Finite Group Databasebeta

← Group #13017364

Character table — Group #13017364

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222244444444444444445555555588888888888888101010101010101010101010161616161616161620202020202020202020202020202020202020202020202020202020404040404040
order12222222444444445888810101010101010444444444420202020404040404040404044448888888820202020202020204444888888888888888888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1−i−iii
χ511111111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ711111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i−i−i−i−iiiii11−i−iii
χ811111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iii−i−i−i−iiiiiiiii−i−i−i−i11ii−i−i
χ9111111111111-1-1-1-111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ10111111111111-1-1-1-111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i11−i−iii
χ12111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii11ii−i−i
χ13111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ14111111111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ15111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1111111111111ii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1ii−i−i
χ16111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1111111111111−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-1−i−iii
χ171-1-11-111-1-1-111ii−i−i111-1-111-1-1-11-111-1-1-1-111i−i1-1-111111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−i11-1-1i−ii−i11-1-111-1-1ii−i−iii−i−ii−i1-11-1
χ181-1-11-111-1-1-111ii−i−i111-1-111-1-1-11-111-1-1-1-111i−i1-1-111111-1-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−i11-1-1−ii−ii-1-111-1-111−i−iii−i−iiii−i-11-11
χ191-1-11-111-1-1-111ii−i−i111-1-111-1-1-11-1-1-11111-1-1i−i1-1-111111-1-1-1-1-1-11111-1-1-1-111ii−i−iii−i−i−i−iii-1-1111-1-11−i−iiiii−i−i11-1-1-1-111−ii−iii−i
χ201-1-11-111-1-1-111ii−i−i111-1-111-1-1-11-1-1-11111-1-1i−i1-1-111111-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i−i−iii-1-111-111-1ii−i−i−i−iii-1-11111-1-1−iii−i−ii
χ211-1-11-111-1-1-111ii−i−i1-1-11111-1-1-11-111-1-1-1-111−ii1-1-11-1-1-1-1111111-1-1ii−i−iii−i−iii−i−i−i−iiiii−i−i-1-111i−ii−i11-1-111-1-1−i−iii−i−iii−ii-11-11
χ221-1-11-111-1-1-111ii−i−i1-1-11111-1-1-11-111-1-1-1-111−ii1-1-11-1-1-1-1111111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-111−ii−ii-1-111-1-111ii−i−iii−i−i−ii1-11-1
χ231-1-11-111-1-1-111ii−i−i1-1-11111-1-1-11-1-1-11111-1-1−ii1-1-11-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iii−i−iii11-1-11-1-11−i−iiiii−i−i-1-11111-1-1i−ii−i−ii
χ241-1-11-111-1-1-111ii−i−i1-1-11111-1-1-11-1-1-11111-1-1−ii1-1-11-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iii11-1-1-111-1ii−i−i−i−iii11-1-1-1-111i−i−iii−i
χ251-1-11-111-1-1-111−i−iii111-1-111-1-1-11-111-1-1-1-111−ii1-1-111111-1-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii11-1-1i−ii−i-1-111-1-111ii−i−iii−i−i−ii-11-11
χ261-1-11-111-1-1-111−i−iii111-1-111-1-1-11-111-1-1-1-111−ii1-1-111111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii11-1-1−ii−ii11-1-111-1-1−i−iii−i−iii−ii1-11-1
χ271-1-11-111-1-1-111−i−iii111-1-111-1-1-11-1-1-11111-1-1−ii1-1-111111-1-1-1-1-1-11111-1-1-1-111−i−iii−i−iiiii−i−i-1-1111-1-11ii−i−i−i−iii11-1-1-1-111i−ii−i−ii
χ281-1-11-111-1-1-111−i−iii111-1-111-1-1-11-1-1-11111-1-1−ii1-1-111111-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iiiii−i−i-1-111-111-1−i−iiiii−i−i-1-11111-1-1i−i−iii−i
χ291-1-11-111-1-1-111−i−iii1-1-11111-1-1-11-111-1-1-1-111i−i1-1-11-1-1-1-1111111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii-1-111i−ii−i-1-111-1-111−i−iii−i−iiii−i1-11-1
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χ311-1-11-111-1-1-111−i−iii1-1-11111-1-1-11-1-1-11111-1-1i−i1-1-11-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−iii−i−i11-1-11-1-11ii−i−i−i−iii-1-11111-1-1−ii−iii−i
χ321-1-11-111-1-1-111−i−iii1-1-11111-1-1-11-1-1-11111-1-1i−i1-1-11-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i11-1-1-111-1−i−iiiii−i−i11-1-1-1-111−iii−i−ii
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χ3622222222-2-2-2-20000200002222222-2-2-2-2-2-2-2-200-2-2-2-2000000002222−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i0000000000000000000000
χ37222-2-22-2-20000000022−22−22-222-2-2-22222-2-2-2-200000022−2−222−2−200002-22-22-22-20000000000002−22−20000000000002−22−22−22−2000000
χ38222-2-22-2-20000000022−22−22-222-2-2-22222-2-2-2-200000022−2−222−2−20000-22-22-22-220000000000002−22−2000000000000−22−22−22−22000000
χ39222-2-22-2-20000000022−22−22-222-2-2-2-2-2-2-2222200000022−2−222−2−200002i−2i2i−2i−2i2i−2i2i000000000000−22−22000000000000i2−i2i2−i2−i2i2−i2i2000000
