Finite Group Databasebeta

← Group #13013902

Character table — Group #13013902

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order122222444444445101010101010102020202020202020202020208888888844202020202020202088881616161616161616161616161616161644
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-111-1-111-1-1i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−iii−i−ii−i
χ101-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-111-1-111-1-1i−iiiii−i−i−i−i11-1-1-1-111-1-111−i−iii−i−iiii−i
χ111-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-111-1-111-1-1−ii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii−ii
χ121-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-111-1-111-1-1−ii−i−i−i−iiiii11-1-1-1-111-1-111ii−i−iii−i−i−ii
χ131-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-111i−iiiii−i−i−i−i-1-111ii−i−i−i−iii-1-11111-1-1−ii
χ141-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-111i−iiiii−i−i−i−i-1-111−i−iiiii−i−i11-1-1-1-111−ii
χ151-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-111−ii−i−i−i−iiiii-1-111ii−i−i−i−iii11-1-1-1-111i−i
χ161-1-111-1-1-11111-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-111-1-111−ii−i−i−i−iiiii-1-111−i−iiiii−i−i-1-11111-1-1i−i
χ172222222222-2-2-2-22222222222-2-2-2-222-2-2-2-222-2-2-2-22200000000002-22-2000000000000000000
χ182222222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-22222-2-20000000000-22-22000000000000000000
χ192222-2-22-22-200002222-2-2-2-22-200002-200000022220000000000000-20-200000000i2−i2i2−i2i2−i2i2−i200
χ202222-2-22-22-200002222-2-2-2-22-200002-200000022220000000000000-20-200000000−i2i2−i2i2−i2i2−i2i200
χ212222-2-22-22-200002222-2-2-2-22-200002-2000000-2-2-2-20000000000000202000000002−22−2−22−2200
χ222222-2-22-22-200002222-2-2-2-22-200002-2000000-2-2-2-2000000000000020200000000−22−222−22−200
χ232222-2-2-22-2200002222-2-2-2-2-220000-220000220000220000000000-20-20i2−i2i2−i2i2−i2i2−i20000000000
χ242222-2-2-22-2200002222-2-2-2-2-220000-220000220000220000000000-20-20−i2i2−i2i2−i2i2−i2i20000000000
χ252222-2-2-22-2200002222-2-2-2-2-220000-220000-2-20000-2-2000000000020202−22−2−22−220000000000
χ262222-2-2-22-2200002222-2-2-2-2-220000-220000-2-20000-2-200000000002020−22−222−22−20000000000
χ272-2-222-2-2-222-2-2222-2-2222-2-222-2-2-2-2-2-222222222-2-2-2-200000000002-2-22000000000000000000
χ282-2-222-2-2-222-2-2222-2-2222-2-222-2-2-2-2-2-22222-2-2-2-222220000000000-222-2000000000000000000
χ292-2-22-222-2-2200002-2-22-2-222-2200002-20000220000-2-20000000000-2020i2−i2−i2i2i2−i2−i2i20000000000
χ302-2-22-222-2-2200002-2-22-2-222-2200002-20000220000-2-20000000000-2020−i2i2i2−i2−i2i2i2−i20000000000
χ312-2-22-222-2-2200002-2-22-2-222-2200002-20000-2-2000022000000000020-202−2−22−222−20000000000
χ322-2-22-222-2-2200002-2-22-2-222-2200002-20000-2-2000022000000000020-20−222−22−2−220000000000
χ332-2-22-22-222-200002-2-22-2-2222-20000-2200000022-2-2000000000000020-200000000i2−i2−i2i2−i2i2i2−i200
χ342-2-22-22-222-200002-2-22-2-2222-20000-2200000022-2-2000000000000020-200000000−i2i2i2−i2i2−i2−i2i200
χ352-2-22-22-222-200002-2-22-2-2222-20000-22000000-2-2220000000000000-202000000002−2−222−2−2200
χ362-2-22-22-222-200002-2-22-2-2222-20000-22000000-2-2220000000000000-20200000000−222−2−222−200
χ3744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-10000000000000000000000
χ3844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4111111110000000000000000000000
χ394444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-11111-1-11111000000000055−5−555−5−50000000000000000000000
χ404444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-11111-1-111110000000000−5−555−5−5550000000000000000000000
χ41444444-4-4-4-4000044444444-4-40000-4-400000000000000000000000000000000000000000000
