Finite Group Databasebeta

← Group #13018191

Character table — Group #13018191

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222444444445101010101010102020202020202020444420202020202020202020202020202020202020202020202044444444444422448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ511111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-2000000000000000022-2-222-2-222-2-200000000000000000000
χ18222222222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-20000000000000000-2-222-2-222-2-22200000000000000000000
χ1922222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-22222000000000000000022-2-222-2-2-2-22200000000000000000000
χ2022222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-222220000000000000000-2-222-2-22222-2-200000000000000000000
χ2122-222-2-2-200002-200222-2-2-22-200000000002i−2i22-2-20000000000002i2i2i2i−2i−2i−2i−2i22-2-2-2-2220000002i−2i0000000000000000
χ2222-222-2-2-200002-200222-2-2-22-200000000002i−2i22-2-20000000000002i2i2i2i−2i−2i−2i−2i-2-22222-2-2000000−2i2i0000000000000000
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χ2422-222-2-2-200002-200222-2-2-22-20000000000−2i2i22-2-2000000000000−2i−2i−2i−2i2i2i2i2i-2-22222-2-20000002i−2i0000000000000000
χ2522-222-2-2-20000-2200222-2-2-22-2000000002-200-2-22200002222-2-2-2-2000000002222-2-2-2-200002-2000000000000000000
χ2622-222-2-2-20000-2200222-2-2-22-2000000002-200-2-22200002222-2-2-2-200000000-2-2-2-222220000-22000000000000000000
χ2722-222-2-2-20000-2200222-2-2-22-200000000-2200-2-2220000-2-2-2-22222000000002222-2-2-2-20000-22000000000000000000
χ2822-222-2-2-20000-2200222-2-2-22-200000000-2200-2-2220000-2-2-2-2222200000000-2-2-2-2222200002-2000000000000000000
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χ342-2-22-22-22-2-222000022-22-22-2-2-2-2-2-222220000000000000000000000000000002i−2i002i−2i00−2i2i0000−1−i1+i1+i−1−i0000−1+i1−i1−i−1+i0000
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χ432-2-2-22-222-22-2200002-22-222-2-2-2-222-2-2220000000000000000000000000000−2i2i00−2i2i002i−2i00000000001+i−1−i−1−i1+i00001−i−1+i−1+i1−i
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χ454444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ464444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000000000
χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111111155−5−555−5−555−5−555−5−500000000000000000000000000000000
χ48444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111−5−555−5−555−5−555−5−55500000000000000000000000000000000
χ4944444444-4-4-4-444-4-4-1-1-1-1-1-1-1-11111111144-4-4-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
χ5044444444-4-4-4-444-4-4-1-1-1-1-1-1-1-111111111-4-444-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5144444444-4-4-4-4-4-444-1-1-1-1-1-1-1-11111111100001111-1-1-1-155−5−555−5−5−5−555−5−55500000000000000000000000000000000
χ5244444444-4-4-4-4-4-444-1-1-1-1-1-1-1-11111111100001111-1-1-1-1−5−555−5−55555−5−555−5−500000000000000000000000000000000
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χ55444-4-4-4-444-4-440000-11111-1-1-1-1-11111-1-100005−55−555−5−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000000000000000000000000
χ56444-4-4-4-444-4-440000-11111-1-1-1-1-11111-1-10000−55−55−5−555−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ1800000000000000000000000000000000
χ57444-4-4-4-444-4-440000-11111-1-1-1-1-11111-1-10000−55−55−5−555ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ1800000000000000000000000000000000
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χ59444-4-4-4-44-444-40000-11111-1-1-111-1-1-1-11100005−55−5−5−555−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ1800000000000000000000000000000000
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χ7544-4-4-444-40000004i−4i-111-1-11-11−i5i5i5−i5i5−i5−i5i50000−555−5−iii−iζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ1900000000000000000000000000000000
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χ7744-4-4-444-4000000−4i4i-111-1-11-11i5−i5−i5i5−i5i5i5−i50000−555−5i−i−ii−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ1900000000000000000000000000000000
χ7844-4-4-444-4000000−4i4i-111-1-11-11i5−i5−i5i5−i5i5i5−i50000−555−5i−i−iiζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ1900000000000000000000000000000000
χ7944-4-4-444-4000000−4i4i-111-1-11-11−i5i5i5−i5i5−i5−i5i500005−5−55i−i−ii−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ1900000000000000000000000000000000
χ8044-4-4-444-4000000−4i4i-111-1-11-11−i5i5i5−i5i5−i5−i5i500005−5−55i−i−iiζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ1900000000000000000000000000000000
χ814-444-4-44-40000000044-4-44-4-44000000000000000000000000000000000000004i−4i00−4i4i000000000000000000000000
χ824-444-4-44-40000000044-4-44-4-4400000000000000000000000000000000000000−4i4i004i−4i000000000000000000000000
χ834-44-444-4-4000000004-444-4-4-440000000000000000000000000000000000004i−4i00−4i4i00000000000000000000000000
χ844-44-444-4-4000000004-444-4-4-44000000000000000000000000000000000000−4i4i004i−4i00000000000000000000000000
χ858-888-8-88-800000000-2-222-222-22i5−2i52i5−2i5−2i52i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ868-888-8-88-800000000-2-222-222-2−2i52i5−2i52i52i5−2i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ878-88-888-8-800000000-22-2-2222-22i5−2i5−2i52i52i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ888-88-888-8-800000000-22-2-2222-2−2i52i52i5−2i5−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ898-8-88-88-8888-8-80000-2-22-22-222-2-2-2-22222000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-8-8880000-2-22-22-2222222-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ918-8-8-88-8888-88-80000-22-22-2-222-2-222-2-222000000000000000000000000000000000000000000000000000000000000
χ928-8-8-88-888-88-880000-22-22-2-22222-2-222-2-2000000000000000000000000000000000000000000000000000000000000

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