Finite Group Databasebeta

← Group #13017503

Character table — Group #13017503

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222222244445101010101010101010101010101010444420202020202020202020202020202020202020202020202022224444224444444444444488888888
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
χ911111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
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χ18222222222222-2-2-2-222222222222222220000-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222-2-22200000000000000000000
χ1922222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-220000-2-2-2-2222200000000000000002222-2-2-2-2-2-22200000000000000000000
χ2022222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-220000-2-2-2-222220000000000000000-2-2-2-2222222-2-200000000000000000000
χ212222-2-2-2-222-2-200002222-2-2-22222-2-2-2-2-2000000000000000000000000000022-2-200002-2000000000000002−22−22−22−2
χ222222-2-2-2-222-2-200002222-2-2-22222-2-2-2-2-2000000000000000000000000000022-2-200002-200000000000000−22−22−22−22
χ232222-2-2-2-222-2-200002222-2-2-22222-2-2-2-2-20000000000000000000000000000-2-2220000-2200000000000000i2−i2i2−i2−i2i2−i2i2
χ242222-2-2-2-222-2-200002222-2-2-22222-2-2-2-2-20000000000000000000000000000-2-2220000-2200000000000000−i2i2−i2i2i2−i2i2−i2
χ252222-2-2-2-2-2-22200002222-2-2-2-2-2-2-22222-2000000000000000000000000000022-2-20000-22000000000000002−2−222−2−22
χ262222-2-2-2-2-2-22200002222-2-2-2-2-2-2-22222-2000000000000000000000000000022-2-20000-2200000000000000−222−2−222−2
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χ2922-2-22-2-222-22-2000022-2-222-222-2-222-2-2-2000000000000000000000000000000002i2i−2i−2i002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
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χ3122-2-22-2-222-22-2000022-2-222-222-2-222-2-2-200000000000000000000000000000000−2i−2i2i2i00−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
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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
χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111111155−5−555−5−555−5−555−5−500000000000000000000000000000000
χ48444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111−5−555−5−555−5−555−5−55500000000000000000000000000000000
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χ5044444444-4-4-4-444-4-4-1-1-1-1-1-1-111111111-1-4-444-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ5344-4-4-444-44-4-44000044-4-4-4-4444-4-4-4-4444000000000000000000000000000000000000000000000000000000000000
χ5444-4-4-444-44-4-440000-1-11111-1-1-11111-1-1-100005−55−555−5−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000000000000
χ5544-4-4-444-44-4-440000-1-11111-1-1-11111-1-1-100005−55−555−5−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000000000000
χ5644-4-4-444-44-4-440000-1-11111-1-1-11111-1-1-10000−55−55−5−555−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000000000000
χ5744-4-4-444-44-4-440000-1-11111-1-1-11111-1-1-10000−55−55−5−555ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000000000000
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χ6044-4-4-444-4-444-40000-1-11111-111-1-1-1-111-100005−55−5−5−555ζ4−ζ12+ζ28−ζ36−ζ4+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−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000000000000
χ6144-4-4-444-4-444-40000-1-11111-111-1-1-1-111-10000−55−5555−5−5−ζ4−ζ12+ζ28+ζ36ζ4+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−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000000000000
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χ804-4-444-44-4000000-44-111-11-115−5−55−555−5-10000−555−51-1-11ζ4−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
χ814-4-444-44-4000000-44-111-11-11−555−55−5−55-100005−5−551-1-11−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−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000000000000
χ824-4-444-44-4000000-44-111-11-11−555−55−5−55-100005−5−551-1-11ζ4+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+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000000000000
χ834-4-44-44-44000000004-4-444-4400000000-4000000000000000000000000000000004i−4i−4i4i000000000000000000000000
χ844-4-44-44-44000000004-4-444-4400000000-400000000000000000000000000000000−4i4i4i−4i000000000000000000000000
χ858888-8-8-8-888-8-80000-2-2-2-2222-2-2-2-222222000000000000000000000000000000000000000000000000000000000000
χ868888-8-8-8-8-8-8880000-2-2-2-22222222-2-2-2-22000000000000000000000000000000000000000000000000000000000000
χ8788-8-88-8-888-88-80000-2-222-2-22-2-222-2-2222000000000000000000000000000000000000000000000000000000000000
χ8888-8-88-8-88-88-880000-2-222-2-2222-2-222-2-22000000000000000000000000000000000000000000000000000000000000
χ898-88-888-8-800000000-22-222-2-225−2525−25−2525−25252000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-800000000-22-222-2-2−2525−252525−2525−252000000000000000000000000000000000000000000000000000000000000
χ918-8-88-88-8800000000-222-2-22-225−25−252525−25−25252000000000000000000000000000000000000000000000000000000000000
χ928-8-88-88-8800000000-222-2-22-2−252525−25−252525−252000000000000000000000000000000000000000000000000000000000000

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