Finite Group Databasebeta

← Group #13019674

Character table — Group #13019674

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122224444444444448888888888881010101010101010101010101616161616161616161620202020202020202020202020202020202040404040404040408080
order12222222444444445101010101010102020202020202020202020204444444444442410101010202020202288888888888888888888888824
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
χ911111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1
χ1111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11
χ1211111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1311111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-11
χ1411111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-11
χ1511111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1
χ1611111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1
χ17222222222222-2-2-2-222222222-2-2-2-22222-2-2-2-222-2-2222222-2-20000000000-2-200000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2-2-22200000000002200000000000000000000000000
χ1922222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-200000000002200000000000000000000000000
χ2022222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2222222-2-2220000000000-2-200000000000000000000000000
χ21222-22-2-2-20000002i−2i222-22-2-2-2000000002i2i−2i−2i002-22i2i−2i−2i002-2000000000000i2i2−i2−i222−2−2i2i2−i2−i222−2−20000000000
χ22222-22-2-2-20000002i−2i222-22-2-2-2000000002i2i−2i−2i002-22i2i−2i−2i002-2000000000000−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000000000
χ23222-22-2-2-20000002i−2i222-22-2-2-2000000002i2i−2i−2i00-22−2i−2i2i2i00-2200000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000
χ24222-22-2-2-20000002i−2i222-22-2-2-2000000002i2i−2i−2i00-22−2i−2i2i2i00-22000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000
χ25222-22-2-2-2000000−2i2i222-22-2-2-200000000−2i−2i2i2i002-2−2i−2i2i2i002-2000000000000i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000000000
χ26222-22-2-2-2000000−2i2i222-22-2-2-200000000−2i−2i2i2i002-2−2i−2i2i2i002-2000000000000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000
χ27222-22-2-2-2000000−2i2i222-22-2-2-200000000−2i−2i2i2i00-222i2i−2i−2i00-2200000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000
χ28222-22-2-2-2000000−2i2i222-22-2-2-200000000−2i−2i2i2i00-222i2i−2i−2i00-22000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000
χ2922-22-22-2-22i2i−2i−2i000022-22-22-2-200002i2i−2i−2i00002-2002i−2i2i−2i2-20000000000000000000000000000002−2i2−i22−2i2−i200
χ3022-22-22-2-22i2i−2i−2i000022-22-22-2-200002i2i−2i−2i00002-2002i−2i2i−2i2-2000000000000000000000000000000−22−i2i2−22−i2i200
χ3122-22-22-2-22i2i−2i−2i000022-22-22-2-200002i2i−2i−2i0000-2200−2i2i−2i2i-22000000000000000000000000000000i2−i2−22−i2i22−200
χ3222-22-22-2-22i2i−2i−2i000022-22-22-2-200002i2i−2i−2i0000-2200−2i2i−2i2i-22000000000000000000000000000000−i2i22−2i2−i2−2200
χ3322-22-22-2-2−2i−2i2i2i000022-22-22-2-20000−2i−2i2i2i00002-200−2i2i−2i2i2-20000000000000000000000000000002−2−i2i22−2−i2i200
χ3422-22-22-2-2−2i−2i2i2i000022-22-22-2-20000−2i−2i2i2i00002-200−2i2i−2i2i2-2000000000000000000000000000000−22i2−i2−22i2−i200
χ3522-22-22-2-2−2i−2i2i2i000022-22-22-2-20000−2i−2i2i2i0000-22002i−2i2i−2i-22000000000000000000000000000000i2−i22−2−i2i2−2200
χ3622-22-22-2-2−2i−2i2i2i000022-22-22-2-20000−2i−2i2i2i0000-22002i−2i2i−2i-22000000000000000000000000000000−i2i2−22i2−i22−200
χ372-2-222-2-222-22-200002-2-222-2-2200002-22-200000022000000-2-200000000002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ382-2-222-2-222-22-200002-2-222-2-2200002-22-200000022000000-2-200000000002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ392-2-222-2-222-22-200002-2-222-2-2200002-22-2000000-2-2000000220000000000-222−22−22−22−2−22−22−22−220000000000
χ402-2-222-2-222-22-200002-2-222-2-2200002-22-2000000-2-2000000220000000000-22−22−22−22−222−22−22−22−20000000000
χ412-2-222-2-22-22-2200002-2-222-2-220000-22-2200000022000000-2-20000000000-22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ422-2-222-2-22-22-2200002-2-222-2-220000-22-2200000022000000-2-20000000000-22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ432-2-222-2-22-22-2200002-2-222-2-220000-22-22000000-2-20000002200000000002-22−22−2−22−22−22−222−22−20000000000
