Finite Group Databasebeta

← Group #13023931

Character table — Group #13023931

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122224444444444444888888888888888810101010101010101010161616161616161620202040404040404040404040404080808080
order1222444445888810101020202020444420202020404040404040404022444488882020202020202020488444416161616161616168888
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
χ91111-1-111-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1ii−i−iii−i−ii−ii−i
χ101111-1-111-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1−i−iii−i−iii−ii−ii
χ111111-1-111-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11
χ121111-1-111-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-111-1
χ131111-1-111-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111ii−i−iii−i−i−ii−ii
χ141111-1-111-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111−i−iii−i−iiii−ii−i
χ151111-1-111-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-111-1-1-1-111-111-1
χ161111-1-111-1111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1-1-1-11111-1-11-1-11
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
χ19222222-2-2-22000022222220000-2-2-2-2000000002222-2-2000000000000-2000000i2−i2i2−i2i2−i2i2−i20000
χ20222222-2-2-22000022222220000-2-2-2-2000000002222-2-2000000000000-2000000−i2i2−i2i2−i2i2−i2i20000
χ21222222-2-2-22000022222220000-2-2-2-200000000-2-2-2-22200000000000020000002−22−2−22−220000
χ22222222-2-2-22000022222220000-2-2-2-200000000-2-2-2-2220000000000002000000−22−222−22−20000
χ232222-2-222-22-2-222222-2-2-2-20000-2-222-2-2-2-2222222-2-2-2-22222000000002-2-20000000000000000
χ242222-2-222-22-2-222222-2-2-2-20000-2-222-2-2-2-22222-2-22222-2-2-2-200000000-2220000000000000000
χ252222-2-2-2-2220000222-2-2-2-2000022-2-20000000022-2-222000000000000-20000002−2−222−2−220000
χ262222-2-2-2-2220000222-2-2-2-2000022-2-20000000022-2-222000000000000-2000000−222−2−222−20000
χ272222-2-2-2-2220000222-2-2-2-2000022-2-200000000-2-222-2-20000000000002000000i2−i2−i2i2−i2i2i2−i20000
χ282222-2-2-2-2220000222-2-2-2-2000022-2-200000000-2-222-2-20000000000002000000−i2i2i2−i2i2−i2−i2i20000
χ292-22-2002-2022-200-22-20000002i−2i002-222-2-20000002i−2i2i−2i2i2i−2i−2i00002i2i−2i−2i0002-200000000000000
χ302-22-2002-2022-200-22-20000002i−2i002-222-2-2000000−2i2i−2i2i−2i−2i2i2i00002i2i−2i−2i000-2200000000000000
χ312-22-2002-2022-200-22-2000000−2i2i002-222-2-20000002i−2i2i−2i2i2i−2i−2i0000−2i−2i2i2i000-2200000000000000
χ322-22-2002-2022-200-22-2000000−2i2i002-222-2-2000000−2i2i−2i2i−2i−2i2i2i0000−2i−2i2i2i0002-200000000000000
χ332-22-2002-202-2200-22-200002-200002-2-2-2220000002i−2i2i−2i−2i−2i2i2i22-2-20000000002i−2i000000000000
χ342-22-2002-202-2200-22-200002-200002-2-2-222000000−2i2i−2i2i2i2i−2i−2i22-2-2000000000−2i2i000000000000
χ352-22-2002-202-2200-22-20000-2200002-2-2-2220000002i−2i2i−2i−2i−2i2i2i-2-222000000000−2i2i000000000000
χ362-22-2002-202-2200-22-20000-2200002-2-2-222000000−2i2i−2i2i2i2i−2i−2i-2-2220000000002i−2i000000000000
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
χ414444-4-444-4-144-4-4-1-1-1111144-4-411-1-1-1-1-1-111110000000000-1-1-1-111110000000000000000000
χ424444-4-444-4-144-4-4-1-1-11111-4-44411-1-1-1-1-1-1111100000000001111-1-1-1-10000000000000000000
