Finite Group Databasebeta

← Group #13026536

Character table — Group #13026536

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444444488888888888888881010101016161616161616162020202020202020202040408080808080808080
order12222244444451010101010101044442020202020202020202020204444202020202020202022222244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1ii−i−iii−i−i
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−iii−i−iii
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ911111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111i−ii−ii−ii−i
χ1011111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111−ii−ii−ii−ii
χ1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-11-11-1-11-11
χ1211111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-11-111-11-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-11-1-111-1-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-111-1-111-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111i−i−ii−iii−i
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111−iii−ii−i−ii
χ17222222-2-2000022222222002-200000000-2-2-2-22222000022-2-2-2-222-2-200000000000000
χ18222222-2-2000022222222002-200000000-2-2-2-2-2-2-2-2000022-2-222-2-22200000000000000
χ19222222-2-200002222222200-2200000000-2-2-2-222220000-2-222-2-2-2-22200000000000000
χ20222222-2-200002222222200-2200000000-2-2-2-2-2-2-2-20000-2-2222222-2-200000000000000
χ212-22-22-22-20000222-2-2-2-222i−2i000000000022-2-200002i2i−2i−2i0000002-22-22i2i−2i−2i0000000000
χ222-22-22-22-20000222-2-2-2-222i−2i000000000022-2-200002i2i−2i−2i000000-22-22−2i−2i2i2i0000000000
χ232-22-22-22-20000222-2-2-2-22−2i2i000000000022-2-20000−2i−2i2i2i0000002-22-2−2i−2i2i2i0000000000
χ242-22-22-22-20000222-2-2-2-22−2i2i000000000022-2-20000−2i−2i2i2i000000-22-222i2i−2i−2i0000000000
χ252-22-22-2-222i2i−2i−2i222-2-2-2-2200002i2i2i2i−2i−2i−2i−2i-2-222000000000000002-2-2200002i−2i00000000
χ262-22-22-2-222i2i−2i−2i222-2-2-2-2200002i2i2i2i−2i−2i−2i−2i-2-22200000000000000-222-20000−2i2i00000000
χ272-22-22-2-22−2i−2i2i2i222-2-2-2-220000−2i−2i−2i−2i2i2i2i2i-2-222000000000000002-2-220000−2i2i00000000
χ282-22-22-2-22−2i−2i2i2i222-2-2-2-220000−2i−2i−2i−2i2i2i2i2i-2-22200000000000000-222-200002i−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
χ3144444444-4-4-4-4-1-1-1-1-1-1-1-144-4-411111111-1-1-1-10000-1-1-1-1111100000000000000000000
χ3244444444-4-4-4-4-1-1-1-1-1-1-1-1-4-44411111111-1-1-1-100001111-1-1-1-100000000000000000000
χ33444444-4-40000-1-1-1-1-1-1-1-1004-455−5−555−5−5111100005−55−5-1-11100000000000000000000
χ34444444-4-40000-1-1-1-1-1-1-1-1004-4−5−555−5−55511110000−55−55-1-11100000000000000000000
χ35444444-4-40000-1-1-1-1-1-1-1-100-4455−5−555−5−511110000−55−5511-1-100000000000000000000
χ36444444-4-40000-1-1-1-1-1-1-1-100-44−5−555−5−555111100005−55−511-1-100000000000000000000
χ374444-4-40000004-4-44-4-444000000000000000044-4-40000000000000000000000000000
χ384444-4-40000004-4-44-4-4440000000000000000-4-4440000000000000000000000000000
χ3944-4-400002i−2i2i−2i400-4004-400002i−2i2i−2i2i−2i2i−2i0000004i−4i000000000000002-22-20000000000
χ4044-4-400002i−2i2i−2i400-4004-400002i−2i2i−2i2i−2i2i−2i000000−4i4i00000000000000-22-220000000000
χ4144-4-40000−2i2i−2i2i400-4004-40000−2i2i−2i2i−2i2i−2i2i0000004i−4i00000000000000-22-220000000000
χ4244-4-40000−2i2i−2i2i400-4004-40000−2i2i−2i2i−2i2i−2i2i000000−4i4i000000000000002-22-20000000000
χ434-44-44-44-40000-1-1-11111-14i−4i00i5i5−i5−i5−i5−i5i5i5-1-1110000−i−iii5−55−500000000000000000000
χ444-44-44-44-40000-1-1-11111-14i−4i00−i5−i5i5i5i5i5−i5−i5-1-1110000−i−iii−55−5500000000000000000000
χ454-44-44-44-40000-1-1-11111-1−4i4i00i5i5−i5−i5−i5−i5i5i5-1-1110000ii−i−i−55−5500000000000000000000
χ464-44-44-44-40000-1-1-11111-1−4i4i00−i5−i5i5i5i5i5−i5−i5-1-1110000ii−i−i5−55−500000000000000000000
χ474-44-44-4-444i4i−4i−4i-1-1-11111-10000−i−i−i−iiiii11-1-10000i5−i5−i5i55−5−5500000000000000000000
χ484-44-44-4-444i4i−4i−4i-1-1-11111-10000−i−i−i−iiiii11-1-10000−i5i5i5−i5−555−500000000000000000000
χ494-44-44-4-44−4i−4i4i4i-1-1-11111-10000iiii−i−i−i−i11-1-10000i5−i5−i5i5−555−500000000000000000000
χ504-44-44-4-44−4i−4i4i4i-1-1-11111-10000iiii−i−i−i−i11-1-10000−i5i5i5−i55−5−5500000000000000000000
χ514-44-4-440000004-4-4-444-4400000000000000000000000000004-4000000000000000000
χ524-44-4-440000004-4-4-444-440000000000000000000000000000-44000000000000000000
χ534-4-4400002-2-22400400-4-400002-22-2-22-2200004i−4i00000000000000002i−2i−2i2i0000000000
χ544-4-4400002-2-22400400-4-400002-22-2-22-220000−4i4i0000000000000000−2i2i2i−2i0000000000
χ554-4-440000-222-2400400-4-40000-22-222-22-200004i−4i0000000000000000−2i2i2i−2i0000000000
χ564-4-440000-222-2400400-4-40000-22-222-22-20000−4i4i00000000000000002i−2i−2i2i0000000000
χ578888-8-8000000-222-222-2-200000000000025−2525−2500000000000000000000000000000000
χ588888-8-8000000-222-222-2-2000000000000−2525−252500000000000000000000000000000000
χ5988-8-800004i−4i4i−4i-225−25225−25-220000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000000000
χ6088-8-800004i−4i4i−4i-2−25252−2525-220000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000000000
χ6188-8-80000−4i4i−4i4i-225−25225−25-2200002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000000000
χ6288-8-80000−4i4i−4i4i-2−25252−2525-2200002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000000000000
χ638-88-8-88000000-2222-2-22-200000000000025−25−252500000000000000000000000000000000
χ648-88-8-88000000-2222-2-22-2000000000000−252525−2500000000000000000000000000000000
χ658-8-8800004-4-44-225−25-2−2525220000−1−51+5−1+51−51+5−1−51−5−1+5000000000000000000000000000000000000
χ668-8-8800004-4-44-2−2525-225−25220000−1+51−5−1−51+51−5−1+51+5−1−5000000000000000000000000000000000000
χ678-8-880000-444-4-225−25-2−25252200001+5−1−51−5−1+5−1−51+5−1+51−5000000000000000000000000000000000000
χ688-8-880000-444-4-2−2525-225−252200001−5−1+51+5−1−5−1+51−5−1−51+5000000000000000000000000000000000000

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