Finite Group Databasebeta

← Group #13024850

Character table — Group #13024850

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order1222224444588881010101010101020202020404040404040404044448888442020202020202020448888888888161616161616161622
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-11-111ii−i−iii−i−iii−i−iii−i−i1-1
χ101111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-11-111−i−iii−i−iii−i−iii−i−iii1-1
χ111111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1-1-1-1-1-11-1-1-1-111111-111ii−i−iii−i−i−i−iii−i−iii-11
χ121111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-111-1-1-1-1-1-1-11-1-1-1-111111-111−i−iii−i−iiiii−i−iii−i−i-11
χ131111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-1-1-11111111-11111-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-111-11
χ141111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-1-1-11111111-11111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-11
χ151111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-1-1-1111111-11-1-1-1-11111-11-1-111-1-1-1-111-1-11111-1-11-1
χ161111-1-1-1-111111-1-111-1-1-1-111-1-111111-1-1-1-1-1-1111111-11-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1111-1
χ1722222222222-2-2-2-222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000022-2-2000000000000000000
χ1822222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000-2-222000000000000000000
χ19222222-2-2-2-2200002222222-2-2-2-20000000022-2-200000000000000-220000000000i2−i2i2−i2i2−i2i2−i200
χ20222222-2-2-2-2200002222222-2-2-2-20000000022-2-200000000000000-220000000000−i2i2−i2i2−i2i2−i2i200
χ21222222-2-2-2-2200002222222-2-2-2-200000000-2-222000000000000002-200000000002−22−2−22−2200
χ22222222-2-2-2-2200002222222-2-2-2-200000000-2-222000000000000002-20000000000−22−222−22−200
χ232222-2-222-2-22000022-2-2-2-22-222-200000000222200000000000000-2-200000000002−2−222−2−2200
χ242222-2-222-2-22000022-2-2-2-22-222-200000000222200000000000000-2-20000000000−222−2−222−200
χ252222-2-222-2-22000022-2-2-2-22-222-200000000-2-2-2-200000000000000220000000000i2−i2−i2i2−i2i2i2−i200
χ262222-2-222-2-22000022-2-2-2-22-222-200000000-2-2-2-200000000000000220000000000−i2i2i2−i2i2−i2−i2i200
χ272222-2-2-2-2222-2-22222-2-2-2-222-2-22-2-2-2-2222222-2-2222200000000002-2-2-2000000000000000000
χ282222-2-2-2-2222-2-22222-2-2-2-222-2-22-2-2-2-22222-2-222-2-2-2-20000000000-2222000000000000000000
χ2922-2-22-22-2-2220000-2-222-2-2222-2-200000000000022-2-20000000000002-2i2−i2i2−i2i2−i2i2−i20000000000
χ3022-2-22-22-2-2220000-2-222-2-2222-2-200000000000022-2-20000000000002-2−i2i2−i2i2−i2i2−i2i20000000000
χ3122-2-22-22-2-2220000-2-222-2-2222-2-2000000000000-2-222000000000000-222−22−2−22−220000000000
χ3222-2-22-22-2-2220000-2-222-2-2222-2-2000000000000-2-222000000000000-22−22−222−22−20000000000
χ3322-2-2-22-22-2220000-2-2-2-22222-22-200000000000022-2-2000000000000-22i2−i2−i2i2−i2i2i2−i20000000000
χ3422-2-2-22-22-2220000-2-2-2-22222-22-200000000000022-2-2000000000000-22−i2i2i2−i2i2−i2−i2i20000000000
χ3522-2-2-22-22-2220000-2-2-2-22222-22-2000000000000-2-2220000000000002-22−2−222−2−220000000000
χ3622-2-2-22-22-2220000-2-2-2-22222-22-2000000000000-2-2220000000000002-2−222−2−222−20000000000
χ374444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-10000000000000000000000
χ384444444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4111111110000000000000000000000
χ394444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-111111111000000000055−5−555−5−50000000000000000000000
χ404444444444-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1111111110000000000−5−555−5−5550000000000000000000000
χ414444-4-4-4-444-144-4-4-1-11111-1-111-1-1-1-1-11111000000004-4-1-1-1-111110000000000000000000000
