Finite Group Databasebeta

← Group #13018158

Character table — Group #13018158

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222444444445101010101010102020202020202020224410101010101010102020202020202020202020202020202022224444444444444444444488888888
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
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χ2022222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000-2-2-2-2222200000000-2-2-2-22222-2-22200000000000000000000
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χ28222-2-22-2-2-2-2220000222-2-2-2-22-2-2-2-2222200000000000000000000000000000000−2i2i−2i2i2i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
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χ412-2-2-2-2222-22-2200002-2-222-2-22-2-222-2-22200000000000000000000000000002-22-2000000-22000000000000i2−i2−i2i2i2−i2−i2i2
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χ442-2-2-2-2222-22-2200002-2-222-2-22-2-222-2-2220000000000000000000000000000-22-220000002-2000000000000−222−22−2−22
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
χ464444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-411111111-1-1-1-1-1-1-1-11111111100000000000000000000000000000000
χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000055−5−555−5−51111111155−5−555−5−500000000000000000000000000000000
χ48444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000−5−555−5−55511111111−5−555−5−55500000000000000000000000000000000
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χ5044444444-4-4-4-444-4-4-1-1-1-1-1-1-1-111111111-4-44411111111-1-1-1-11111-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ5244444444-4-4-4-4-4-444-1-1-1-1-1-1-1-1111111110000−5−555−5−5551111-1-1-1-155−5−555−5−500000000000000000000000000000000
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χ814-4-4444-4-4-444-40000-11111-1-1-111-1-1-1-1110000−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+ζ36−555−55−5−55−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
χ824-4-4444-4-4-444-40000-11111-1-1-111-1-1-1-1110000−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−ζ365−5−55−555−5−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
χ834-4-4444-4-4-444-40000-11111-1-1-111-1-1-1-1110000ζ4−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−ζ36−555−55−5−55ζ4−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
χ844-4-4444-4-4-444-40000-11111-1-1-111-1-1-1-1110000ζ4+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+ζ365−5−55−555−5ζ4+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
χ85888-8-88-8-888-8-80000-2-2-22222-2-2-2-2-22222000000000000000000000000000000000000000000000000000000000000
χ86888-8-88-8-8-8-8880000-2-2-22222-22222-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ8788-8-88-8-8800000000-2-222-22-222i5−2i52i5−2i5−2i52i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ8888-8-88-8-8800000000-2-222-22-22−2i52i5−2i52i52i5−2i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ898-88-88-88-800000000-22-2-222-222i5−2i5−2i52i52i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-800000000-22-2-222-22−2i52i52i5−2i5−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000000000
χ918-8-8-8-88888-88-80000-222-2-222-2-2-222-2-222000000000000000000000000000000000000000000000000000000000000
χ928-8-8-8-8888-88-880000-222-2-222-222-2-222-2-2000000000000000000000000000000000000000000000000000000000000

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