Finite Group Databasebeta

← Group #13014299

Character table — Group #13014299

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111224444448888881616161616161616161616161616162020202040404040404040404040808080808080
order12222244510101010102020202048820202020404040404040404044442288888888444444
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ4111111111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ51111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ61111111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9222222222222222222-200-2-2-2-2000000002222-2-200000000000000
χ10222222222222222222-200-2-2-2-200000000-2-2-2-22200000000000000
χ1122-2-22-22-22-22-22-222-2-200000000000000000002-222−2−222−2−2000000
χ1222-2-22-22-22-22-22-222-2-200000000000000000002-2−2−222−2−222000000
χ1322-2-22-22-22-22-22-222-2-20000000000000000000-22i2i2−i2−i2−i2−i2i2i2000000
χ1422-2-22-22-22-22-22-222-2-20000000000000000000-22−i2−i2i2i2i2i2−i2−i2000000
χ1522-2-22-2-222-22-22-2-2-2220000000000000002i−2i2i−2i0000000000001+i−1−i1−i−1+i
χ1622-2-22-2-222-22-22-2-2-2220000000000000002i−2i2i−2i000000000000−1−i1+i−1+i1−i
χ1722-2-22-2-222-22-22-2-2-222000000000000000−2i2i−2i2i0000000000001−i−1+i1+i−1−i
χ1822-2-22-2-222-22-22-2-2-222000000000000000−2i2i−2i2i000000000000−1+i1−i−1−i1+i
χ1944444444-1-1-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2044444444-1-1-1-1-1-1-1-1-1-14-4-4-1-1-1-11111111100000000000000000000
χ2144444444-1-1-1-1-1-1-1-1-1-1-40011115555−5−5−5−500000000000000000000
χ2244444444-1-1-1-1-1-1-1-1-1-1-4001111−5−5−5−5555500000000000000000000
χ23444444-4-4444444-4-4-4-400000000000000000000000000000000000
χ24444444-4-4-1-1-1-1-1-1111100055−5−5−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ3800000000000000000000
χ25444444-4-4-1-1-1-1-1-1111100055−5−5ζ6−ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ3800000000000000000000
χ26444444-4-4-1-1-1-1-1-11111000−5−555ζ6−ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ3800000000000000000000
χ27444444-4-4-1-1-1-1-1-11111000−5−555−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ3800000000000000000000
χ284444-4-4004444-4-40000000000000000000000000000000002-20000
χ294444-4-4004444-4-4000000000000000000000000000000000-220000
χ3044-4-4-44004-44-4-44000002i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ3144-4-4-44004-44-4-4400000−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ3244-4-4-4400-11-111-15−55−502i−2i−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ12−ζ14−ζ28ζ6−ζ12+ζ14+ζ28−ζ6−ζ12−ζ14+ζ28ζ6+ζ12+ζ14−ζ28ζ4−ζ22−ζ36−ζ38−ζ4+ζ22+ζ36+ζ38−ζ4−ζ22+ζ36−ζ38ζ4+ζ22−ζ36+ζ3800000000000000000000
χ3344-4-4-4400-11-111-15−55−502i−2iζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6−ζ12−ζ14+ζ28ζ6+ζ12+ζ14−ζ28−ζ6+ζ12−ζ14−ζ28ζ6−ζ12+ζ14+ζ28−ζ4−ζ22+ζ36−ζ38ζ4+ζ22−ζ36+ζ38ζ4−ζ22−ζ36−ζ38−ζ4+ζ22+ζ36+ζ3800000000000000000000
χ3444-4-4-4400-11-111-15−55−50−2i2i−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ12+ζ14+ζ28−ζ6+ζ12−ζ14−ζ28ζ6+ζ12+ζ14−ζ28−ζ6−ζ12−ζ14+ζ28−ζ4+ζ22+ζ36+ζ38ζ4−ζ22−ζ36−ζ38ζ4+ζ22−ζ36+ζ38−ζ4−ζ22+ζ36−ζ3800000000000000000000
χ3544-4-4-4400-11-111-15−55−50−2i2iζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6+ζ12+ζ14−ζ28−ζ6−ζ12−ζ14+ζ28ζ6−ζ12+ζ14+ζ28−ζ6+ζ12−ζ14−ζ28ζ4+ζ22−ζ36+ζ38−ζ4−ζ22+ζ36−ζ38−ζ4+ζ22+ζ36+ζ38ζ4−ζ22−ζ36−ζ3800000000000000000000
χ3644-4-4-4400-11-111-1−55−5502i−2iζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ4−ζ22−ζ36−ζ38−ζ4+ζ22+ζ36+ζ38−ζ4−ζ22+ζ36−ζ38ζ4+ζ22−ζ36+ζ38−ζ6−ζ12−ζ14+ζ28ζ6+ζ12+ζ14−ζ28−ζ6+ζ12−ζ14−ζ28ζ6−ζ12+ζ14+ζ2800000000000000000000
χ3744-4-4-4400-11-111-1−55−5502i−2i−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ4−ζ22+ζ36−ζ38ζ4+ζ22−ζ36+ζ38ζ4−ζ22−ζ36−ζ38−ζ4+ζ22+ζ36+ζ38−ζ6+ζ12−ζ14−ζ28ζ6−ζ12+ζ14+ζ28−ζ6−ζ12−ζ14+ζ28ζ6+ζ12+ζ14−ζ2800000000000000000000
χ3844-4-4-4400-11-111-1−55−550−2i2iζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ4+ζ22+ζ36+ζ38ζ4−ζ22−ζ36−ζ38ζ4+ζ22−ζ36+ζ38−ζ4−ζ22+ζ36−ζ38ζ6+ζ12+ζ14−ζ28−ζ6−ζ12−ζ14+ζ28ζ6−ζ12+ζ14+ζ28−ζ6+ζ12−ζ14−ζ2800000000000000000000
χ3944-4-4-4400-11-111-1−55−550−2i2i−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ4+ζ22−ζ36+ζ38−ζ4−ζ22+ζ36−ζ38−ζ4+ζ22+ζ36+ζ38ζ4−ζ22−ζ36−ζ38ζ6−ζ12+ζ14+ζ28−ζ6+ζ12−ζ14−ζ28ζ6+ζ12+ζ14−ζ28−ζ6−ζ12−ζ14+ζ2800000000000000000000
χ404-44-4000044-4-40000000000000000000002i−2i−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ414-44-4000044-4-40000000000000000000002i−2i−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ424-44-4000044-4-4000000000000000000000−2i2i2i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ434-44-4000044-4-4000000000000000000000−2i2i2i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ444-4-4400004-4-4400000000000000000000022-2-200i2−i2−i2i2−i2i2i2−i2000000
χ454-4-4400004-4-4400000000000000000000022-2-200−i2i2i2−i2i2−i2−i2i2000000
χ464-4-4400004-4-44000000000000000000000-2-222002−2−222−2−22000000
χ474-4-4400004-4-44000000000000000000000-2-22200−222−2−222−2000000
χ488888-8-800-2-2-2-22225−25−252500000000000000000000000000000000000
χ498888-8-800-2-2-2-222−252525−2500000000000000000000000000000000000
χ5088-8-88-88-8-22-22-22-2-22200000000000000000000000000000000000
χ5188-8-88-8-88-22-22-2222-2-200000000000000000000000000000000000
χ5216-1616-160000-4-44400000000000000000000000000000000000000000
χ5316-16-16160000-444-400000000000000000000000000000000000000000

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