χ424444-4-4-4-444-144-4-4-1-11111-1-111-1-1-1-1-1111100000000-441111-1-1-1-10000000000000000000000
χ434444-4-4-4-444-1-4-444-1-11111-1-111-11111-1-1-1-1000000000055−5−5−5−5550000000000000000000000
χ444444-4-4-4-444-1-4-444-1-11111-1-111-11111-1-1-1-10000000000−5−55555−5−50000000000000000000000
χ4544-4-44-4-444-440000-4-444-4-44-4-444000000000000000000000000000000000000000000000000
χ4644-4-44-4-444-4-1000011-1-111-111-1-155−5−555−5−50000000000−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−ζ360000000000000000000000
χ4744-4-44-4-444-4-1000011-1-111-111-1-155−5−555−5−50000000000ζ4−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+ζ360000000000000000000000
χ4844-4-44-4-444-4-1000011-1-111-111-1-1−5−555−5−5550000000000−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+ζ360000000000000000000000
χ4944-4-44-4-444-4-1000011-1-111-111-1-1−5−555−5−5550000000000ζ4+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−ζ360000000000000000000000
χ5044-4-4-444-44-440000-4-4-4-4444-44-44000000000000000000000000000000000000000000000000
χ5144-4-4-444-44-4-100001111-1-1-11-11-155−5−5−5−5550000000000−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+ζ360000000000000000000000
χ5244-4-4-444-44-4-100001111-1-1-11-11-155−5−5−5−5550000000000ζ4−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−ζ360000000000000000000000
χ5344-4-4-444-44-4-100001111-1-1-11-11-1−5−55555−5−50000000000−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−ζ360000000000000000000000
χ5444-4-4-444-44-4-100001111-1-1-11-11-1−5−55555−5−50000000000ζ4+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+ζ360000000000000000000000
χ554-44-400000040022−224-40000-40000000022−2222−224i−4i002i2−2i22i2−2i200000000000000000000000000000000
χ564-44-400000040022−224-40000-40000000022−2222−22−4i4i00−2i22i2−2i22i200000000000000000000000000000000
χ574-44-4000000400−22224-40000-400000000−2222−22224i−4i00−2i22i2−2i22i200000000000000000000000000000000
χ584-44-4000000400−22224-40000-400000000−2222−2222−4i4i002i2−2i22i2−2i200000000000000000000000000000000
χ594-4-44000000422−2200-440000-4000022−2222−220000004i−4i2i2−2i2−2i22i200000000000000000000000000000000
χ604-4-44000000422−2200-440000-4000022−2222−22000000−4i4i−2i22i22i2−2i200000000000000000000000000000000
χ614-4-440000004−222200-440000-40000−2222−22220000004i−4i−2i22i22i2−2i200000000000000000000000000000000
χ624-4-440000004−222200-440000-40000−2222−2222000000−4i4i2i2−2i2−2i22i200000000000000000000000000000000
χ63888888-8-8-8-8-20000-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ648888-8-888-8-8-20000-2-22222-22-2-22000000000000000000000000000000000000000000000000
χ6588-8-88-88-8-88-2000022-2-222-2-2-222000000000000000000000000000000000000000000000000
χ6688-8-8-88-88-88-200002222-2-2-2-22-22000000000000000000000000000000000000000000000000
χ678-88-8000000-20042−42-2225−2525−252000010−10−1010−22−220000000000000000000000000000000000000000
χ688-88-8000000-20042−42-22−2525−252520000−101010−10−22−220000000000000000000000000000000000000000
χ698-88-8000000-200−4242-2225−2525−2520000−101010−102−22−20000000000000000000000000000000000000000
χ708-88-8000000-200−4242-22−2525−25252000010−10−10102−22−20000000000000000000000000000000000000000
χ718-8-88000000-242−42002-225−25−252520000−22−2210−10−10100000000000000000000000000000000000000000
χ728-8-88000000-242−42002-2−252525−2520000−22−22−101010−100000000000000000000000000000000000000000
χ738-8-88000000-2−4242002-225−25−2525200002−22−2−101010−100000000000000000000000000000000000000000
χ748-8-88000000-2−4242002-2−252525−25200002−22−210−10−10100000000000000000000000000000000000000000

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