Finite Group Databasebeta

← Group #13021080

Character table — Group #13021080

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122224444444444448888888888881010101010101010101010101616161616161616161620202020202020202020202020202020202040404040404040408080
order12222222444444445101010101010102020202020202020202020204444444444442410101010202020204488888888888888888888888824
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
χ911111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1
χ1111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11
χ1211111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1311111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-11
χ1411111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-11
χ1511111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1
χ1611111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1
χ17222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2222222-2-20000000000-2-200000000000000000000000000
χ18222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22200000000002200000000000000000000000000
χ1922222222-2-2-2-222-2-222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-222-2-200000000002200000000000000000000000000
χ2022222222-2-2-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-2222222-2-2220000000000-2-200000000000000000000000000
χ2122-222-2-2-200002i−2i00222-2-22-2-200002i2i−2i−2i0000002-22i2i−2i−2i002-2000000000000i2i2−i2−i222−2−2i2i2−i2−i222−2−20000000000
χ2222-222-2-2-200002i−2i00222-2-22-2-200002i2i−2i−2i0000002-22i2i−2i−2i002-2000000000000−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000000000
χ2322-222-2-2-200002i−2i00222-2-22-2-200002i2i−2i−2i000000-22−2i−2i2i2i00-2200000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000
χ2422-222-2-2-200002i−2i00222-2-22-2-200002i2i−2i−2i000000-22−2i−2i2i2i00-22000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000
χ2522-222-2-2-20000−2i2i00222-2-22-2-20000−2i−2i2i2i0000002-2−2i−2i2i2i002-2000000000000i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000000000
χ2622-222-2-2-20000−2i2i00222-2-22-2-20000−2i−2i2i2i0000002-2−2i−2i2i2i002-2000000000000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000
χ2722-222-2-2-20000−2i2i00222-2-22-2-20000−2i−2i2i2i000000-222i2i−2i−2i00-2200000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000
χ2822-222-2-2-20000−2i2i00222-2-22-2-20000−2i−2i2i2i000000-222i2i−2i−2i00-22000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000
χ292-222-22-2-22i2i−2i−2i000022-22-2-22-22i2i−2i−2i00000000002-2000000-2200000000002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000
χ302-222-22-2-22i2i−2i−2i000022-22-2-22-22i2i−2i−2i00000000002-2000000-2200000000002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000
χ312-222-22-2-22i2i−2i−2i000022-22-2-22-22i2i−2i−2i0000000000-220000002-20000000000−2i2ii2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000
χ322-222-22-2-22i2i−2i−2i000022-22-2-22-22i2i−2i−2i0000000000-220000002-20000000000−2i2i−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000
χ332-222-22-2-2−2i−2i2i2i000022-22-2-22-2−2i−2i2i2i00000000002-2000000-220000000000−2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000
χ342-222-22-2-2−2i−2i2i2i000022-22-2-22-2−2i−2i2i2i00000000002-2000000-220000000000−2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000
χ352-222-22-2-2−2i−2i2i2i000022-22-2-22-2−2i−2i2i2i0000000000-220000002-200000000002i−2ii2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000
χ362-222-22-2-2−2i−2i2i2i000022-22-2-22-2−2i−2i2i2i0000000000-220000002-200000000002i−2i−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000
χ372-22-22-22-22i−2i2i−2i00002-22-22-22-22i−2i2i−2i000000002-2002i−2i2i−2i2-20000000000000000000000000000002−2i2−i22−2i2−i200
χ382-22-22-22-22i−2i2i−2i00002-22-22-22-22i−2i2i−2i000000002-2002i−2i2i−2i2-2000000000000000000000000000000−22−i2i2−22−i2i200
χ392-22-22-22-22i−2i2i−2i00002-22-22-22-22i−2i2i−2i00000000-2200−2i2i−2i2i-22000000000000000000000000000000i2−i2−22−i2i22−200
χ402-22-22-22-22i−2i2i−2i00002-22-22-22-22i−2i2i−2i00000000-2200−2i2i−2i2i-22000000000000000000000000000000−i2i22−2i2−i2−2200
χ412-22-22-22-2−2i2i−2i2i00002-22-22-22-2−2i2i−2i2i000000002-200−2i2i−2i2i2-20000000000000000000000000000002−2−i2i22−2−i2i200
χ422-22-22-22-2−2i2i−2i2i00002-22-22-22-2−2i2i−2i2i000000002-200−2i2i−2i2i2-2000000000000000000000000000000−22i2−i2−22i2−i200
χ432-22-22-22-2−2i2i−2i2i00002-22-22-22-2−2i2i−2i2i00000000-22002i−2i2i−2i-22000000000000000000000000000000i2−i22−2−i2i2−2200
χ442-22-22-22-2−2i2i−2i2i00002-22-22-22-2−2i2i−2i2i00000000-22002i−2i2i−2i-22000000000000000000000000000000−i2i2−22i2−i22−200
χ452-2-22-2-2220000002-222-2-22-2-220000000022-2-22-2220000-22-2-20000000000002i−2i−2i2i00002i−2i−2i2i00000000000000
