Finite Group Databasebeta

← Group #13027408

Character table — Group #13027408

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122222224444444455888888888888881010101010101016162020202032323232404040404040404040404040404040408080
order1224488884458810101044202020202020404040404040404022488882444881010202044448888161616161616161624
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111-1-111111111111111-1-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i-1-1
χ611111111111111111-1-111111111111111-1-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii-1-1
χ711111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii11
χ811111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iiiiiii−i−i−i−i11
χ91111111-1-1-1-111-111111-1-1-1-1111111-1-1-1-1111-1-1111-1-1-11-111-1-11111-1-1-1-111-1-111-1-1-11
χ101111111-1-1-1-111-111111-1-1-1-1111111-1-1-1-1111-1-1111-1-1-11-111-1-1-1-1-1-11111-1-111-1-111-11
χ111111111-1-1-1-111-111111-1-1-1-1111111-1-1-1-1111-1-111-11-1-11-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ121111111-1-1-1-111-111111-1-1-1-1111111-1-1-1-1111-1-111-11-1-11-1-1-111-1-1-1-1111111-1-111-1-11-1
χ131111111-1-1-1-111-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-11-111-1111-1-1ii−i−i−i−iiiii−i−i−i−iii1-1
χ141111111-1-1-1-111-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-11-111-1111-1-1−i−iiiii−i−i−i−iiiii−i−i1-1
χ151111111-1-1-1-111-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1111-11-1-111ii−i−i−i−iii−i−iiiii−i−i-11
χ161111111-1-1-1-111-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1111-11-1-111−i−iiiii−i−iii−i−i−i−iii-11
χ1722222-2-222-2-22-2222222-2-2-2-222-2-2-2-2222222222-2-200-2-2-220000000000000000000000
χ1822222-2-222-2-22-22222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-22200222-20000000000000000000000
χ1922222-2-2-2-2222-2-222222222222-2-2-2-2-2-2-2-2222-2-2-2-20022-2-20000000000000000000000
χ2022222-2-2-2-2222-2-2222-2-2222222-2-2-2-2-2-2-2-2-2-2-2222200-2-2220000000000000000000000
χ2122-22-200220020-2-2-222200002-2000022-2-2-22-2220000000-20000000000002−22−22−22−200
χ2222-22-200220020-2-2-222200002-2000022-2-2-22-2220000000-2000000000000−22−22−22−2200
χ2322-22-200220020-2-2-22-2-200002-2000022-2-22-22-2-200000002000000000000i2−i2i2−i2−i2i2−i2i200
χ2422-22-200220020-2-2-22-2-200002-2000022-2-22-22-2-200000002000000000000−i2i2−i2i2i2−i2i2−i200
χ2522-22-200-2-200202-2-222200002-20000-2-222-22-2-2-2000000020000000000002−2−222−2−2200
χ2622-22-200-2-200202-2-222200002-20000-2-222-22-2-2-200000002000000000000−222−2−222−200
χ2722-22-200-2-200202-2-22-2-200002-20000-2-2222-22220000000-2000000000000i2−i2−i2i2−i2i2i2−i200
χ2822-22-200-2-200202-2-22-2-200002-20000-2-2222-22220000000-2000000000000−i2i2i2−i2i2−i2−i2i200
χ2922-2-222200002-20-2-22220000-2222-2-200002-2-200220000-20000000002-22-20000000000
χ3022-2-222200002-20-2-22220000-2222-2-200002-2-200220000-2000000000-22-220000000000
χ3122-2-222200002-20-2-22-2-20000-2222-2-20000-22200-2-2000020000000002i−2i−2i2i0000000000
χ3222-2-222200002-20-2-22-2-20000-2222-2-20000-22200-2-200002000000000−2i2i2i−2i0000000000
χ3322-2-22-2-20000220-2-22220000-22-2-22200002-2-200-2-200002000002i−2i2i−2i00000000000000
χ3422-2-22-2-20000220-2-22220000-22-2-22200002-2-200-2-20000200000−2i2i−2i2i00000000000000
χ3522-2-22-2-20000220-2-22-2-20000-22-2-2220000-22200220000-2000002-2-2200000000000000
χ3622-2-22-2-20000220-2-22-2-20000-22-2-2220000-22200220000-200000-222-200000000000000
