Finite Group Databasebeta

← Group #13017510

Character table — Group #13017510

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222444422445101010101010102020202020202020444410101010202020202020202020202020202020202020202022224444224422444444444488888888
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
χ911111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
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χ1922222222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-200002222-2-2-2-200000000000000002222-2-2-2-222-2-200000000000000000000
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χ5244444444-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-4-4441111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ734-44-44-44-4000000004-44-44-44-400000000000000000000000000000000000000004i−4i−4i4i000000000000000000000000
χ744-44-44-44-4000000004-44-44-44-40000000000000000000000000000000000000000−4i4i4i−4i000000000000000000000000
χ754-4-4444-4-4000000004-4-4444-4-400000000000000000000000000000000000044-4-40000000000000000000000000000
χ764-4-4444-4-4000000004-4-4444-4-4000000000000000000000000000000000000-4-4440000000000000000000000000000
χ774-4-4-4-44440000004-4-11111-1-1-15−5−55−555−5004-45−5−55-1-11155−5−5−5−555-1-1-1-1111100000000000000000000000000000000
χ784-4-4-4-44440000004-4-11111-1-1-15−5−55−555−500-445−5−55-1-111−5−55555−5−51111-1-1-1-100000000000000000000000000000000
χ794-4-4-4-44440000004-4-11111-1-1-1−555−55−5−55004-4−555−5-1-111−5−55555−5−5-1-1-1-1111100000000000000000000000000000000
χ804-4-4-4-44440000004-4-11111-1-1-1−555−55−5−5500-44−555−5-1-11155−5−5−5−5551111-1-1-1-100000000000000000000000000000000
χ814-4-4-4-4444000000-44-11111-1-1-15−5−55−555−54-400−555−511-1-1-1-1-1-1111155−5−5−5−55500000000000000000000000000000000
χ824-4-4-4-4444000000-44-11111-1-1-15−5−55−555−5-4400−555−511-1-11111-1-1-1-1−5−55555−5−500000000000000000000000000000000
χ834-4-4-4-4444000000-44-11111-1-1-1−555−55−5−554-4005−5−5511-1-1-1-1-1-11111−5−55555−5−500000000000000000000000000000000
χ844-4-4-4-4444000000-44-11111-1-1-1−555−55−5−55-44005−5−5511-1-11111-1-1-1-155−5−5−5−55500000000000000000000000000000000
χ85888-8-88-8-88i8i−8i−8i0000-2-2-222-222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000000000000000
χ86888-8-88-8-8−8i−8i8i8i0000-2-2-222-2222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000000000000000
χ8788-88-8-88-88i−8i8i−8i0000-2-22-222-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-88-8−8i8i−8i8i0000-2-22-222-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000000000000000
χ898-88-88-88-800000000-22-22-22-222i5−2i52i5−2i5−2i52i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-800000000-22-22-22-22−2i52i5−2i52i52i5−2i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ918-8-8888-8-800000000-222-2-2-2222i5−2i5−2i52i52i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ928-8-8888-8-800000000-222-2-2-222−2i52i52i5−2i5−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000000000

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