Finite Group Databasebeta

← Group #13021075

Character table — Group #13021075

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122224444444444448888888888881010101010101010101010101616161616161616161620202020202020202020202020202020202040404040404040408080
order12222222444444445101010101010102020202020202020202020204444444444444420202020202020204488888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii11
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i11
χ911111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-1
χ1011111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-1
χ1111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11
χ1211111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11
χ1311111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-11
χ1411111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1511111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1611111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1
χ17222222222222-2-2-2-222222222-2-2-2-22222-2-2-2-22222-2-2-22222-20000000000-2-200000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2222-2-2-2-2200000000002200000000000000000000000000
χ1922222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-222222222222-2-2-2-220000000000-2-200000000000000000000000000
χ2022222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22222-200000000002200000000000000000000000000
χ2122-2-222-2-20000002-2222-22-2-2-20000000022-2-222-2-222-20000-200000000000022−2−222−2−222−2−222−2−20000000000
χ2222-2-222-2-20000002-2222-22-2-2-20000000022-2-222-2-222-20000-2000000000000−2−222−2−222−2−222−2−2220000000000
χ2322-2-222-2-20000002-2222-22-2-2-20000000022-2-2-2-222-2-2200002000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000
χ2422-2-222-2-20000002-2222-22-2-2-20000000022-2-2-2-222-2-2200002000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000
χ2522-2-222-2-2000000-22222-22-2-2-200000000-2-22222-2-2-2-2200002000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ2622-2-222-2-2000000-22222-22-2-2-200000000-2-22222-2-2-2-2200002000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ2722-2-222-2-2000000-22222-22-2-2-200000000-2-222-2-22222-20000-200000000000022−2−2−2−222−2−22222−2−20000000000
χ2822-2-222-2-2000000-22222-22-2-2-200000000-2-222-2-22222-20000-2000000000000−2−22222−2−222−2−2−2−2220000000000
χ292-22-22-22-222-2-2000022-22-22-2-2000022-2-2000000002-220000-200000000002-22−22−22−22−22−22−22−22−20000000000
χ302-22-22-22-222-2-2000022-22-22-2-2000022-2-2000000002-220000-200000000002-2−22−22−22−22−22−22−22−220000000000
χ312-22-22-22-222-2-2000022-22-22-2-2000022-2-200000000-22-2000020000000000-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ322-22-22-22-222-2-2000022-22-22-2-2000022-2-200000000-22-2000020000000000-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ332-22-22-22-2-2-222000022-22-22-2-20000-2-222000000002-220000-20000000000-222−22−2−22−22−22−222−22−20000000000
χ342-22-22-22-2-2-222000022-22-22-2-20000-2-222000000002-220000-20000000000-22−22−222−22−22−22−2−22−220000000000
χ352-22-22-22-2-2-222000022-22-22-2-20000-2-22200000000-22-20000200000000002-2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ362-22-22-22-2-2-222000022-22-22-2-20000-2-22200000000-22-20000200000000002-2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ372-22-2-22-222-22-200002-22-2-22-2200002-22-200002-22-200022-2-200000000000000000000000000000i2−i2i2−i2i2−i2i2−i200
χ382-22-2-22-222-22-200002-22-2-22-2200002-22-200002-22-200022-2-200000000000000000000000000000−i2i2−i2i2−i2i2−i2i200
χ392-22-2-22-222-22-200002-22-2-22-2200002-22-20000-22-22000-2-222000000000000000000000000000002−22−2−22−2200
χ402-22-2-22-222-22-200002-22-2-22-2200002-22-20000-22-22000-2-22200000000000000000000000000000−22−222−22−200
χ412-22-2-22-22-22-2200002-22-2-22-220000-22-2200002-22-2000-2-222000000000000000000000000000002−2−222−2−2200
χ422-22-2-22-22-22-2200002-22-2-22-220000-22-2200002-22-2000-2-22200000000000000000000000000000−222−2−222−200
χ432-22-2-22-22-22-2200002-22-2-22-220000-22-220000-22-2200022-2-200000000000000000000000000000i2−i2−i2i2−i2i2i2−i200
χ442-22-2-22-22-22-2200002-22-2-22-220000-22-220000-22-2200022-2-200000000000000000000000000000−i2i2i2−i2i2−i2−i2i200
χ452-2-222-2-2200002-20022-2-2-2-22222-2-20000000000002-2-22-22-2200000000000000002-2-222-2-2200000000000000
