Finite Group Databasebeta

← Group #12137607

Character table — Group #12137607

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222222222222444444444444444444888888888888888888888888888888888888888161616161616161616161616161620202020404040404040404040408080
order1222244445510101010101022444410101010202020202020202024444881010101010101010202020202020202020202020202020202020202020202020482020202040404040404040402244244488888848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-11111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ6111111111111111111111-1-11111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ911111111111111111-1-1-1-11111111111111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11-1
χ1011111111111111111-1-1-1-11111111111111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-11
χ1111111111111111111-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ1211111111111111111-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ1311111111111111111-1-1-1-1-1-111111111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-11111-1-1-1-11111-1-1-11
χ1411111111111111111-1-1-1-1-1-111111111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1
χ1511111111111111111-1-1-1-1-1-1111111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-111-1-1111-1
χ1611111111111111111-1-1-1-1-1-1111111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-111-1-1-11
χ17222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222222−1+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+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ18222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ19222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+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+52-2-21−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ20222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ21222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-22-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ22222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2222-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ23222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+522-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ24222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222-2221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ25222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ26222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ27222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-2-21+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ28222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ29222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-22-2-21+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+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ30222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2222-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ31222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2-2221+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+521−521−521−521−521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ32222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222-2221+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ33222-2-222-2-22222222222-2-200-2-2-2-22-22-22-22-2000000022220000-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i000000
χ34222-2-222-2-22222222222-2-200-2-2-2-22-22-22-22-2000000022220000-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i000000
χ35222-2-222-2-222222222-2-22200-2-2-2-22-22-22-22-20000000-2-2-2-20000222200000000000000000000000000000000000000002i−2i−2i2i000000
χ36222-2-222-2-222222222-2-22200-2-2-2-22-22-22-22-20000000-2-2-2-2000022220000000000000000000000000000000000000000−2i2i2i−2i000000
χ37222-2-2-2-22222222222000000-2-2-2-2-22-22-22-222-200000000022220000-2-2-2-20000000000000000000000000000002-22-20000002-20000
χ38222-2-2-2-22222222222000000-2-2-2-2-22-22-22-222-200000000022220000-2-2-2-2000000000000000000000000000000-22-22000000-220000
χ39222-2-2-2-22222222222000000-2-2-2-2-22-22-22-22-22000000000-2-2-2-2000022220000000000000000000000000000002-22-2000000-220000
χ40222-2-2-2-22222222222000000-2-2-2-2-22-22-22-22-22000000000-2-2-2-200002222000000000000000000000000000000-22-220000002-20000
χ4122-22-2-22-2222-2-2-2-2222-22-20022-2-2-22-222-22-200000002-22-200002-22-200000000000000000000000000000000002-2-222-20000000000
χ4222-22-2-22-2222-2-2-2-2222-22-20022-2-2-22-222-22-200000002-22-200002-22-20000000000000000000000000000000000-222-2-220000000000
χ4322-22-2-22-2222-2-2-2-222-22-220022-2-2-22-222-22-20000000-22-220000-22-2200000000000000000000000000000000002-2-22-220000000000
χ4422-22-2-22-2222-2-2-2-222-22-220022-2-2-22-222-22-20000000-22-220000-22-220000000000000000000000000000000000-222-22-20000000000
χ4522-2-222-2-2222-2-2-2-222000000-2-2222222-2-2-2-2002-2000000000000000000022-2-222-2-2000000000000000000000022-2-2000000002-200
χ4622-2-222-2-2222-2-2-2-222000000-2-2222222-2-2-2-2002-2000000000000000000022-2-222-2-20000000000000000000000-2-22200000000-2200
χ4722-2-222-2-2222-2-2-2-222000000-2-2222222-2-2-2-200-220000000000000000000-2-222-2-222000000000000000000000022-2-200000000-2200
χ4822-2-222-2-2222-2-2-2-222000000-2-2222222-2-2-2-200-220000000000000000000-2-222-2-2220000000000000000000000-2-222000000002-200
χ4922-2-22-222-222-2-2-2-2222-2-2222-2-222-2-2-2-222220000-22-22-22-20000-22-2200000000000022-2-222-2-20000002-22-200000000000000000000
χ5022-2-22-222-222-2-2-2-2222-2-22-2-2-2-222-2-2-2-2222200002-222-22-20000-22-22000000000000-2-222-2-222000000-22-2200000000000000000000
χ5122-2-22-222-222-2-2-2-222-222-222-2-222-2-2-2-222220000-2-22-22-2200002-22-200000000000022-2-222-2-2000000-22-2200000000000000000000
χ5222-2-22-222-222-2-2-2-222-222-2-2-2-2-222-2-2-2-22222000022-2-22-2200002-22-2000000000000-2-222-2-2220000002-22-200000000000000000000
χ5322-2-22-222-2−1+52−1−521−521−521+521+52−1+52−1−522-2-22221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000-22-2−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−1+52−1+521−521−52−1−52−1−521+521+5200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000000000
χ5422-2-22-222-2−1+52−1−521−521−521+521+52−1+52−1−522-2-22221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000-22-2−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18−1+52−1+521−521−52−1−52−1−521+521+5200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.