Finite Group Databasebeta

← Group #13026245

Character table — Group #13026245

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122224444444444444888888888888888810101010101010101010161616161616161620202040404040404040404040404080808080
order1222444425888810101020202020224410102020404040404040404022224488881010101020202020488224416161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1
χ6111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ911111-1-11-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1ii−i−iii−i−ii−ii−i
χ1011111-1-11-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1−i−iii−i−iii−ii−ii
χ1111111-1-11-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11
χ1211111-1-11-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-111-1
χ1311111-1-11-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111ii−i−iii−i−i−ii−ii
χ1411111-1-11-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111−i−iii−i−iiii−ii−i
χ1511111-1-11-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-111-1-1-1-111-111-1
χ1611111-1-11-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-1-1-11111-1-11-1-11
χ172222222222-2-2-2-2222222200002222-2-2-2-2-2-2-2-2222222-2-2-2-2000000002-2-20000000000000000
χ182222222222-2-2-2-2222222200002222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2220000000000000000
χ1922222-2-22-22-2-222222-2-2-2-20000-2-222-2-2-2-2222222-2-2-2-22222000000002-2-20000000000000000
χ2022222-2-22-22-2-222222-2-2-2-20000-2-222-2-2-2-22222-2-22222-2-2-2-200000000-2220000000000000000
χ212222-222-2-22000022222220000-2-2-2-20000000022-2-222000000000000-2000000i2−i2i2−i2i2−i2i2−i20000
χ222222-222-2-22000022222220000-2-2-2-20000000022-2-222000000000000-2000000−i2i2−i2i2−i2i2−i2i20000
χ232222-222-2-22000022222220000-2-2-2-200000000-2-222-2-200000000000020000002−22−2−22−220000
χ242222-222-2-22000022222220000-2-2-2-200000000-2-222-2-20000000000002000000−22−222−22−20000
χ252222-2-2-2-2220000222-2-2-2-2000022-2-2000000002222-2-2000000000000-20000002−2−222−2−220000
χ262222-2-2-2-2220000222-2-2-2-2000022-2-2000000002222-2-2000000000000-2000000−222−2−222−20000
χ272222-2-2-2-2220000222-2-2-2-2000022-2-200000000-2-2-2-2220000000000002000000i2−i2−i2i2−i2i2i2−i20000
χ282222-2-2-2-2220000222-2-2-2-2000022-2-200000000-2-2-2-2220000000000002000000−i2i2i2−i2i2−i2−i2i20000
χ292-2-22-2002022-200-2-220000002-200-2222-2-20000002-22-222-2-2000022-2-20002-200000000000000
χ302-2-22-2002022-200-2-220000002-200-2222-2-2000000-22-22-2-222000022-2-2000-2200000000000000
χ312-2-22-2002022-200-2-22000000-2200-2222-2-20000002-22-222-2-20000-2-222000-2200000000000000
χ322-2-22-2002022-200-2-22000000-2200-2222-2-2000000-22-22-2-2220000-2-2220002-200000000000000
χ332-2-22-200202-2200-2-2200002-20000-22-2-2220000002-22-2-2-22222-2-20000000002-2000000000000
χ342-2-22-200202-2200-2-2200002-20000-22-2-222000000-22-2222-2-222-2-2000000000-22000000000000
χ352-2-22-200202-2200-2-220000-220000-22-2-2220000002-22-2-2-222-2-222000000000-22000000000000
χ362-2-22-200202-2200-2-220000-220000-22-2-222000000-22-2222-2-2-2-2220000000002-2000000000000
χ37444444444-14444-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-10000000000-1-1-1-1-1-1-1-10000000000000000000
χ38444444444-14444-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10000000000111111110000000000000000000
χ39444444444-1-4-4-4-4-1-1-1-1-1-1-10000-1-1-1-11111111100000000005−55−55−55−50000000000000000000
χ40444444444-1-4-4-4-4-1-1-1-1-1-1-10000-1-1-1-1111111110000000000−55−55−55−550000000000000000000
