Finite Group Databasebeta

← Group #13024570

Character table — Group #13024570

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222444444444448888888888888161616161616161616162020202020204040404040404040404040404080808080
order12222222244510101010101010410101010202020202020202044202020202020202022444424444888888884444
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
χ91111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-111-111-1-111-1-111-1-11-11-1
χ101111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-111-1-111-111-1-1-1-111-1-111-11-11
χ111111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-111-1-11-1-111ii−i−i−i−iiii−i−ii
χ121111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-111-1-11-1-111−i−iiiii−i−i−iii−i
χ131111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-1-11111-1-111-1-1-11-11
χ141111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-1-111-1-111-1-1111-11-1
χ151111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-1111-1-1ii−i−i−i−iii−iii−i
χ161111-1-111-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ17222222222-2-222222222-22222-2-2-2-2-2-2-2-2000000000022-2-2-2-220000000000000000
χ18222222222-2-222222222-22222-2-2-2-2-2-2-2-20000000000-2-22222-20000000000000000
χ192222-2-222-22222222222-2-2-2-2-2-2-2-2-2222200000000002222-2-2-20000000000000000
χ202222-2-222-22222222222-2-2-2-2-2-2-2-2-222220000000000-2-2-2-22220000000000000000
χ2122-2-2002-202i−2i222-2-2-22-20000000002i2i−2i−2i00000000002-22i−2i0000000i2−i22−2i2−i22−20000
χ2222-2-2002-202i−2i222-2-2-22-20000000002i2i−2i−2i00000000002-22i−2i0000000−i2i2−22−i2i2−220000
χ2322-2-2002-202i−2i222-2-2-22-20000000002i2i−2i−2i0000000000-22−2i2i00000002−2−i2i2−22i2−i20000
χ2422-2-2002-202i−2i222-2-2-22-20000000002i2i−2i−2i0000000000-22−2i2i0000000−22i2−i22−2−i2i20000
χ2522-2-2002-20−2i2i222-2-2-22-2000000000−2i−2i2i2i00000000002-2−2i2i0000000i2−i2−22i2−i2−220000
χ2622-2-2002-20−2i2i222-2-2-22-2000000000−2i−2i2i2i00000000002-2−2i2i0000000−i2i22−2−i2i22−20000
χ2722-2-2002-20−2i2i222-2-2-22-2000000000−2i−2i2i2i0000000000-222i−2i00000002−2i2−i2−22−i2i20000
χ2822-2-2002-20−2i2i222-2-2-22-2000000000−2i−2i2i2i0000000000-222i−2i0000000−22−i2i22−2i2−i20000
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
χ31444444444-4-4-1-1-1-1-1-1-1-1-4-1-1-1-1111111110055−5−555−5−500000000000000000000000
χ32444444444-4-4-1-1-1-1-1-1-1-1-4-1-1-1-11111111100−5−555−5−55500000000000000000000000
χ33444444-4-4-4004-4-44-4-444044-4-400000000000000000000000000000000000000000
χ34444444-4-4-400-111-111-1-10-1-11155−5−55−55−500−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
χ35444444-4-4-400-111-111-1-10-1-11155−5−55−55−500ζ4−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
χ36444444-4-4-400-111-111-1-10-1-111−5−555−55−5500−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
χ37444444-4-4-400-111-111-1-10-1-111−5−555−55−5500ζ4+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
χ384444-4-444-444-1-1-1-1-1-1-1-1-411111111-1-1-1-10055−5−5−5−55500000000000000000000000
χ394444-4-444-444-1-1-1-1-1-1-1-1-411111111-1-1-1-100−5−55555−5−500000000000000000000000
χ404444-4-444-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-111114-4-1-1-1-1111100000000000000000000000
χ414444-4-444-4-4-4-1-1-1-1-1-1-1-141111-1-1-1-11111-441111-1-1-1-100000000000000000000000
χ424444-4-4-4-44004-4-44-4-4440-4-44400000000000000000000000000000000000000000
χ434444-4-4-4-4400-111-111-1-1011-1-155−5−5−55−5500−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
χ444444-4-4-4-4400-111-111-1-1011-1-155−5−5−55−5500ζ4−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
χ454444-4-4-4-4400-111-111-1-1011-1-1−5−5555−55−500−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
χ464444-4-4-4-4400-111-111-1-1011-1-1−5−5555−55−500ζ4+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
χ4744-4-400-440004-4-4-4444-40000000000000000000000000004i−4i00000000000000000
χ4844-4-400-440004-4-4-4444-4000000000000000000000000000−4i4i00000000000000000
χ494-4-444-400000400400-4-404-40000000000000000000000000002i−2i2i−2i000000000000
χ504-4-444-400000400400-4-404-4000000000000000000000000000−2i2i−2i2i000000000000
χ514-4-44-4400000400400-4-40-440000000000000000000000000002i−2i−2i2i000000000000
χ524-4-44-4400000400400-4-40-44000000000000000000000000000−2i2i2i−2i000000000000
χ5388-8-8008-808i−8i-2-2-2222-22000000000−2i−2i2i2i000000000000000000000000000000000
χ5488-8-8008-80−8i8i-2-2-2222-220000000002i2i−2i−2i000000000000000000000000000000000
χ5588-8-800-88000-2222-2-2-220000000002i5−2i5−2i52i5000000000000000000000000000000000
χ5688-8-800-88000-2222-2-2-22000000000−2i52i52i5−2i5000000000000000000000000000000000
χ578-88-80000000800-800-880000000000000000000000000000000000000000000000
χ588-88-80000000-225−25225−252-200000−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ360000000000000000000000000000000000000
χ598-88-80000000-225−25225−252-2000002ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ360000000000000000000000000000000000000
χ608-88-80000000-2−25252−25252-200000−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ360000000000000000000000000000000000000
χ618-88-80000000-2−25252−25252-2000002ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ360000000000000000000000000000000000000
χ628-8-888-800000-225−25-2−2525220-2225−2500000000000000000000000000000000000000000
χ638-8-888-800000-2−2525-225−25220-22−252500000000000000000000000000000000000000000
χ648-8-88-8800000-225−25-2−25252202-2−252500000000000000000000000000000000000000000
χ658-8-88-8800000-2−2525-225−252202-225−2500000000000000000000000000000000000000000

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