χ462-2-222-2-2200002-20022-2-2-2-22222-2-20000000000002-2-22-22-220000000000000000-222-2-222-200000000000000
χ472-2-222-2-2200002-20022-2-2-2-22222-2-2000000000000-222-22-22-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ482-2-222-2-2200002-20022-2-2-2-22222-2-2000000000000-222-22-22-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ492-2-222-2-220000-220022-2-2-2-222-2-2220000000000002-2-2-22-2220000000000002-2-22000000002-2-220000000000
χ502-2-222-2-220000-220022-2-2-2-222-2-2220000000000002-2-2-22-222000000000000-222-200000000-222-20000000000
χ512-2-222-2-220000-220022-2-2-2-222-2-222000000000000-2222-22-2-20000000000002i−2i−2i2i00000000−2i2i2i−2i0000000000
χ522-2-222-2-220000-220022-2-2-2-222-2-222000000000000-2222-22-2-2000000000000−2i2i2i−2i000000002i−2i−2i2i0000000000
χ534444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000044-1-1-1-1-1-1-1-10000000000000000000000000000
χ544444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-4-4111111110000000000000000000000000000
χ55444444444444-4-4-4-4-1-1-1-1-1-1-1-11111-1-1-1-111110000000000000055−5−555−5−50000000000000000000000000000
χ56444444444444-4-4-4-4-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000−5−555−5−5550000000000000000000000000000
χ5744444444-4-4-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000004-4-1-1-1-111110000000000000000000000000000
χ5844444444-4-4-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000-441111-1-1-1-10000000000000000000000000000
χ5944444444-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000055−5−5−5−5550000000000000000000000000000
χ6044444444-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000−5−55555−5−50000000000000000000000000000
χ614444-4-4-4-44-4-4400004-4-4-4444-400004-4-44000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-4-440000-1111-1-1-115−55−5-111-15−55−500000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ634444-4-4-4-44-4-440000-1111-1-1-115−55−5-111-15−55−500000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ644444-4-4-4-44-4-440000-1111-1-1-11−55−55-111-1−55−5500000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ654444-4-4-4-44-4-440000-1111-1-1-11−55−55-111-1−55−5500000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ664444-4-4-4-4-444-400004-4-4-4444-40000-444-4000000000000000000000000000000000000000000000000000000
χ674444-4-4-4-4-444-40000-1111-1-1-115−55−51-1-11−55−5500000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ684444-4-4-4-4-444-40000-1111-1-1-115−55−51-1-11−55−5500000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ694444-4-4-4-4-444-40000-1111-1-1-11−55−551-1-115−55−500000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ704444-4-4-4-4-444-40000-1111-1-1-11−55−551-1-115−55−500000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ7144-4-4-4-444000000004-4-444-4-4400000000000000000004-4-44000000000000000000000000000000000000000
χ7244-4-4-4-444000000004-4-444-4-440000000000000000000-444-4000000000000000000000000000000000000000
χ734-4-44-444-4000000004-444-4-44-40000000000004-4-440000000000000000000000000000000000000000000000
χ744-4-44-444-4000000004-444-4-44-4000000000000-444-40000000000000000000000000000000000000000000000
χ7588-8-888-8-80000008-8-2-2-22-222200000000-2-22200000000000000000000000000000000000000000000000000
χ7688-8-888-8-8000000-88-2-2-22-22220000000022-2-200000000000000000000000000000000000000000000000000
χ7788-8-8-8-88800000000-222-2-222-20000000025−25−252500000000000000000000000000000000000000000000000000
χ7888-8-8-8-88800000000-222-2-222-200000000−252525−2500000000000000000000000000000000000000000000000000
χ798-88-88-88-888-8-80000-2-22-22-2220000-2-222000000000000000000000000000000000000000000000000000000
χ808-88-88-88-8-8-8880000-2-22-22-222000022-2-2000000000000000000000000000000000000000000000000000000
χ818-88-8-88-888-88-80000-22-222-22-20000-22-22000000000000000000000000000000000000000000000000000000
χ828-88-8-88-88-88-880000-22-222-22-200002-22-2000000000000000000000000000000000000000000000000000000
χ838-8-888-8-8800008-800-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-880000-8800-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000000000
χ858-8-88-888-800000000-22-2-222-2225−25−25250000000000000000000000000000000000000000000000000000000000
χ868-8-88-888-800000000-22-2-222-22−252525−250000000000000000000000000000000000000000000000000000000000

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