Finite Group Databasebeta

← Group #13017532

Character table — Group #13017532

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444444444444488888888888888888888888888881010101010101010202020204040404040404040404040404040404040404040
order12222222222244445101010101010101010101010101010222210101010101010101010101010101010202020202020202044444444444422228888888888888888
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
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χ1922222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2200000000000000000000-2-2-2-2222222-2-222-2-2-2-22200000000000000000000
χ2022222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2200000000000000000000-2-2-2-22222-2-222-2-22222-2-200000000000000000000
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χ24222-2-2-22-222-2-200002222-2-2-22222-2-2-2-2-2000000000000000000000000000000-2-2002200-220000−22−2200002−22−20000
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χ3222-22-2-2-222-22-2000022-2-222-222-2-222-2-2-20000000000000000000000000000-2-2002200-220000000000−22−2200002−22−2
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χ3622-22-2-2-22-22-22000022-2-222-2-2-222-2-222-20000000000000000000000000000-2-20022002-20000000000−222−200002−2−22
χ372-2-2-2-222200002-2002-22-22-2-2000000002002-2000000002222-2-2-2-222-2-200002-22-22-22-20000002-20000000000000000
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χ464444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-41111111111111111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ47444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000055−5−555−5−555−5−555−5−51111111100000000000000000000000000000000
χ48444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000−5−555−5−555−5−555−5−5551111111100000000000000000000000000000000
χ4944444444-4-4-4-444-4-4-1-1-1-1-1-1-111111111-144-4-4-1-1-1-1-1-1-1-111111111-1-1-1-1111100000000000000000000000000000000
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χ5644-4-444-4-44-4-440000-1-11111-1-1-11111-1-1-10000ζ4−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+ζ365−55−555−5−500000000000000000000000000000000
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χ804-4-4-4-444400004-400-11-11-111−555−55−5−55-100-44−5−55555−5−51111-1-1-1-1-1-1115−5−5500000000000000000000000000000000
χ814-4-4-4-44440000-4400-11-11-1115−5−55−555−5-14-400-1-1-1-11111−5−55555−5−511-1-15−5−5500000000000000000000000000000000
χ824-4-4-4-44440000-4400-11-11-1115−5−55−555−5-1-44001111-1-1-1-155−5−5−5−55511-1-15−5−5500000000000000000000000000000000
χ834-4-4-4-44440000-4400-11-11-111−555−55−5−55-14-400-1-1-1-1111155−5−5−5−55511-1-1−555−500000000000000000000000000000000
χ844-4-4-4-44440000-4400-11-11-111−555−55−5−55-1-44001111-1-1-1-1−5−55555−5−511-1-1−555−500000000000000000000000000000000
χ85888-8-8-88-888-8-80000-2-2-2-2222-2-2-2-222222000000000000000000000000000000000000000000000000000000000000
χ86888-8-8-88-8-8-8880000-2-2-2-22222222-2-2-2-22000000000000000000000000000000000000000000000000000000000000
χ8788-88-8-8-888-88-80000-2-222-2-22-2-222-2-2222000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-8-88-88-880000-2-222-2-2222-2-222-2-22000000000000000000000000000000000000000000000000000000000000
χ898-88-88-8-8800000000-222-2-22-225−2525−25−2525−25252000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-8800000000-222-2-22-2−2525−252525−2525−252000000000000000000000000000000000000000000000000000000000000
χ918-8-888-88-800000000-22-222-2-225−25−252525−25−25252000000000000000000000000000000000000000000000000000000000000
χ928-8-888-88-800000000-22-222-2-2−252525−25−252525−252000000000000000000000000000000000000000000000000000000000000

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