χ4144444-4-44-4-144-4-4-1-1-1111144-4-411-1-1-1-1-1-111110000000000-1-1-1-111110000000000000000000
χ4244444-4-44-4-144-4-4-1-1-11111-4-44411-1-1-1-1-1-1111100000000001111-1-1-1-10000000000000000000
χ4344444-4-44-4-1-4-444-1-1-11111000011-1-11111-1-1-1-100000000005−55−5−55−550000000000000000000
χ4444444-4-44-4-1-4-444-1-1-11111000011-1-11111-1-1-1-10000000000−55−555−55−50000000000000000000
χ4544-4-4000004002i2−2i24-4-400000000000000002i22i2−2i2−2i24-400002i2−2i22i2−2i2000000000000000000000000000
χ4644-4-4000004002i2−2i24-4-400000000000000002i22i2−2i2−2i2-440000−2i22i2−2i22i2000000000000000000000000000
χ4744-4-400000400−2i22i24-4-40000000000000000−2i2−2i22i22i24-40000−2i22i2−2i22i2000000000000000000000000000
χ4844-4-400000400−2i22i24-4-40000000000000000−2i2−2i22i22i2-4400002i2−2i22i2−2i2000000000000000000000000000
χ494-44-404i−4i0040000-44-44i4i−4i−4i00000000000000000000002i2−2i2−2i22i200000000022−220000000000000000
χ504-44-404i−4i0040000-44-44i4i−4i−4i0000000000000000000000−2i22i22i2−2i2000000000−22220000000000000000
χ514-44-40−4i4i0040000-44-4−4i−4i4i4i00000000000000000000002i2−2i2−2i22i2000000000−22220000000000000000
χ524-44-40−4i4i0040000-44-4−4i−4i4i4i0000000000000000000000−2i22i22i2−2i200000000022−220000000000000000
χ534-4-44400-4040000-4-4400000000004-400000000004-4-440000000000000000000000000000000
χ544-4-44400-4040000-4-4400000000004-40000000000-444-40000000000000000000000000000000
χ554-4-44-40040-14-40011-15−55−5004-45−51-1-1-1115−55−500000000005−5−55-1-1110000000000000000000
χ564-4-44-40040-14-40011-15−55−500-445−51-1-1-1115−55−50000000000−555−511-1-10000000000000000000
χ574-4-44-40040-14-40011-1−55−55004-4−551-1-1-111−55−550000000000−555−5-1-1110000000000000000000
χ584-4-44-40040-14-40011-1−55−5500-44−551-1-1-111−55−5500000000005−5−5511-1-10000000000000000000
χ594-4-44-40040-1-440011-15−55−54-4005−51-111-1-1−55−550000000000-1-1115−5−550000000000000000000
χ604-4-44-40040-1-440011-15−55−5-44005−51-111-1-1−55−55000000000011-1-1−555−50000000000000000000
χ614-4-44-40040-1-440011-1−55−554-400−551-111-1-15−55−50000000000-1-111−555−50000000000000000000
χ624-4-44-40040-1-440011-1−55−55-4400−551-111-1-15−55−5000000000011-1-15−5−550000000000000000000
χ638888-888-8-8-20000-2-2-2-2-2-2-200002222000000000000000000000000000000000000000000000
χ648888-8-8-8-88-20000-2-2-222220000-2-222000000000000000000000000000000000000000000000
χ6588-8-800000-2004i2−4i2-2222i5−2i5−2i52i50000000010−1010−10−i2−i2i2i20000000000000000000000000000000000000
χ6688-8-800000-2004i2−4i2-222−2i52i52i5−2i500000000−1010−1010−i2−i2i2i20000000000000000000000000000000000000
χ6788-8-800000-200−4i24i2-2222i5−2i5−2i52i500000000−1010−1010i2i2−i2−i20000000000000000000000000000000000000
χ6888-8-800000-200−4i24i2-222−2i52i52i5−2i50000000010−1010−10i2i2−i2−i20000000000000000000000000000000000000
χ698-88-808i−8i00-200002-22−2i−2i2i2i0000000010−10−1010i10−i10−i10i100000000000000000000000000000000000000
χ708-88-808i−8i00-200002-22−2i−2i2i2i00000000−101010−10−i10i10i10−i100000000000000000000000000000000000000
χ718-88-80−8i8i00-200002-222i2i−2i−2i0000000010−10−1010−i10i10i10−i100000000000000000000000000000000000000
χ728-88-80−8i8i00-200002-222i2i−2i−2i00000000−101010−10i10−i10−i10i100000000000000000000000000000000000000
χ738-8-88800-80-2000022-225−2525−250000−2525-22000000000000000000000000000000000000000000000
χ748-8-88800-80-2000022-2−2525−2525000025−25-22000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).