χ3744444444444-144-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000440000-1-1-1-1000000000000000000
χ3844444444444-144-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000-4-400001111000000000000000000
χ394444444-4-4-4-4-14-4-1-1-1001111-1-1-1-1-1-1111100000004-40000-1-111000000000000000000
χ404444444-4-4-4-4-14-4-1-1-1001111-1-1-1-1-1-111110000000-44000011-1-1000000000000000000
χ4144444-4-444-4-4-1-44-1-1-1001111-1-11111-1-1-1-100000000000005−55−5000000000000000000
χ4244444-4-444-4-4-1-44-1-1-1001111-1-11111-1-1-1-10000000000000−55−55000000000000000000
χ4344444-4-4-4-444-1-4-4-1-1-100-1-1-1-1-1-11111111100000000000005−5−55000000000000000000
χ4444444-4-4-4-444-1-4-4-1-1-100-1-1-1-1-1-1111111110000000000000−555−5000000000000000000
χ45444-4-4000000400444440000-4-400000000-4-4400000000000000000000000000000000
χ46444-4-4000000400444-4-40000-4-40000000044-400000000000000000000000000000000
χ474-400022−222i2−2i22i−2i40000-44i−4i2i2i−2i−2i0022−22002i2−2i20000022−222i2−2i2002-2000000000000000000000000
χ484-400022−222i2−2i22i−2i40000-4−4i4i2i2i−2i−2i0022−22002i2−2i200000−2222−2i22i200-22000000000000000000000000
χ494-400022−22−2i22i2−2i2i40000-44i−4i−2i−2i2i2i0022−2200−2i22i200000−22222i2−2i200-22000000000000000000000000
χ504-400022−22−2i22i2−2i2i40000-4−4i4i−2i−2i2i2i0022−2200−2i22i20000022−22−2i22i2002-2000000000000000000000000
χ514-4000−22222i2−2i2−2i2i40000-44i−4i−2i−2i2i2i00−2222002i2−2i20000022−22−2i22i200-22000000000000000000000000
χ524-4000−22222i2−2i2−2i2i40000-4−4i4i−2i−2i2i2i00−2222002i2−2i200000−22222i2−2i2002-2000000000000000000000000
χ534-4000−2222−2i22i22i−2i40000-44i−4i2i2i−2i−2i00−222200−2i22i200000−2222−2i22i2002-2000000000000000000000000
χ544-4000−2222−2i22i22i−2i40000-4−4i4i2i2i−2i−2i00−222200−2i22i20000022−222i2−2i200-22000000000000000000000000
χ55888-8-8000000-200-2-2-20025−2525−25220000000000000000000000000000000000000000000
χ56888-8-8000000-200-2-2-200−2525−2525220000000000000000000000000000000000000000000
χ5788-88-8008800-20-822-2000000-220000-2-22200000000000000000000000000000000000
χ5888-88-800-8-800-20822-2000000-22000022-2-200000000000000000000000000000000000
χ5988-8-88880000-2-8022-20000002-2-2-222000000000000000000000000000000000000000
χ6088-8-88-8-80000-28022-20000002-222-2-2000000000000000000000000000000000000000
χ618-800042−424i2−4i24i−4i-20025−25200−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ3800−2210−10−i2i2i10−i1000000000000000000000000000000000000
χ628-800042−424i2−4i24i−4i-200−2525200−2ζ22−2ζ38−2ζ6−2ζ142ζ22+2ζ382ζ6+2ζ1400−22−1010−i2i2−i10i1000000000000000000000000000000000000
χ638-800042−42−4i24i2−4i4i-20025−252002ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ3800−2210−10i2−i2−i10i1000000000000000000000000000000000000
χ648-800042−42−4i24i2−4i4i-200−25252002ζ22+2ζ382ζ6+2ζ14−2ζ22−2ζ38−2ζ6−2ζ1400−22−1010i2−i2i10−i1000000000000000000000000000000000000
χ658-8000−42424i2−4i2−4i4i-20025−252002ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ38002−2−1010−i2i2i10−i1000000000000000000000000000000000000
χ668-8000−42424i2−4i2−4i4i-200−25252002ζ22+2ζ382ζ6+2ζ14−2ζ22−2ζ38−2ζ6−2ζ14002−210−10−i2i2−i10i1000000000000000000000000000000000000
χ678-8000−4242−4i24i24i−4i-20025−25200−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38002−2−1010i2−i2−i10i1000000000000000000000000000000000000
χ688-8000−4242−4i24i24i−4i-200−2525200−2ζ22−2ζ38−2ζ6−2ζ142ζ22+2ζ382ζ6+2ζ14002−210−10i2−i2i10−i1000000000000000000000000000000000000

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