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χ42222-2-22-2-2000000002−22−222-222-2-2-22222-2-2-2-2000000−2−222−2−2220000-22-22-22-22000000000000−22−220000000000002−22−22−22−2000000
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χ652-2-2-222-220000000022−2−222-2-2-22-2222-2-222-2-200000022−2−2−2−22200002i−2i−2i2i2i−2i−2i2i0000000000002−2−22000000000000i2−i2−i2i2i2−i2−i2i2000000
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χ682-2-2-222-220000000022−2−222-2-2-22-22-2-222-2-22200000022−2−2−2−2220000-222-22-2-22000000000000−222−2000000000000−222−22−2−22000000
χ692-2-2-222-22000000002−222−22-2-2-22-2222-2-222-2-2000000−2−22222−2−200002i−2i−2i2i2i−2i−2i2i000000000000−222−2000000000000−i2i2i2−i2−i2i2i2−i2000000
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χ75444444444444-4-4-4-4-14444-1-1-1-1-1-1-100000000-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111110000000000000000000000000000000000
χ76444444444444-4-4-4-4-1-4-4-4-4-1-1-1-1-1-1-10000000044-1-1-1-1111111110000000000001111-1-1-1-10000000000000000000000000000000000
χ7744-444-4-4-44-44-44-44-4-1000011-111-1-100000000001-11-15−55−55−55−5000000000000-11-115−55−50000000000000000000000000000000000
χ7844-444-4-4-44-44-44-44-4-1000011-111-1-100000000001-11-1−55−55−55−55000000000000-11-11−55−550000000000000000000000000000000000
χ7944-444-4-4-44-44-4-44-44-1000011-111-1-100000000001-11-15−55−55−55−50000000000001-11-1−55−550000000000000000000000000000000000
χ8044-444-4-4-44-44-4-44-44-1000011-111-1-100000000001-11-1−55−55−55−550000000000001-11-15−55−50000000000000000000000000000000000
χ8144-4-4-4-4440000000040000-444-44-4-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-4-4440000000040000-444-44-4-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ834-444-4-4-44-444-44i−4i−4i4i-10000111-1-1-11000000000011-1-15−55−5−55−55000000000000−iii−ii5−i5−i5i50000000000000000000000000000000000
χ844-444-4-4-44-444-44i−4i−4i4i-10000111-1-1-11000000000011-1-1−55−555−55−5000000000000−iii−i−i5i5i5−i50000000000000000000000000000000000
χ854-444-4-4-44-444-4−4i4i4i−4i-10000111-1-1-11000000000011-1-15−55−5−55−55000000000000i−i−ii−i5i5i5−i50000000000000000000000000000000000
χ864-444-4-4-44-444-4−4i4i4i−4i-10000111-1-1-11000000000011-1-1−55−555−55−5000000000000i−i−iii5−i5−i5i50000000000000000000000000000000000
χ874-44-44-44-40000000040000-44-44-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ884-44-44-44-40000000040000-44-44-4-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ894-4-44-444-4-4-4444i4i−4i−4i-144-4-4-1-1111-11000000004i−4i-111-1-1-1-1-11111000000000000−i−iii−i−iii0000000000000000000000000000000000
χ904-4-44-444-4-4-4444i4i−4i−4i-1-4-444-1-1111-1100000000−4i4i-111-11111-1-1-1-1000000000000−i−iiiii−i−i0000000000000000000000000000000000
χ914-4-44-444-4-4-444−4i−4i4i4i-144-4-4-1-1111-1100000000−4i4i-111-1-1-1-1-11111000000000000ii−i−iii−i−i0000000000000000000000000000000000
χ924-4-44-444-4-4-444−4i−4i4i4i-1-4-444-1-1111-11000000004i−4i-111-11111-1-1-1-1000000000000ii−i−i−i−iii0000000000000000000000000000000000
χ9388888888-8-8-8-80000-20000-2-2-2-2-2-2-20000000000222200000000000000000000000000000000000000000000000000000000000000
χ94888-8-88-8-800000000-242−4242−42-22-2-222200000000000000−2−222−2−222000000000000000000000000000000000000000000000000000000
χ95888-8-88-8-800000000-2−4242−4242-22-2-22220000000000000022−2−222−2−2000000000000000000000000000000000000000000000000000000
χ9688-888-8-8-8-88-880000-2000022-222-2-20000000000-22-2200000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-8-88800000000-200002-2-22-2220000000000000010−10−101010−10−1010000000000000000000000000000000000000000000000000000000
χ9888-8-8-8-88800000000-200002-2-22-22200000000000000−101010−10−101010−10000000000000000000000000000000000000000000000000000000
χ998-888-8-8-888-8-880000-20000222-2-2-220000000000-2-22200000000000000000000000000000000000000000000000000000000000000
χ1008-88-88-88-800000000-200002-22-222-20000000000000010−10−1010−101010−10000000000000000000000000000000000000000000000000000000
χ1018-88-88-88-800000000-200002-22-222-200000000000000−101010−1010−10−1010000000000000000000000000000000000000000000000000000000
χ1028-8-88-888-888-8-80000-20000-2-2222-2200000000002-2-2200000000000000000000000000000000000000000000000000000000000000
χ1038-8-8-888-8800000000-242−42−4242-2222-22-200000000000000−2−22222−2−2000000000000000000000000000000000000000000000000000000
χ1048-8-8-888-8800000000-2−424242−42-2222-22-20000000000000022−2−2−2−222000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.