Finite Group Databasebeta

← Group #13103508

Character table — Group #13103508

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size111122222222224444444455558888888888888888881010101010101010101010101010101010101010101020202020202020202020202020202020202020202525252525252525404040405050505050505050
order12442455101020202020510101020202020224455101010101010102020202020202020202488888888888810101010202020201010202040404040404040404040404040404040444444444040404044448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ31111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ51111111111111111111111-1-1-1-1111111111111111111-1-11111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111ii−i−i-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111111111111-1-11111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111−i−iii-1-1-1-1
χ71111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-1−i−iii1111
χ81111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-1ii−i−i1111
χ91111-1-1111111111-1-11-1-111111111-1-1-1-1-111-11111-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ101111-1-1111111111-1-11-1-111111111-1-1-1-1-111-11111-1-1-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ111111-1-1111111111-1-11-1-111111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ121111-1-1111111111-1-11-1-111111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ131111-1-1111111111-1-11-1-111-1-1-1-111-1-1-1-1-111-11111-1-1-1-11111-1-1ii−i−i−i−iii-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii-1-111
χ141111-1-1111111111-1-11-1-111-1-1-1-111-1-1-1-1-111-11111-1-1-1-11111-1-1−i−iiiii−i−i-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111
χ151111-1-1111111111-1-11-1-111-1-1-1-111-1-1-1-1-111-11111-1-1-1-111-1-111ii−i−i−i−iii-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i11-1-1
χ161111-1-1111111111-1-11-1-111-1-1-1-111-1-1-1-1-111-11111-1-1-1-111-1-111−i−iiiii−i−i-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii11-1-1
χ1711-1-11-11111-1-1-1-11111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-11-1i−ii−ii−ii−ii−ii−i1111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1i−ii−i1-11-1i−ii−i
χ1811-1-11-11111-1-1-1-11111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-11-1i−ii−i−ii−ii−ii−ii1111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-111-1-111i−ii−i-11-11i−ii−i
χ1911-1-11-11111-1-1-1-11111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-11-1−ii−iii−ii−ii−ii−i1111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-111−ii−ii-11-11−ii−ii
χ2011-1-11-11111-1-1-1-11111-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-11-1−ii−ii−ii−ii−ii−ii1111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−ii−ii1-11-1−ii−ii
χ2111-1-11-11111-1-1-1-11111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11i−ii−i1-11-1-11-11-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111−i−iiiii−i−ii−ii−i−iii−i−ii−ii
χ2211-1-11-11111-1-1-1-11111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11i−ii−i-11-111-11-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1ii−i−i−i−iiii−ii−ii−i−ii−ii−ii
χ2311-1-11-11111-1-1-1-11111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11−ii−ii1-11-1-11-11-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111ii−i−i−i−iii−ii−iii−i−iii−ii−i
χ2411-1-11-11111-1-1-1-11111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11−ii−ii-11-111-11-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1−i−iiiii−i−i−ii−ii−iii−ii−ii−i
χ2511-1-1-111111-1-1-1-11-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-11111-11i−i−iii−i−iii−i−ii1111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-111-1-1i−i−ii-11-11i−i−ii
χ2611-1-1-111111-1-1-1-11-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-11111-11i−i−ii−iii−i−iii−i1111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111i−i−ii1-11-1i−i−ii
χ2711-1-1-111111-1-1-1-11-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-11111-11−iii−ii−i−iii−i−ii1111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-111-1-111−iii−i1-11-1−iii−i
χ2811-1-1-111111-1-1-1-11-1-1111-1-111-1-111-1-1-1-1-1111-1-1-1-11111-11−iii−i−iii−i−iii−i1111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-111-1-1−iii−i-11-11−iii−i
χ2911-1-1-111111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-111111-1i−i−ii1-1-11-111-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−ii−i−iii−i−ii−iii−i
χ3011-1-1-111111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-111111-1i−i−ii-111-11-1-11-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iiii−i−ii−iii−i−iii−i
χ3111-1-1-111111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-111111-1−iii−i1-1-11-111-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iii−iii−i−iii−ii−i−ii
χ3211-1-1-111111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-111111-1−iii−i-111-11-1-11-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−i−iii−ii−i−iii−i−ii
χ33222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−52222222−1+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+52−1−52−1−5222000022222222−1+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+52−1−5200000000000000000000