χ434444-4-444-4-1-4-444-1-1-11111000011-1-11111-1-1-1-100000000005−55−5−55−550000000000000000000
χ444444-4-444-4-1-4-444-1-1-11111000011-1-11111-1-1-1-10000000000−55−555−55−50000000000000000000
χ4544-4-44-4000400004-4-444-4-4000000000000000000000022−2222−2200000000022−220000000000000000
χ4644-4-44-4000400004-4-444-4-40000000000000000000000−2222−2222000000000−22220000000000000000
χ4744-4-4-44000400004-4-4-4-444000000000000000000000022−2222−22000000000−22220000000000000000
χ4844-4-4-44000400004-4-4-4-4440000000000000000000000−2222−222200000000022−220000000000000000
χ494-44-4004-40-14-4001-11i5−i5i5−i5004i−4ii5−i5-11-1-111i5i5−i5−i500000000005−5−55−i−iii0000000000000000000
χ504-44-4004-40-14-4001-11i5−i5i5−i500−4i4ii5−i5-11-1-111i5i5−i5−i50000000000−555−5ii−i−i0000000000000000000
χ514-44-4004-40-14-4001-11−i5i5−i5i5004i−4i−i5i5-11-1-111−i5−i5i5i50000000000−555−5−i−iii0000000000000000000
χ524-44-4004-40-14-4001-11−i5i5−i5i500−4i4i−i5i5-11-1-111−i5−i5i5i500000000005−5−55ii−i−i0000000000000000000
χ534-44-4004-40-1-44001-11i5−i5i5−i54-400i5−i5-1111-1-1−i5−i5i5i50000000000-1-111i5−i5−i5i50000000000000000000
χ544-44-4004-40-1-44001-11i5−i5i5−i5-4400i5−i5-1111-1-1−i5−i5i5i5000000000011-1-1−i5i5i5−i50000000000000000000
χ554-44-4004-40-1-44001-11−i5i5−i5i54-400−i5i5-1111-1-1i5i5−i5−i50000000000-1-111−i5i5i5−i50000000000000000000
χ564-44-4004-40-1-44001-11−i5i5−i5i5-4400−i5i5-1111-1-1i5i5−i5−i5000000000011-1-1i5−i5−i5i50000000000000000000
χ574-44-400-44040000-44-40000000000-4400000000004i−4i−4i4i0000000000000000000000000000000
χ584-44-400-44040000-44-40000000000-440000000000−4i4i4i−4i0000000000000000000000000000000
χ594-4-44000004002i2−2i2-4-4400000000000000002i2−2i22i2−2i24-400002i2−2i2−2i22i2000000000000000000000000000
χ604-4-44000004002i2−2i2-4-4400000000000000002i2−2i22i2−2i2-440000−2i22i22i2−2i2000000000000000000000000000
χ614-4-4400000400−2i22i2-4-440000000000000000−2i22i2−2i22i24-40000−2i22i22i2−2i2000000000000000000000000000
χ624-4-4400000400−2i22i2-4-440000000000000000−2i22i2−2i22i2-4400002i2−2i2−2i22i2000000000000000000000000000
χ63888888-8-8-8-20000-2-2-2-2-2-2-200002222000000000000000000000000000000000000000000000
χ648888-8-8-8-88-20000-2-2-222220000-2-222000000000000000000000000000000000000000000000
χ6588-8-88-8000-20000-222-2-2220000000010−1010−1010−10−10100000000000000000000000000000000000000
χ6688-8-88-8000-20000-222-2-22200000000−1010−1010−101010−100000000000000000000000000000000000000
χ6788-8-8-88000-20000-22222-2-20000000010−1010−10−101010−100000000000000000000000000000000000000
χ6888-8-8-88000-20000-22222-2-200000000−1010−101010−10−10100000000000000000000000000000000000000
χ698-88-800-880-200002-222i5−2i52i5−2i50000−2i52i52-2000000000000000000000000000000000000000000000
χ708-88-800-880-200002-22−2i52i5−2i52i500002i5−2i52-2000000000000000000000000000000000000000000000
χ718-8-8800000-2004i2−4i222-22i5−2i5−2i52i50000000010−10−1010−i2i2−i2i20000000000000000000000000000000000000
χ728-8-8800000-2004i2−4i222-2−2i52i52i5−2i500000000−101010−10−i2i2−i2i20000000000000000000000000000000000000
χ738-8-8800000-200−4i24i222-22i5−2i5−2i52i500000000−101010−10i2−i2i2−i20000000000000000000000000000000000000
χ748-8-8800000-200−4i24i222-2−2i52i52i5−2i50000000010−10−1010i2−i2i2−i20000000000000000000000000000000000000

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