Finite Group Databasebeta

← Group #13018507

Character table — Group #13018507

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222222244445101010101010101010101010101010444420202020202020202020202020202020202020202020202044444444222244448888888888888888
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
χ9111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222-2-2-2-222-2-222222-2-2-2-2-2-2-2-222200002222-2-2-2-200000000000000002222-2-2-2-222-2-200000000000000000000
χ1822222222-2-2-2-222-2-222222-2-2-2-2-2-2-2-222200002222-2-2-2-20000000000000000-2-2-2-22222-2-22200000000000000000000
χ1922222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22220000-2-2-2-2222200000000000000002222-2-2-2-2-2-22200000000000000000000
χ2022222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22220000-2-2-2-222220000000000000000-2-2-2-2222222-2-200000000000000000000
χ21222-2-2-2-2222-2-20000222-2-22222-2-2-2-22-2-2002i−2i00000000000000002i2i2i2i−2i−2i−2i−2i22-2-222-2-20000002i−2i0000000000000000
χ22222-2-2-2-2222-2-20000222-2-22222-2-2-2-22-2-2002i−2i00000000000000002i2i2i2i−2i−2i−2i−2i-2-222-2-222000000−2i2i0000000000000000
χ23222-2-2-2-2222-2-20000222-2-22222-2-2-2-22-2-200−2i2i0000000000000000−2i−2i−2i−2i2i2i2i2i22-2-222-2-2000000−2i2i0000000000000000
χ24222-2-2-2-2222-2-20000222-2-22222-2-2-2-22-2-200−2i2i0000000000000000−2i−2i−2i−2i2i2i2i2i-2-222-2-2220000002i−2i0000000000000000
χ25222-2-2-2-22-2-2220000222-2-2-2-2-2-222222-2-22i−2i00000000002i2i2i2i−2i−2i−2i−2i0000000022-2-2-2-22200002i−2i000000000000000000
χ26222-2-2-2-22-2-2220000222-2-2-2-2-2-222222-2-22i−2i00000000002i2i2i2i−2i−2i−2i−2i00000000-2-22222-2-20000−2i2i000000000000000000
χ27222-2-2-2-22-2-2220000222-2-2-2-2-2-222222-2-2−2i2i0000000000−2i−2i−2i−2i2i2i2i2i0000000022-2-2-2-2220000−2i2i000000000000000000
χ28222-2-2-2-22-2-2220000222-2-2-2-2-2-222222-2-2−2i2i0000000000−2i−2i−2i−2i2i2i2i2i00000000-2-22222-2-200002i−2i000000000000000000
χ2922-222-2-2-22-22-2000022-2-2-222-2-222-2-2-22200000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ3022-222-2-2-22-22-2000022-2-2-222-2-222-2-2-22200000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ3122-222-2-2-22-22-2000022-2-2-222-2-222-2-2-2220000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
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χ3322-222-2-2-2-22-22000022-2-2-2-2-222-2-222-22200000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
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χ3522-222-2-2-2-22-22000022-2-2-2-2-222-2-222-2220000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
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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
χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144-4-411111111-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
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
χ4944444444-4-4-4-444-4-4-1-1-1-1-111111111-1-1-10000-1-1-1-1111155−5−555−5−555−5−555−5−500000000000000000000000000000000
χ5044444444-4-4-4-444-4-4-1-1-1-1-111111111-1-1-10000-1-1-1-11111−5−555−5−555−5−555−5−55500000000000000000000000000000000
χ5144444444-4-4-4-4-4-444-1-1-1-1-111111111-1-1-100001111-1-1-1-155−5−555−5−5−5−555−5−55500000000000000000000000000000000
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χ55444-4-4-4-4444-4-40000-1-1-111-1-1-1-11111-11100−4i4i55−5−555−5−5−i5−i5i5i5i5i5−i5−i5iiii−i−i−i−i00000000000000000000000000000000
χ56444-4-4-4-4444-4-40000-1-1-111-1-1-1-11111-11100−4i4i−5−555−5−555i5i5−i5−i5−i5−i5i5i5iiii−i−i−i−i00000000000000000000000000000000
χ57444-4-4-4-44-4-4440000-1-1-1111111-1-1-1-1-1114i−4i0055−5−5−5−555−i−i−i−iiiiii5i5−i5−i5−i5−i5i5i500000000000000000000000000000000
χ58444-4-4-4-44-4-4440000-1-1-1111111-1-1-1-1-1114i−4i00−5−55555−5−5−i−i−i−iiiii−i5−i5i5i5i5i5−i5−i500000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.