Finite Group Databasebeta

← Group #13024684

Character table — Group #13024684

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222444444444448888888888888161616161616161616162020202020204040404040404040404040404080808080
order12222244444510101010101010420202020202020202020202022101010101010101022224444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1-1ii−i−iii−i−ii−ii−i
χ10111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1-1−i−iii−i−iii−ii−ii
χ11111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1111-1-11
χ12111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-1-1-111-1-11111-1-1-111-1
χ13111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11-1-111ii−i−iii−i−i−ii−ii
χ14111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11-1-111−i−iii−i−iiii−ii−i
χ15111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111-111-1-111-1-1-1-111-111-1
χ16111111-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111-111-1-1-1-11111-1-11-1-11
χ1722222222-2-2222222222-2-2-2-2-22222-2-2-2-2000000000022-2-222-20000000000000000
χ1822222222-2-2222222222-2-2-2-2-22222-2-2-2-20000000000-2-222-2-220000000000000000
χ19222222-2-222-222222222-2-2-2-2-2-2-2-2-2222200000000002222-2-2-20000000000000000
χ20222222-2-222-222222222-2-2-2-2-2-2-2-2-222220000000000-2-2-2-22220000000000000000
χ2122-2-2-22002-20222-2-22-2-200000000022-2-200000000002-22-20000000i2−i2i2−i2i2−i2i2−i20000
χ2222-2-2-22002-20222-2-22-2-200000000022-2-200000000002-22-20000000−i2i2−i2i2−i2i2−i2i20000
χ2322-2-2-22002-20222-2-22-2-200000000022-2-20000000000-22-2200000002−22−2−22−220000
χ2422-2-2-22002-20222-2-22-2-200000000022-2-20000000000-22-220000000−22−222−22−20000
χ2522-2-2-2200-220222-2-22-2-2000000000-2-22200000000002-2-2200000002−2−222−2−220000
χ2622-2-2-2200-220222-2-22-2-2000000000-2-22200000000002-2-220000000−222−2−222−20000
χ2722-2-2-2200-220222-2-22-2-2000000000-2-2220000000000-222-20000000i2−i2−i2i2−i2i2i2−i20000
χ2822-2-2-2200-220222-2-22-2-2000000000-2-2220000000000-222-20000000−i2i2i2−i2i2−i2−i2i20000
χ2944444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-100000000000000000000000
χ3044444444444-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-1-1-1-1-4-41111111100000000000000000000000
χ3144444444-4-44-1-1-1-1-1-1-1-1-41111-1-1-1-111110055−5−555−5−500000000000000000000000
χ3244444444-4-44-1-1-1-1-1-1-1-1-41111-1-1-1-1111100−5−555−5−55500000000000000000000000
χ33444444-4-444-4-1-1-1-1-1-1-1-1-411111111-1-1-1-10055−5−5−5−55500000000000000000000000
χ34444444-4-444-4-1-1-1-1-1-1-1-1-411111111-1-1-1-100−5−55555−5−500000000000000000000000
χ35444444-4-4-4-4-4-1-1-1-1-1-1-1-14-1-1-1-1111111114-4-1-1-1-1111100000000000000000000000
χ36444444-4-4-4-4-4-1-1-1-1-1-1-1-14-1-1-1-111111111-441111-1-1-1-100000000000000000000000
χ374444-4-44400-44-4-4-4-44440000044-4-40000000000000000000000000000000000000
χ384444-4-44400-4-11111-1-1-1055−5−5-1-1115−55−500−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−ζ3600000000000000000000000
χ394444-4-44400-4-11111-1-1-1055−5−5-1-1115−55−500ζ4−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+ζ3600000000000000000000000
χ404444-4-44400-4-11111-1-1-10−5−555-1-111−55−5500−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+ζ3600000000000000000000000
χ414444-4-44400-4-11111-1-1-10−5−555-1-111−55−5500ζ4+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−ζ3600000000000000000000000
χ424444-4-4-4-40044-4-4-4-444400000-4-4440000000000000000000000000000000000000
χ434444-4-4-4-4004-11111-1-1-1055−5−511-1-1−55−5500−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+ζ3600000000000000000000000
χ444444-4-4-4-4004-11111-1-1-1055−5−511-1-1−55−5500ζ4−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−ζ3600000000000000000000000
χ454444-4-4-4-4004-11111-1-1-10−5−55511-1-15−55−500−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−ζ3600000000000000000000000
χ464444-4-4-4-4004-11111-1-1-10−5−55511-1-15−55−500ζ4+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+ζ3600000000000000000000000
χ4744-4-44-4000004-4-4444-4-40000000000000000000000000004i−4i00000000000000000
χ4844-4-44-4000004-4-4444-4-4000000000000000000000000000−4i4i00000000000000000
χ494-4-44004-400040000-44-4000004-4000000000000000000000002-22-2000000000000
χ504-4-44004-400040000-44-4000004-400000000000000000000000-22-22000000000000
χ514-4-4400-4400040000-44-400000-44000000000000000000000002-2-22000000000000
χ524-4-4400-4400040000-44-400000-4400000000000000000000000-222-2000000000000
χ5388-8-88-800000-222-2-2-22200000000025−25−2525000000000000000000000000000000000
χ5488-8-88-800000-222-2-2-222000000000−252525−25000000000000000000000000000000000
χ5588-8-8-88008-80-2-2-222-222000000000-2-222000000000000000000000000000000000
χ5688-8-8-8800-880-2-2-222-22200000000022-2-2000000000000000000000000000000000
χ578-88-8000000080000-8-880000000000000000000000000000000000000000000000
χ588-88-80000000-225−2525−2522-20−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ3600000000000000000000000000000000000000000
χ598-88-80000000-225−2525−2522-202ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ3600000000000000000000000000000000000000000
χ608-88-80000000-2−2525−252522-20−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ3600000000000000000000000000000000000000000
χ618-88-80000000-2−2525−252522-202ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ3600000000000000000000000000000000000000000
χ628-8-88008-8000-225−25−25252-2200000-2225−250000000000000000000000000000000000000
χ638-8-88008-8000-2−252525−252-2200000-22−25250000000000000000000000000000000000000
χ648-8-8800-88000-225−25−25252-22000002-2−25250000000000000000000000000000000000000
χ658-8-8800-88000-2−252525−252-22000002-225−250000000000000000000000000000000000000

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