χ462-2-22-2-2220000002-222-2-22-2-220000000022-2-22-2220000-22-2-2000000000000−2i2i2i−2i0000−2i2i2i−2i00000000000000
χ472-2-22-2-2220000002-222-2-22-2-220000000022-2-2-22-2-200002-2220000000000002-2-220000-222-200000000000000
χ482-2-22-2-2220000002-222-2-22-2-220000000022-2-2-22-2-200002-222000000000000-222-200002-2-2200000000000000
χ492-2-22-2-222000000-2222-2-22-2-2200000000-2-2222-2-2-20000-222200000000000000002-2-220000-222-20000000000
χ502-2-22-2-222000000-2222-2-22-2-2200000000-2-2222-2-2-20000-22220000000000000000-222-200002-2-220000000000
χ512-2-22-2-222000000-2222-2-22-2-2200000000-2-222-222200002-2-2-200000000000000002i−2i−2i2i00002i−2i−2i2i0000000000
χ522-2-22-2-222000000-2222-2-22-2-2200000000-2-222-222200002-2-2-20000000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000
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
χ55444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000055−5−555−5−50000000000000000000000000000
χ56444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000−5−555−5−5550000000000000000000000000000
χ5744444444-4-4-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-111110000000000000055−5−5−5−5550000000000000000000000000000
χ5844444444-4-4-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000−5−55555−5−50000000000000000000000000000
χ5944444444-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-10000000000004-4-1-1-1-111110000000000000000000000000000
χ6044444444-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000-441111-1-1-1-10000000000000000000000000000
χ61444-4-4-4-444-4-4400004-4-4-4-44444-4-440000000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-444-4-440000-11111-1-1-1-111-15−55−55−55−500000000000000−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−ζ360000000000000000000000000000
χ63444-4-4-4-444-4-440000-11111-1-1-1-111-15−55−55−55−500000000000000ζ4−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+ζ360000000000000000000000000000
χ64444-4-4-4-444-4-440000-11111-1-1-1-111-1−55−55−55−5500000000000000−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+ζ360000000000000000000000000000
χ65444-4-4-4-444-4-440000-11111-1-1-1-111-1−55−55−55−5500000000000000ζ4+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−ζ360000000000000000000000000000
χ66444-4-4-4-44-444-400004-4-4-4-4444-444-40000000000000000000000000000000000000000000000000000000000
χ67444-4-4-4-44-444-40000-11111-1-1-11-1-115−55−5−55−5500000000000000−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−ζ360000000000000000000000000000
χ68444-4-4-4-44-444-40000-11111-1-1-11-1-115−55−5−55−5500000000000000ζ4+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+ζ360000000000000000000000000000
χ69444-4-4-4-44-444-40000-11111-1-1-11-1-11−55−555−55−500000000000000−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+ζ360000000000000000000000000000
χ70444-4-4-4-44-444-40000-11111-1-1-11-1-11−55−555−55−500000000000000ζ4−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−ζ360000000000000000000000000000
χ7144-4-4-444-4000000004-4-4444-4-400000000000044000000-4-40000000000000000000000000000000000000000
χ7244-4-4-444-4000000004-4-4444-4-4000000000000-4-4000000440000000000000000000000000000000000000000
χ734-4-4-444-44000000004-444-4-4-4400000000000000004-4-44000000000000000000000000000000000000000000
χ744-4-4-444-44000000004-444-4-4-440000000000000000-444-4000000000000000000000000000000000000000000
χ7588-888-8-8-800008i−8i00-2-2-222-2220000−2i−2i2i2i000000000000000000000000000000000000000000000000000000
χ7688-888-8-8-80000−8i8i00-2-2-222-22200002i2i−2i−2i000000000000000000000000000000000000000000000000000000
χ7788-8-8-888-800000000-222-2-2-22200002i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000
χ7888-8-8-888-800000000-222-2-2-2220000−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000
χ798-888-88-8-88i8i−8i−8i0000-2-22-222-22−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000
χ808-888-88-8-8−8i−8i8i8i0000-2-22-222-222i2i−2i−2i0000000000000000000000000000000000000000000000000000000000
χ818-88-88-88-88i−8i8i−8i0000-22-22-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ828-88-88-88-8−8i8i−8i8i0000-22-22-22-222i−2i2i−2i0000000000000000000000000000000000000000000000000000000000
χ838-8-88-8-8880000008-8-2-222-222-200000000-2-22200000000000000000000000000000000000000000000000000
χ848-8-88-8-888000000-88-2-222-222-20000000022-2-200000000000000000000000000000000000000000000000000
χ858-8-8-888-8800000000-22-2-2222-20000000025−25−252500000000000000000000000000000000000000000000000000
χ868-8-8-888-8800000000-22-2-2222-200000000−252525−2500000000000000000000000000000000000000000000000000

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