χ42444444-4-4-4-40000-1-1-1-1-1-1-1-11155−5−51155−5−50000000000−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−ζ360000000000000000000000
χ43444444-4-4-4-40000-1-1-1-1-1-1-1-11155−5−51155−5−50000000000ζ4−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+ζ360000000000000000000000
χ44444444-4-4-4-40000-1-1-1-1-1-1-1-111−5−55511−5−5550000000000−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+ζ360000000000000000000000
χ45444444-4-4-4-40000-1-1-1-1-1-1-1-111−5−55511−5−5550000000000ζ4+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−ζ360000000000000000000000
χ4644-4-40000002i−2i2i−2i44-4-40000002i−2i2i−2i002i−2i2i−2i2i2−2i222−2222−222i2−2i200000000000000000000000000000000
χ4744-4-40000002i−2i2i−2i44-4-40000002i−2i2i−2i002i−2i2i−2i−2i22i2−2222−2222−2i22i200000000000000000000000000000000
χ4844-4-4000000−2i2i−2i2i44-4-4000000−2i2i−2i2i00−2i2i−2i2i2i2−2i2−2222−22222i2−2i200000000000000000000000000000000
χ4944-4-4000000−2i2i−2i2i44-4-4000000−2i2i−2i2i00−2i2i−2i2i−2i22i222−2222−22−2i22i200000000000000000000000000000000
χ504-44-40000002i−2i−2i2i4-44-40000002i−2i2i−2i00−2i2i−2i2i2i2−2i2−222222−22−2i22i200000000000000000000000000000000
χ514-44-40000002i−2i−2i2i4-44-40000002i−2i2i−2i00−2i2i−2i2i−2i22i222−22−22222i2−2i200000000000000000000000000000000
χ524-44-4000000−2i2i2i−2i4-44-4000000−2i2i−2i2i002i−2i2i−2i2i2−2i222−22−2222−2i22i200000000000000000000000000000000
χ534-44-4000000−2i2i2i−2i4-44-4000000−2i2i−2i2i002i−2i2i−2i−2i22i2−222222−222i2−2i200000000000000000000000000000000
χ544-4-444-444-4-400004-4-4444-4-4-4-400004400000000000000000000000000000000000000000000
χ554-4-444-444-4-40000-111-1-1-1111155−5−5-1-1−5−5550000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000
χ564-4-444-444-4-40000-111-1-1-1111155−5−5-1-1−5−5550000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000
χ574-4-444-444-4-40000-111-1-1-11111−5−555-1-155−5−50000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000
χ584-4-444-444-4-40000-111-1-1-11111−5−555-1-155−5−50000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000
χ594-4-444-4-4-44444-4-4-111-1-1-111-1-1-1-1-1-1111111000000004i−4i−i−i−i−iiiii0000000000000000000000
χ604-4-444-4-4-44444-4-4-111-1-1-111-1-1-1-1-1-111111100000000−4i4iiiii−i−i−i−i0000000000000000000000
χ614-4-444-4-4-444-4-444-111-1-1-111-1-1111111-1-1-1-10000000000i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ624-4-444-4-4-444-4-444-111-1-1-111-1-1111111-1-1-1-10000000000−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ638888-8-88-88-80000-2-2-2-22222-220000-2200000000000000000000000000000000000000000000
χ648888-8-8-88-880000-2-2-2-222222-200002-200000000000000000000000000000000000000000000
χ6588-8-80000004i−4i4i−4i-2-22225−2525−2500−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000000000000000000
χ6688-8-80000004i−4i4i−4i-2-222−2525−252500−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000000000000000000
χ6788-8-8000000−4i4i−4i4i-2-22225−2525−25002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000000000000000000
χ6888-8-8000000−4i4i−4i4i-2-222−2525−2525002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000000000000000000
χ698-88-80000004i−4i−4i4i-22-2225−25−252500−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000000000000000000
χ708-88-80000004i−4i−4i4i-22-22−252525−2500−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000000000000000000
χ718-88-8000000−4i4i4i−4i-22-2225−25−2525002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000000000000000000
χ728-88-8000000−4i4i4i−4i-22-22−252525−25002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000000000000000000
χ738-8-88-888-8-880000-222-222-2-22-20000-2200000000000000000000000000000000000000000000
χ748-8-88-88-888-80000-222-222-2-2-2200002-200000000000000000000000000000000000000000000

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