Finite Group Databasebeta

← Group #13026521

Character table — Group #13026521

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444444488888888888888881010101016161616161616162020202020202020202040408080808080808080
order12222222444451010101010101024441010101020202020202020202222101020202020202022224444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1i−ii−ii−ii−i
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−ii−ii−ii−ii
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-11
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-111-1
χ911111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ1011111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111
χ1111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii
χ1211111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i
χ1311111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111i−ii−i−ii−ii
χ1411111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111−ii−iii−ii−i
χ1511111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-11-1-11-111-1
χ1611111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-111-11-1-11
χ17222222-2-20000222222222-200-2-2-2-200000000222222-2-20000-2-2220000-2-20000000000
χ18222222-2-20000222222222-200-2-2-2-200000000-2-2-2-222-2-2000022-2-20000220000000000
χ19222222-2-2000022222222-2200-2-2-2-2000000002222-2-2220000-2-2-2-20000220000000000
χ20222222-2-2000022222222-2200-2-2-2-200000000-2-2-2-2-2-222000022220000-2-20000000000
χ212-22-22-22-20000222-22-2-2-2002i−2i22-2-200000000000000002i2i−2i−2i002-22i2i−2i−2i2-20000000000
χ222-22-22-22-20000222-22-2-2-2002i−2i22-2-200000000000000002i2i−2i−2i00-22−2i−2i2i2i-220000000000
χ232-22-22-22-20000222-22-2-2-200−2i2i22-2-20000000000000000−2i−2i2i2i002-2−2i−2i2i2i2-20000000000
χ242-22-22-22-20000222-22-2-2-200−2i2i22-2-20000000000000000−2i−2i2i2i00-222i2i−2i−2i-220000000000
χ252-22-22-2-222i2i−2i−2i222-22-2-2-20000-2-2222i2i2i2i−2i−2i−2i−2i000000000000002-20000-222i−2i00000000
χ262-22-22-2-222i2i−2i−2i222-22-2-2-20000-2-2222i2i2i2i−2i−2i−2i−2i00000000000000-2200002-2−2i2i00000000
χ272-22-22-2-22−2i−2i2i2i222-22-2-2-20000-2-222−2i−2i−2i−2i2i2i2i2i000000000000002-20000-22−2i2i00000000
χ282-22-22-2-22−2i−2i2i2i222-22-2-2-20000-2-222−2i−2i−2i−2i2i2i2i2i00000000000000-2200002-22i−2i00000000
χ29444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000
χ30444444444444-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000
χ3144444444-4-4-4-4-1-1-1-1-1-1-1-144-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000
χ3244444444-4-4-4-4-1-1-1-1-1-1-1-1-4-444-1-1-1-11111111100001111-1-1-1-100000000000000000000
χ33444444-4-40000-1-1-1-1-1-1-1-14-400111155−5−555−5−50000-1-1115−55−500000000000000000000
χ34444444-4-40000-1-1-1-1-1-1-1-14-4001111−5−555−5−5550000-1-111−55−5500000000000000000000
χ35444444-4-40000-1-1-1-1-1-1-1-1-4400111155−5−555−5−5000011-1-1−55−5500000000000000000000
χ36444444-4-40000-1-1-1-1-1-1-1-1-44001111−5−555−5−555000011-1-15−55−500000000000000000000
χ374444-4-40000004-4-444-4-44000000000000000044-4-40000000000000000000000000000
χ384444-4-40000004-4-444-4-440000000000000000-4-4440000000000000000000000000000
χ3944-4-400002i−2i2i−2i4004-400-4000000002i−2i2i−2i2i−2i2i−2i004-40000000000002i−2i2i−2i000000000000
χ4044-4-400002i−2i2i−2i4004-400-4000000002i−2i2i−2i2i−2i2i−2i00-44000000000000−2i2i−2i2i000000000000
χ4144-4-40000−2i2i−2i2i4004-400-400000000−2i2i−2i2i−2i2i−2i2i004-4000000000000−2i2i−2i2i000000000000
χ4244-4-40000−2i2i−2i2i4004-400-400000000−2i2i−2i2i−2i2i−2i2i00-440000000000002i−2i2i−2i000000000000
χ434-44-44-44-40000-1-1-11-1111004i−4i-1-111i5i5−i5−i5−i5−i5i5i500005−55−5−i−iii00000000000000000000
χ444-44-44-44-40000-1-1-11-1111004i−4i-1-111−i5−i5i5i5i5i5−i5−i50000−55−55−i−iii00000000000000000000
χ454-44-44-44-40000-1-1-11-111100−4i4i-1-111i5i5−i5−i5−i5−i5i5i50000−55−55ii−i−i00000000000000000000
χ464-44-44-44-40000-1-1-11-111100−4i4i-1-111−i5−i5i5i5i5i5−i5−i500005−55−5ii−i−i00000000000000000000
χ474-44-44-4-444i4i−4i−4i-1-1-11-1111000011-1-1−i−i−i−iiiii00005−5−55i5−i5−i5i500000000000000000000
χ484-44-44-4-444i4i−4i−4i-1-1-11-1111000011-1-1−i−i−i−iiiii0000−555−5−i5i5i5−i500000000000000000000
χ494-44-44-4-44−4i−4i4i4i-1-1-11-1111000011-1-1iiii−i−i−i−i00005−5−55−i5i5i5−i500000000000000000000
χ504-44-44-4-44−4i−4i4i4i-1-1-11-1111000011-1-1iiii−i−i−i−i0000−555−5i5−i5−i5i500000000000000000000
χ514-44-4-440000004-4-4-4444-400000000000000000000000000004-4000000000000000000
χ524-44-4-440000004-4-4-4444-40000000000000000000000000000-44000000000000000000
χ534-4-4400002-2-22400-4-4004000000002-22-2-22-224-4000000000000002-2-22000000000000
χ544-4-4400002-2-22400-4-4004000000002-22-2-22-22-4400000000000000-222-2000000000000
χ554-4-440000-222-2400-4-400400000000-22-222-22-24-400000000000000-222-2000000000000
χ564-4-440000-222-2400-4-400400000000-22-222-22-2-44000000000000002-2-22000000000000
χ578888-8-8000000-222-2-222-2000025−2525−250000000000000000000000000000000000000000
χ588888-8-8000000-222-2-222-20000−2525−25250000000000000000000000000000000000000000
χ5988-8-800004i−4i4i−4i-225−25-2225−25200000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ6088-8-800004i−4i4i−4i-2−2525-22−2525200000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ6188-8-80000−4i4i−4i4i-225−25-2225−252000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ6288-8-80000−4i4i−4i4i-2−2525-22−25252000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ638-88-8-88000000-2222-2-2-22000025−25−25250000000000000000000000000000000000000000
χ648-88-8-88000000-2222-2-2-220000−252525−250000000000000000000000000000000000000000
χ658-8-8800004-4-44-225−2522−2525-200000000−1−51+5−1+51−51+5−1−51−5−1+500000000000000000000000000000000
χ668-8-8800004-4-44-2−25252225−25-200000000−1+51−5−1−51+51−5−1+51+5−1−500000000000000000000000000000000
χ678-8-880000-444-4-225−2522−2525-2000000001+5−1−51−5−1+5−1−51+5−1+51−500000000000000000000000000000000
χ688-8-880000-444-4-2−25252225−25-2000000001−5−1+51+5−1−5−1+51−5−1−51+500000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.