Finite Group Databasebeta

← Group #13022890

Character table — Group #13022890

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12224444224444445101010101010102020202020202020444420202020202020202020202020202020202020202020202022224444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ9111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ10111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii
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χ13111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ14111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
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χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144-4-4-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000000000
χ48444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4441111111111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ774-4-44−4i4i4i−4i00002−2i−2+2i2+2i−2−2i-15−511-15−5i−i−ii−i5i5−i5i50000ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ3−ζ6+ζ7−ζ14−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ2−ζ11+ζ18−ζ19−ζ2−ζ11−ζ18−ζ19ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14ζ3+ζ6+ζ7+ζ14−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ19−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ14−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ19−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ1400000000000000000000000000000000
χ784-4-44−4i4i4i−4i00002−2i−2+2i2+2i−2−2i-1−5511-1−55i−i−iii5−i5i5−i50000ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ11−ζ18+ζ19ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ3+ζ6−ζ7+ζ14−ζ3−ζ6−ζ7−ζ14ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19ζ2+ζ11+ζ18+ζ19ζ3−ζ6−ζ7+ζ14−ζ3+ζ6+ζ7−ζ14−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ19−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ14ζ2+ζ11−ζ18−ζ19−ζ2−ζ11+ζ18+ζ1900000000000000000000000000000000
χ794-4-44−4i4i4i−4i00002−2i−2+2i2+2i−2−2i-1−5511-1−55i−i−iii5−i5i5−i50000−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ11−ζ18+ζ19ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ3+ζ6−ζ7+ζ14−ζ3−ζ6−ζ7−ζ14ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19ζ2+ζ11+ζ18+ζ19−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ14ζ2−ζ11−ζ18+ζ19−ζ2+ζ11+ζ18−ζ19ζ3+ζ6−ζ7−ζ14−ζ3−ζ6+ζ7+ζ14−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ1900000000000000000000000000000000
χ804-4-44−4i4i4i−4i0000−2+2i2−2i−2−2i2+2i400-4-4400−4i4i4i−4i0000000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000000000000000000000000000
χ814-4-44−4i4i4i−4i0000−2+2i2−2i−2−2i2+2i-15−511-15−5i−i−ii−i5i5−i5i50000−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ3+ζ6−ζ7+ζ14ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ2+ζ11−ζ18+ζ19ζ2+ζ11+ζ18+ζ19−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14−ζ3−ζ6−ζ7−ζ14−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ19−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ14−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ19−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ1400000000000000000000000000000000
χ824-4-44−4i4i4i−4i0000−2+2i2−2i−2−2i2+2i-15−511-15−5i−i−ii−i5i5−i5i50000ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ3+ζ6−ζ7+ζ14ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ2+ζ11−ζ18+ζ19ζ2+ζ11+ζ18+ζ19−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14−ζ3−ζ6−ζ7−ζ14ζ2−ζ11−ζ18+ζ19−ζ2+ζ11+ζ18−ζ19ζ3−ζ6−ζ7+ζ14−ζ3+ζ6+ζ7−ζ14ζ2+ζ11−ζ18−ζ19−ζ2−ζ11+ζ18+ζ19ζ3+ζ6−ζ7−ζ14−ζ3−ζ6+ζ7+ζ1400000000000000000000000000000000
χ834-4-44−4i4i4i−4i0000−2+2i2−2i−2−2i2+2i-1−5511-1−55i−i−iii5−i5i5−i50000ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ11+ζ18−ζ19−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ3−ζ6+ζ7−ζ14ζ3+ζ6+ζ7+ζ14−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19−ζ2−ζ11−ζ18−ζ19−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ14ζ2−ζ11−ζ18+ζ19−ζ2+ζ11+ζ18−ζ19ζ3+ζ6−ζ7−ζ14−ζ3−ζ6+ζ7+ζ14−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ1900000000000000000000000000000000
χ844-4-44−4i4i4i−4i0000−2+2i2−2i−2−2i2+2i-1−5511-1−55i−i−iii5−i5i5−i50000−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ11+ζ18−ζ19−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ3−ζ6+ζ7−ζ14ζ3+ζ6+ζ7+ζ14−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19−ζ2−ζ11−ζ18−ζ19ζ3−ζ6−ζ7+ζ14−ζ3+ζ6+ζ7−ζ14−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ19−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ14ζ2+ζ11−ζ18−ζ19−ζ2−ζ11+ζ18+ζ1900000000000000000000000000000000
χ8588-8-888-8-88-88-80000-2-2-2-22222-2-222-2-222000000000000000000000000000000000000000000000000000000000000
χ8688-8-888-8-8-88-880000-222-222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-8-8888-8-880000-2-2-2-2222222-2-222-2-2000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-8-888-888-80000-222-222-2-222-2-2-2-222000000000000000000000000000000000000000000000000000000000000
χ898-88-88i−8i8i−8i00000000-225−252-22−2525−2i2i−2i2i2i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ908-88-88i−8i8i−8i00000000-2−25252-2225−25−2i2i−2i2i−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ918-88-8−8i8i−8i8i00000000-225−252-22−25252i−2i2i−2i−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ928-88-8−8i8i−8i8i00000000-2−25252-2225−252i−2i2i−2i2i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000000000

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