χ34222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−52222222−1+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+52−1−52−1−52220000-2-2-2-2-2-2-2-2−1+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+5200000000000000000000
χ35222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−5222-2-2-2-2−1+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+52−1−52−1−52-2-200002i2i2i2i−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+ζ700000000000000000000
χ36222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522−1+52−1−522−1+52−1−5222-2-2-2-2−1+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+52−1−52−1−52-2-20000−2i−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−ζ700000000000000000000
χ37222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+52222222−1−52−1+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+5222000022222222−1−52−1−52−1+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+5200000000000000000000
χ38222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+52222222−1−52−1+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+52220000-2-2-2-2-2-2-2-2−1−52−1−52−1+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+521−5200000000000000000000
χ39222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+5222-2-2-2-2−1−52−1+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+52-2-200002i2i2i2i−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+ζ1900000000000000000000
χ40222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522−1−52−1+522−1−52−1+5222-2-2-2-2−1−52−1+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+52-2-20000−2i−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−ζ1900000000000000000000
χ412222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5221−521+5221−521+52222222−1+52−1−52-21−521−521+521+52−1+52−1−52-2−1+52−1+52−1−52−1−521−521−521+521+52-2-2000022-2-222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+5200000000000000000000
χ422222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5221−521+5221−521+52222222−1+52−1−52-21−521−521+521+52−1+52−1−52-2−1+52−1+52−1−52−1−521−521−521+521+52-2-20000-2-222-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−5200000000000000000000
χ432222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5221−521+5221−521+5222-2-2-2-2−1+52−1−52-21−521−521+521+52−1+52−1−52-2−1+52−1+52−1−52−1−521−521−521+521+522200002i2i−2i−2i−2i−2i2i2i1−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ700000000000000000000
χ442222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5221−521+5221−521+5222-2-2-2-2−1+52−1−52-21−521−521+521+52−1+52−1−52-2−1+52−1+52−1−52−1−521−521−521+521+52220000−2i−2i2i2i2i2i−2i−2i1−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ700000000000000000000
χ452222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5221+521−5221+521−52222222−1−52−1+52-21+521+521−521−52−1−52−1+52-2−1−52−1−52−1+52−1+521+521+521−521−52-2-2000022-2-222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−5200000000000000000000
χ462222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5221+521−5221+521−52222222−1−52−1+52-21+521+521−521−52−1−52−1+52-2−1−52−1−52−1+52−1+521+521+521−521−52-2-20000-2-222-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+5200000000000000000000
χ472222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5221+521−5221+521−5222-2-2-2-2−1−52−1+52-21+521+521−521−52−1−52−1+52-2−1−52−1−52−1+52−1+521+521+521−521−522200002i2i−2i−2i−2i−2i2i2i1+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ1900000000000000000000
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χ1038-8−8i8i00−2+25−2−252−252+254ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ7-2002002i−2i00001−521+520−2ζ2−ζ6+ζ14+2ζ182ζ2+ζ6−ζ14−2ζ18−ζ2+2ζ6−2ζ14+ζ18ζ2−2ζ6+2ζ14−ζ18−1+52−1−520−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−2ζ3+2ζ7+ζ11−ζ192ζ3−2ζ7−ζ11+ζ19ζ3−ζ7+2ζ11−2ζ19−ζ3+ζ7−2ζ11+2ζ1900000000000000000000000000000000000000000000000000000000000000
χ1048-8−8i8i00−2+25−2−252−252+254ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ7-2002002i−2i00001−521+5202ζ2+ζ6−ζ14−2ζ18−2ζ2−ζ6+ζ14+2ζ18ζ2−2ζ6+2ζ14−ζ18−ζ2+2ζ6−2ζ14+ζ18−1+52−1−520−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ72ζ3−2ζ7−ζ11+ζ19−2ζ3+2ζ7+ζ11−ζ19−ζ3+ζ7−2ζ11+2ζ19ζ3−ζ7+2ζ11−2ζ1900000000000000000000000000000000000000000000000000000000000000
χ1058-8−8i8i00−2−25−2+252+252−254ζ3+4ζ7−4ζ3−4ζ74ζ11+4ζ19−4ζ11−4ζ19-2002002i−2i00001+521−520−ζ2+2ζ6−2ζ14+ζ18ζ2−2ζ6+2ζ14−ζ182ζ2+ζ6−ζ14−2ζ18−2ζ2−ζ6+ζ14+2ζ18−1−52−1+520−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ3+ζ7−2ζ11+2ζ19ζ3−ζ7+2ζ11−2ζ19−2ζ3+2ζ7+ζ11−ζ192ζ3−2ζ7−ζ11+ζ1900000000000000000000000000000000000000000000000000000000000000
χ1068-8−8i8i00−2−25−2+252+252−254ζ3+4ζ7−4ζ3−4ζ74ζ11+4ζ19−4ζ11−4ζ19-2002002i−2i00001+521−520ζ2−2ζ6+2ζ14−ζ18−ζ2+2ζ6−2ζ14+ζ18−2ζ2−ζ6+ζ14+2ζ182ζ2+ζ6−ζ14−2ζ18−1−52−1+520−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19ζ3−ζ7+2ζ11−2ζ19−ζ3+ζ7−2ζ11+2ζ192ζ3−2ζ7−ζ11+ζ19−2ζ3+2ζ7+ζ11−ζ1900000000000000000000000000000000000000000000000000000000000000

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