Finite Group Databasebeta

← Group #13021088

Character table — Group #13021088

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order12222222444444510101010101010202020202020202020202020444444442410101010202020204444888888888888888824
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
χ911111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-1
χ1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-11
χ1211111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-11-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-11
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2222-2-2-2-22000000000022-2-2000000000000000000
χ182222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-22222-20000000000-2-222000000000000000000
χ1922222222-2-222-2-222222222-2-2-2-22222-2-2-2-2222-2-2-2-220000000000-2-222000000000000000000
χ2022222222-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-2-22222-2000000000022-2-2000000000000000000
χ2122-222-2-2-2002i−2i00222-2-22-2-200002i2i−2i−2i00000002-22-2000000000002i−2i00000000002−2i2−i22−2i2−i200
χ2222-222-2-2-2002i−2i00222-2-22-2-200002i2i−2i−2i00000002-22-2000000000002i−2i0000000000−22−i2i2−22−i2i200
χ2322-222-2-2-2002i−2i00222-2-22-2-200002i2i−2i−2i0000000-22-2200000000000−2i2i0000000000i2−i2−22−i2i22−200
χ2422-222-2-2-2002i−2i00222-2-22-2-200002i2i−2i−2i0000000-22-2200000000000−2i2i0000000000−i2i22−2i2−i2−2200
χ2522-222-2-2-200−2i2i00222-2-22-2-20000−2i−2i2i2i00000002-22-200000000000−2i2i00000000002−2−i2i22−2−i2i200
χ2622-222-2-2-200−2i2i00222-2-22-2-20000−2i−2i2i2i00000002-22-200000000000−2i2i0000000000−22i2−i2−22i2−i200
χ2722-222-2-2-200−2i2i00222-2-22-2-20000−2i−2i2i2i0000000-22-22000000000002i−2i0000000000i2−i22−2−i2i2−2200
χ2822-222-2-2-200−2i2i00222-2-22-2-20000−2i−2i2i2i0000000-22-22000000000002i−2i0000000000−i2i2−22i2−i22−200
χ292-2-22-22-2200002-222-22-2-2-220000000022-2-222-22-2-22-2000000000000002i−2i002i−2i000000000000
χ302-2-22-22-2200002-222-22-2-2-220000000022-2-222-22-2-22-200000000000000−2i2i00−2i2i000000000000
χ312-2-22-22-2200002-222-22-2-2-220000000022-2-2-2-22-222-22000000000000002-200-22000000000000
χ322-2-22-22-2200002-222-22-2-2-220000000022-2-2-2-22-222-2200000000000000-22002-2000000000000
χ332-2-22-22-220000-2222-22-2-2-2200000000-2-22222-2-222-2-200000000000000002i−2i002i−2i0000000000
χ342-2-22-22-220000-2222-22-2-2-2200000000-2-22222-2-222-2-20000000000000000−2i2i00−2i2i0000000000
χ352-2-22-22-220000-2222-22-2-2-2200000000-2-222-2-222-2-22200000000000000002-200-220000000000
χ362-2-22-22-220000-2222-22-2-2-2200000000-2-222-2-222-2-2220000000000000000-22002-20000000000
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
χ394444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000000055−5−555−5−50000000000000000000000
χ404444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000−5−555−5−5550000000000000000000000
χ4144444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-11111000000000055−5−5−5−5550000000000000000000000
χ4244444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-111110000000000−5−55555−5−50000000000000000000000
χ4344444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-1000000004-4-1-1-1-111110000000000000000000000
χ4444444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-100000000-441111-1-1-1-10000000000000000000000
χ45444-4-4-4-444-400004-4-4-4-444444-4-4000000000000000000000000000000000000000000000000
χ46444-4-4-4-444-40000-11111-1-1-1-1-1115−55−55−55−50000000000−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
χ47444-4-4-4-444-40000-11111-1-1-1-1-1115−55−55−55−50000000000ζ4−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
χ48444-4-4-4-444-40000-11111-1-1-1-1-111−55−55−55−550000000000−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
χ49444-4-4-4-444-40000-11111-1-1-1-1-111−55−55−55−550000000000ζ4+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
χ50444-4-4-4-44-4400004-4-4-4-4444-4-444000000000000000000000000000000000000000000000000
χ51444-4-4-4-44-440000-11111-1-1-111-1-15−55−5−55−550000000000−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−ζ360000000000000000000000
χ52444-4-4-4-44-440000-11111-1-1-111-1-15−55−5−55−550000000000ζ4+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+ζ360000000000000000000000
χ53444-4-4-4-44-440000-11111-1-1-111-1-1−55−555−55−50000000000−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+ζ360000000000000000000000
χ54444-4-4-4-44-440000-11111-1-1-111-1-1−55−555−55−50000000000ζ4−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−ζ360000000000000000000000
χ5544-4-4-444-40000004-4-4444-4-40000000000004-440000-400000000000000000000000000000000
χ5644-4-4-444-40000004-4-4444-4-4000000000000-44-40000400000000000000000000000000000000
χ574-444-4-44-400000044-4-44-44-400000000000000044-4-4000000000000000000000000000000000
χ584-444-4-44-400000044-4-44-44-4000000000000000-4-444000000000000000000000000000000000
χ594-44-444-4-40000004-444-4-44-40000000000004-4-40000400000000000000000000000000000000
χ604-44-444-4-40000004-444-4-44-4000000000000-4440000-400000000000000000000000000000000
χ614-4-4-44-4440000004-44-44-4-44000000000000000000000000000000004-4000000000000000000
χ624-4-4-44-4440000004-44-44-4-4400000000000000000000000000000000-44000000000000000000
χ6388-888-8-8-8008i−8i00-2-2-222-2220000−2i−2i2i2i00000000000000000000000000000000000000000000
χ6488-888-8-8-800−8i8i00-2-2-222-22200002i2i−2i−2i00000000000000000000000000000000000000000000
χ6588-8-8-888-8000000-222-2-2-22200002i5−2i5−2i52i500000000000000000000000000000000000000000000
χ6688-8-8-888-8000000-222-2-2-2220000−2i52i52i5−2i500000000000000000000000000000000000000000000
χ678-888-8-88-8000000-2-222-22-222i5−2i52i5−2i5000000000000000000000000000000000000000000000000
χ688-888-8-88-8000000-2-222-22-22−2i52i5−2i52i5000000000000000000000000000000000000000000000000
χ698-88-888-8-8000000-22-2-222-222i5−2i5−2i52i5000000000000000000000000000000000000000000000000
χ708-88-888-8-8000000-22-2-222-22−2i52i52i5−2i5000000000000000000000000000000000000000000000000
χ718-8-88-88-8800008-8-2-22-2222-200000000-2-2220000000000000000000000000000000000000000
χ728-8-88-88-880000-88-2-22-2222-20000000022-2-20000000000000000000000000000000000000000
χ738-8-8-88-888000000-22-22-222-20000000025−25−25250000000000000000000000000000000000000000
χ748-8-8-88-888000000-22-22-222-200000000−252525−250000000000000000000000000000000000000000

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