−521−522−1−52−1+5221+521−52-2-2-2-2−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1+52-21+521+521−521−521+521+521−521−522200-200−2i−2i2i2i2i2i−2i−2i−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−52ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ190000000000000000
χ4922-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5221−521+5221−521+52-2-222−1+52−1−52-21−521−521+521+52−1+52−1−522−1+52−1+52−1−52−1−521−521−521+521+522-200-2002-22-22-22-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+520000000000000000
χ5022-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5221−521+5221−521+52-2-222−1+52−1−52-21−521−521+521+52−1+52−1−522−1+52−1+52−1−52−1−521−521−521+521+522-200-200-22-22-22-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−520000000000000000
χ5122-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5221−521+5221−521+52-2-2-2-2−1+52−1−52-21−521−521+521+52−1+52−1−522−1+52−1+52−1−52−1−521−521−521+521+52-22002002i−2i2i−2i−2i2i−2i2i1−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.