Finite Group Databasebeta

← Group #13019497

Character table — Group #13019497

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222222244445101010101010101010101010101010444420202020202020202020202020202020202020202020202044444444444444448888888888888888
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
χ511111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
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−i−i−iiiii−i−i−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−iiiii−i−i−i−iiiii−i−i
χ13111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
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
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
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χ1922222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22220000-2-2-2-22222000000000000000022-2-2-2-222-2-22200000000000000000000
χ2022222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22220000-2-2-2-222220000000000000000-2-22222-2-222-2-200000000000000000000
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χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144-4-411111111-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
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
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χ55444-44-4-4-40000004-4-1-1-1115−55−55−55−511-1000055−5−5-1-111ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000000000000000000000000
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χ724-444-4-4-440000−4i4i00-11-11-15−5−555−5−551-110000i−ii−i−i5i5−i5i5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000000000000000000000000
χ734-444-4-4-440000−4i4i00-11-11-1−555−5−555−51-110000i−ii−ii5−i5i5−i5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000000000000000000000000
χ744-444-4-4-440000−4i4i00-11-11-1−555−5−555−51-110000i−ii−ii5−i5i5−i5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000000000000000000000000
χ754-44-4-444-44-44-40000-11-1-11-1-111-1-111-111004-4i5−i5−i5i5i5−i5−i5i5−i5−i5i5i5i5i5−i5−i5-1-1-1-1111100000000000000000000000000000000
χ764-44-4-444-44-44-40000-11-1-11-1-111-1-111-111004-4−i5i5i5−i5−i5i5i5−i5i5i5−i5−i5−i5−i5i5i5-1-1-1-1111100000000000000000000000000000000
χ774-44-4-444-44-44-40000-11-1-11-1-111-1-111-11100-44i5−i5−i5i5i5−i5−i5i5i5i5−i5−i5−i5−i5i5i51111-1-1-1-100000000000000000000000000000000
χ784-44-4-444-44-44-40000-11-1-11-1-111-1-111-11100-44−i5i5i5−i5−i5i5i5−i5−i5−i5i5i5i5i5−i5−i51111-1-1-1-100000000000000000000000000000000
χ794-44-4-444-4-44-440000-11-1-1111-1-111-1-1-1114i−4i00i5−i5−i5i5−i5i5i5−i5−i−i−i−iiiii−5−55555−5−500000000000000000000000000000000
χ804-44-4-444-4-44-440000-11-1-1111-1-111-1-1-1114i−4i00−i5i5i5−i5i5−i5−i5i5−i−i−i−iiiii55−5−5−5−55500000000000000000000000000000000
χ814-44-4-444-4-44-440000-11-1-1111-1-111-1-1-111−4i4i00i5−i5−i5i5−i5i5i5−i5iiii−i−i−i−i55−5−5−5−55500000000000000000000000000000000
χ824-44-4-444-4-44-440000-11-1-1111-1-111-1-1-111−4i4i00−i5i5i5−i5i5−i5−i5i5iiii−i−i−i−i−5−55555−5−500000000000000000000000000000000
χ834-4-4444-4-4000000004-4-44-400000000-444000000000000000000000000000000000000004i−4i00000000000000000000
χ844-4-4444-4-4000000004-4-44-400000000-44400000000000000000000000000000000000000−4i4i00000000000000000000
χ8588-88-8-88-888-8-80000-2-2222-2-2-2-22222-2-22000000000000000000000000000000000000000000000000000000000000
χ8688-88-8-88-8-8-8880000-2-22222222-2-2-2-2-2-22000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-88-8800000000-2-22-2-225−2525−25−2525−2525222000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-8800000000-2-22-2-2−2525−252525−2525−25222000000000000000000000000000000000000000000000000000000000000
χ898-8-8888-8-800000000-222-2225−25−2525−252525−252-2-2000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-800000000-222-22−252525−2525−25−25252-2-2000000000000000000000000000000000000000000000000000000000000
χ918-8-8-88-8888-8-880000-2222-2-2-22222-2-2-22-2000000000000000000000000000000000000000000000000000000000000
χ928-8-8-88-888-888-80000-2222-222-2-2-2-222-22-2000000000000000000000000000000000000000000000000000000000000

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