Finite Group Databasebeta

← Group #13017096

Character table — Group #13017096

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222444444445101010101010102020202020202020444420202020202020202020202020202020202020202020202044444444444444448888888888888888
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
χ171-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ181-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−i1-1i−i-11−ii-11−ii-11−ii-11−ii
χ191-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii-11−iii−i-11i−i-11−ii1-1−ii1-1
χ201-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii-11−ii−ii1-1−ii1-1i−i-11i−i-11
χ211-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1ii−i−i-11−ii1-1i−i-11−ii1-1i−i-11−ii
χ221-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1ii−i−i-11−ii-11−ii1-1i−i-11−ii1-1i−i
χ231-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−i−iii1-1i−ii−i-11−ii1-1−ii1-1i−i-11
χ241-111-1-11-1ii−i−i1-1i−i111-1-1-11-1iiii−i−i−i−i-11−ii11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−i−iii1-1i−i−ii1-1i−i-11i−i-11−ii1-1
χ251-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii1-1−ii
χ261-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii1-1−ii-11i−i-11i−i-11i−i-11i−i
χ271-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−i-11i−ii−i1-1i−i1-1−ii-11−ii-11
χ281-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−i-11i−i−ii-11−ii-11i−i1-1i−i1-1
χ291-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−i−iii-11i−i1-1−ii-11i−i1-1−ii-11i−i
χ301-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−i−iii-11i−i-11i−i1-1−ii-11i−i1-1−ii
χ311-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-111-1-111ii−i−i1-1−iii−i1-1−ii-11−ii-11i−i1-1
χ321-111-1-11-1−i−iii1-1−ii111-1-1-11-1−i−i−i−iiiii-11i−i11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-111-1-111ii−i−i1-1−ii−ii-11i−i1-1i−i1-1−ii-11
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χ43444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111111155−5−555−5−555−5−555−5−500000000000000000000000000000000
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χ5644-4-4-4-4444-44-40000-11111-1-1-1-1-111-1-1110000−55−55−55−55−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
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χ774-4-4-4444-44i−4i−4i4i0000-111-1-11-11−i−iiiii−i−i00005−5−55i5−i5−i5i5ζ2−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−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ1900000000000000000000000000000000
χ784-4-4-4444-44i−4i−4i4i0000-111-1-11-11−i−iiiii−i−i0000−555−5−i5i5i5−i5−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−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ1900000000000000000000000000000000
χ794-4-4-4444-44i−4i−4i4i0000-111-1-11-11−i−iiiii−i−i0000−555−5−i5i5i5−i5ζ2+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+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ1900000000000000000000000000000000
χ804-4-4-4444-4−4i4i4i−4i00004-4-444-44-4−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4444-4−4i4i4i−4i0000-111-1-11-11ii−i−i−i−iii00005−5−55−i5i5i5−i5−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−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ1900000000000000000000000000000000
χ824-4-4-4444-4−4i4i4i−4i0000-111-1-11-11ii−i−i−i−iii00005−5−55−i5i5i5−i5ζ2−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+ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ1900000000000000000000000000000000
χ834-4-4-4444-4−4i4i4i−4i0000-111-1-11-11ii−i−i−i−iii0000−555−5i5−i5−i5i5−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−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
χ844-4-4-4444-4−4i4i4i−4i0000-111-1-11-11ii−i−i−i−iii0000−555−5i5−i5−i5i5ζ2+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+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
χ85888-88-8-8-800000000-2-22-22-22225−2525−2525−2525−25000000000000000000000000000000000000000000000000000000000000
χ86888-88-8-8-800000000-2-22-22-222−2525−2525−2525−2525000000000000000000000000000000000000000000000000000000000000
χ8788-88-88-8-800000000-22-22-2-22225−25−252525−25−2525000000000000000000000000000000000000000000000000000000000000
χ8888-88-88-8-800000000-22-22-2-222−252525−25−252525−25000000000000000000000000000000000000000000000000000000000000
χ898-88-8-88-8800000000-2-222-222-22i5−2i52i5−2i5−2i52i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-8800000000-2-222-222-2−2i52i5−2i52i52i5−2i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ918-8-888-8-8800000000-22-2-2222-22i5−2i5−2i52i5−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ928-8-888-8-8800000000-22-2-2222-2−2i52i52i5−2i52i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000000000

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