Finite Group Databasebeta

← Group #13026405

Character table — Group #13026405

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444444488888888888888881010101016161616161616162020202020202020202040408080808080808080
order12222244444451010101010101044442020202020202020202020204444202020202020202044444444442288888888
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
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−i
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1
χ911111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11-11-11-11-1
χ1011111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-11-11-11-11
χ1111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111i−ii−i−ii−ii
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−ii−iii−ii−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−i−iii−i−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−iii−i−iii−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
χ17222222-2-20000222222222-200-2-2-2-200000000222222-2-20000-2-22-200002-20000000000
χ18222222-2-20000222222222-200-2-2-2-200000000-2-2-2-222-2-2000022-220000-220000000000
χ19222222-2-2000022222222-2200-2-2-2-2000000002222-2-2220000-2-2-220000-220000000000
χ20222222-2-2000022222222-2200-2-2-2-200000000-2-2-2-2-2-2220000222-200002-20000000000
χ212-2-222-22-200002-2-2222-2-2002i−2i22-2-200000000000000002i2i−2i−2i002-22i2i−2i−2i-220000000000
χ222-2-222-22-200002-2-2222-2-2002i−2i22-2-200000000000000002i2i−2i−2i00-22−2i−2i2i2i2-20000000000
χ232-2-222-22-200002-2-2222-2-200−2i2i22-2-20000000000000000−2i−2i2i2i002-2−2i−2i2i2i-220000000000
χ242-2-222-22-200002-2-2222-2-200−2i2i22-2-20000000000000000−2i−2i2i2i00-222i2i−2i−2i2-20000000000
χ252-2-222-2-2222-2-22-2-2222-2-20000-2-2222222-2-2-2-200000000000000220000-2-22-200000000
χ262-2-222-2-2222-2-22-2-2222-2-20000-2-2222222-2-2-2-200000000000000-2-2000022-2200000000
χ272-2-222-2-22-2-2222-2-2222-2-20000-2-222-2-2-2-2222200000000000000220000-2-2-2200000000
χ282-2-222-2-22-2-2222-2-2222-2-20000-2-222-2-2-2-2222200000000000000-2-20000222-200000000
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
χ374444-4-40000004-4-44-4-444000000000000000044-4-40000000000000000000000000000
χ384444-4-40000004-4-44-4-4440000000000000000-4-4440000000000000000000000000000
χ3944-4-400002i−2i2i−2i400-4004-4000000002i−2i2i−2i2i−2i2i−2i004i−4i0000000000002-22-2000000000000
χ4044-4-400002i−2i2i−2i400-4004-4000000002i−2i2i−2i2i−2i2i−2i00−4i4i000000000000-22-22000000000000
χ4144-4-40000−2i2i−2i2i400-4004-400000000−2i2i−2i2i−2i2i−2i2i004i−4i000000000000-22-22000000000000
χ4244-4-40000−2i2i−2i2i400-4004-400000000−2i2i−2i2i−2i2i−2i2i00−4i4i0000000000002-22-2000000000000
χ434-44-400002i−2i−2i2i400-400-44000000002i−2i2i−2i−2i2i−2i2i4-4000000000000002i−2i−2i2i000000000000
χ444-44-400002i−2i−2i2i400-400-44000000002i−2i2i−2i−2i2i−2i2i-4400000000000000−2i2i2i−2i000000000000
χ454-44-40000−2i2i2i−2i400-400-4400000000−2i2i−2i2i2i−2i2i−2i4-400000000000000−2i2i2i−2i000000000000
χ464-44-40000−2i2i2i−2i400-400-4400000000−2i2i−2i2i2i−2i2i−2i-44000000000000002i−2i−2i2i000000000000
χ474-4-444-44-40000-111-1-1-111004i−4i-1-11155−5−5−5−5550000i5−i5i5−i5−i−iii00000000000000000000
χ484-4-444-44-40000-111-1-1-111004i−4i-1-111−5−55555−5−50000−i5i5−i5i5−i−iii00000000000000000000
χ494-4-444-44-40000-111-1-1-11100−4i4i-1-11155−5−5−5−5550000−i5i5−i5i5ii−i−i00000000000000000000
χ504-4-444-44-40000-111-1-1-11100−4i4i-1-111−5−55555−5−50000i5−i5i5−i5ii−i−i00000000000000000000
χ514-4-444-4-4444-4-4-111-1-1-111000011-1-1-1-1-1-111110000i5−i5−i5i5i5−i5−i5i500000000000000000000
χ524-4-444-4-4444-4-4-111-1-1-111000011-1-1-1-1-1-111110000−i5i5i5−i5−i5i5i5−i500000000000000000000
χ534-4-444-4-44-4-444-111-1-1-111000011-1-11111-1-1-1-10000i5−i5−i5i5−i5i5i5−i500000000000000000000
χ544-4-444-4-44-4-444-111-1-1-111000011-1-11111-1-1-1-10000−i5i5i5−i5i5−i5−i5i500000000000000000000
χ554-4-44-440000004444-4-4-4-400000000000000000000000000004i−4i000000000000000000
χ564-4-44-440000004444-4-4-4-40000000000000000000000000000−4i4i000000000000000000
χ578888-8-8000000-222-222-2-2000025−2525−250000000000000000000000000000000000000000
χ588888-8-8000000-222-222-2-20000−2525−25250000000000000000000000000000000000000000
χ5988-8-800004i−4i4i−4i-225−25225−25-2200000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ6088-8-800004i−4i4i−4i-2−25252−2525-2200000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ6188-8-80000−4i4i−4i4i-225−25225−25-22000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ6288-8-80000−4i4i−4i4i-2−25252−2525-22000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ638-88-800004i−4i−4i4i-225−252−25252-200000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000
χ648-88-800004i−4i−4i4i-2−2525225−252-200000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000
χ658-88-80000−4i4i4i−4i-225−252−25252-2000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000
χ668-88-80000−4i4i4i−4i-2−2525225−252-2000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000
χ678-8-88-88000000-2-2-2-22222000025−25−25250000000000000000000000000000000000000000
χ688-8-88-88000000-2-2-2-222220000−252525−250000000000000000000000000000000000000000

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