Finite Group Databasebeta

← Group #13018509

Character table — Group #13018509

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222222244445101010101010101010101010101010444420202020202020202020202020202020202020202020202044444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−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
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χ1922222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2220000-2-2-2-2222200000000000000002222-2-2-2-2-2-22200000000000000000000
χ2022222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2220000-2-2-2-222220000000000000000-2-2-2-2222222-2-200000000000000000000
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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
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χ734-4-444-4-440000-4400-1111-115−5−55−555−5-1-100001-11-1−55−55−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−ζ36ζ4−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−ζ3600000000000000000000000000000000
χ744-4-444-4-440000-4400-1111-115−5−55−555−5-1-100001-11-1−55−55ζ4−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+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000000000000
χ754-4-444-4-440000-4400-1111-11−555−55−5−55-1-100001-11-15−55−5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−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−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000000000000
χ764-4-444-4-440000-4400-1111-11−555−55−5−55-1-100001-11-15−55−5ζ4+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−ζ36−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−ζ3600000000000000000000000000000000
χ774-4-44-444-44-4-440000-1-1111-1-1-11111-1-1-114i−4i005−5−555−5−55−i−i−i−iiiiii5i5−i5−i5−i5−i5i5i500000000000000000000000000000000
χ784-4-44-444-44-4-440000-1-1111-1-1-11111-1-1-114i−4i00−555−5−555−5−i−i−i−iiiii−i5−i5i5i5i5i5−i5−i500000000000000000000000000000000
χ794-4-44-444-44-4-440000-1-1111-1-1-11111-1-1-11−4i4i005−5−555−5−55iiii−i−i−i−i−i5−i5i5i5i5i5−i5−i500000000000000000000000000000000
χ804-4-44-444-44-4-440000-1-1111-1-1-11111-1-1-11−4i4i00−555−5−555−5iiii−i−i−i−ii5i5−i5−i5−i5−i5i5i500000000000000000000000000000000
χ814-4-44-444-4-444-40000-1-1111-111-1-1-1-111-11004i−4i5−5−55−555−5i5i5−i5−i5−i5−i5i5i5−i−i−i−iiiii00000000000000000000000000000000
χ824-4-44-444-4-444-40000-1-1111-111-1-1-1-111-11004i−4i−555−55−5−55−i5−i5i5i5i5i5−i5−i5−i−i−i−iiiii00000000000000000000000000000000
χ834-4-44-444-4-444-40000-1-1111-111-1-1-1-111-1100−4i4i5−5−55−555−5−i5−i5i5i5i5i5−i5−i5iiii−i−i−i−i00000000000000000000000000000000
χ844-4-44-444-4-444-40000-1-1111-111-1-1-1-111-1100−4i4i−555−55−5−55i5i5−i5−i5−i5−i5i5i5iiii−i−i−i−i00000000000000000000000000000000
χ8588-8-888-8-888-8-80000-2-2-2222-2-2-2-222222-2000000000000000000000000000000000000000000000000000000000000
χ8688-8-888-8-8-8-8880000-2-2-22222222-2-2-2-22-2000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-8-88800000000-22-22-2-225−2525−25−2525−252522000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-8-88800000000-22-22-2-2−2525−252525−2525−2522000000000000000000000000000000000000000000000000000000000000
χ898-88-88-88-800000000-222-22-225−25−252525−25−25252-2000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-800000000-222-22-2−252525−25−252525−252-2000000000000000000000000000000000000000000000000000000000000
χ918-88-8-88-888-88-80000-2-22-2-22-2-222-2-22222000000000000000000000000000000000000000000000000000000000000
χ928-88-8-88-88-88-880000-2-22-2-2222-2-222-2-222000000000000000000000000000000000000000000000000000000000000

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