χ442-2-222-2-22-22-2200002-2-222-2-220000-22-22000000-2-20000002200000000002-2−22−222−22−22−22−2−22−220000000000
χ452-2-2-2222-200002-2002-2-2-2222-222-2-200000000222-20000-2-2-2200000000000000002i−2i−2i2i00002i−2i−2i2i0000000000
χ462-2-2-2222-200002-2002-2-2-2222-222-2-200000000222-20000-2-2-220000000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000
χ472-2-2-2222-200002-2002-2-2-2222-222-2-200000000-2-2-220000222-200000000000000002-2-220000-222-20000000000
χ482-2-2-2222-200002-2002-2-2-2222-222-2-200000000-2-2-220000222-20000000000000000-222-200002-2-220000000000
χ492-2-2-2222-20000-22002-2-2-2222-2-2-2220000000022-220000-2-22-20000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000
χ502-2-2-2222-20000-22002-2-2-2222-2-2-2220000000022-220000-2-22-2000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000
χ512-2-2-2222-20000-22002-2-2-2222-2-2-22200000000-2-22-2000022-220000000000002-2-2200002-2-2200000000000000
χ522-2-2-2222-20000-22002-2-2-2222-2-2-22200000000-2-22-2000022-22000000000000-222-20000-222-200000000000000
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
χ6144-4-4-4-4440000000044-4-4-4-44400000000000000004-4-44000000000000000000000000000000000000000000
χ6244-4-4-4-4440000000044-4-4-4-4440000000000000000-444-4000000000000000000000000000000000000000000
χ634-444-4-44-44i−4i−4i4i00004-444-4-44-400004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ644-444-4-44-44i−4i−4i4i0000-11-1-111-115−55−5−iii−ii5−i5i5−i500000000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ654-444-4-44-44i−4i−4i4i0000-11-1-111-115−55−5−iii−ii5−i5i5−i500000000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ664-444-4-44-44i−4i−4i4i0000-11-1-111-11−55−55−iii−i−i5i5−i5i500000000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ674-444-4-44-44i−4i−4i4i0000-11-1-111-11−55−55−iii−i−i5i5−i5i500000000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ684-444-4-44-4−4i4i4i−4i00004-444-4-44-40000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ694-444-4-44-4−4i4i4i−4i0000-11-1-111-115−55−5i−i−ii−i5i5−i5i500000000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ704-444-4-44-4−4i4i4i−4i0000-11-1-111-115−55−5i−i−ii−i5i5−i5i500000000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ714-444-4-44-4−4i4i4i−4i0000-11-1-111-11−55−55i−i−iii5−i5i5−i500000000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ724-444-4-44-4−4i4i4i−4i0000-11-1-111-11−55−55i−i−iii5−i5i5−i500000000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ734-44-4-44-44000000004-44-4-44-440000000000004-4000000-440000000000000000000000000000000000000000
χ744-44-4-44-44000000004-44-4-44-44000000000000-440000004-40000000000000000000000000000000000000000
χ75888-88-8-8-80000008i−8i-2-2-22-222200000000−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ76888-88-8-8-8000000−8i8i-2-2-22-2222000000002i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7788-88-88-8-88i8i−8i−8i0000-2-22-22-2220000−2i−2i2i2i000000000000000000000000000000000000000000000000000000
χ7888-88-88-8-8−8i−8i8i8i0000-2-22-22-22200002i2i−2i−2i000000000000000000000000000000000000000000000000000000
χ7988-8-8-8-88800000000-2-22222-2-225−25−25250000000000000000000000000000000000000000000000000000000000
χ8088-8-8-8-88800000000-2-22222-2-2−252525−250000000000000000000000000000000000000000000000000000000000
χ818-88-8-88-8800000000-22-222-22-20000000025−25−252500000000000000000000000000000000000000000000000000
χ828-88-8-88-8800000000-22-222-22-200000000−252525−2500000000000000000000000000000000000000000000000000
χ838-8-888-8-888-88-80000-222-2-222-20000-22-22000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-88-880000-222-2-222-200002-22-2000000000000000000000000000000000000000000000000000000
χ858-8-8-8888-800008-800-2222-2-2-22-2-2220000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-80000-8800-2222-2-2-2222-2-20000000000000000000000000000000000000000000000000000000000

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