Finite Group Databasebeta

← Group #13014222

Character table — Group #13014222

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111224444448888881616161616161616161616161616162020202040404040404040404040808080808080
order124424245102020101010202020448202020202020202040404040224488888888882416161616
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ4111111111111111111111111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ5111111111111111111-1-11-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ6111111111111111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111
χ7111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ8111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ922222222222222222200-200000000-2-2-2-2222200000000-2-2000000
χ1022222222222222222200-200000000-2-2-2-2-2-2-2-20000000022000000
χ1122-2-22-22-222-2-2222-2-2-200000000000000022-2-2000000000000i2−i2i2−i2
χ1222-2-22-22-222-2-2222-2-2-200000000000000022-2-2000000000000−i2i2−i2i2
χ1322-2-22-22-222-2-2222-2-2-2000000000000000-2-2220000000000002−2−22
χ1422-2-22-22-222-2-2222-2-2-2000000000000000-2-222000000000000−222−2
χ1522-2-22-2-2222-2-22-2-222-200000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i000000
χ1622-2-22-2-2222-2-22-2-222-200000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i000000
χ1722-2-22-2-2222-2-22-2-222-20000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i000000
χ1822-2-22-2-2222-2-22-2-222-20000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i000000
χ1944444444-1-1-1-1-1-1-1-1-1-100-45555−5−5−5−5111100000000000000000000
χ2044444444-1-1-1-1-1-1-1-1-1-100-4−5−5−5−55555111100000000000000000000
χ2144444444-1-1-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2244444444-1-1-1-1-1-1-1-1-1-1-4-4411111111-1-1-1-100000000000000000000
χ23444444-4-444444-4-4-4-4400000000000000000000000000000000000
χ24444444-4-4-1-1-1-1-11111-1000−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−ζ3855−5−500000000000000000000
χ25444444-4-4-1-1-1-1-11111-1000ζ6−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+ζ38−5−55500000000000000000000
χ26444444-4-4-1-1-1-1-11111-1000ζ6−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+ζ3855−5−500000000000000000000
χ27444444-4-4-1-1-1-1-11111-1000−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−ζ38−5−55500000000000000000000
χ284444-4-4004444-40000-42-202-22-22-22-2000000000000000000000000
χ294444-4-4004444-40000-4-220-22-22-22-22000000000000000000000000
χ304444-4-400-1-1-1-115−55−512-20ζ6−ζ12−ζ14−ζ28−ζ6+ζ12+ζ14+ζ28−ζ6−ζ12+ζ14−ζ28ζ6+ζ12−ζ14+ζ28−ζ4+ζ22−ζ36−ζ38ζ4−ζ22+ζ36+ζ38−ζ4−ζ22−ζ36+ζ38ζ4+ζ22+ζ36−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000000000000
χ314444-4-400-1-1-1-115−55−512-20−ζ6−ζ12+ζ14−ζ28ζ6+ζ12−ζ14+ζ28ζ6−ζ12−ζ14−ζ28−ζ6+ζ12+ζ14+ζ28−ζ4−ζ22−ζ36+ζ38ζ4+ζ22+ζ36−ζ38−ζ4+ζ22−ζ36−ζ38ζ4−ζ22+ζ36+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000000000000
χ324444-4-400-1-1-1-115−55−51-220ζ6+ζ12−ζ14+ζ28−ζ6−ζ12+ζ14−ζ28−ζ6+ζ12+ζ14+ζ28ζ6−ζ12−ζ14−ζ28ζ4+ζ22+ζ36−ζ38−ζ4−ζ22−ζ36+ζ38ζ4−ζ22+ζ36+ζ38−ζ4+ζ22−ζ36−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000000000000000000
χ334444-4-400-1-1-1-115−55−51-220−ζ6+ζ12+ζ14+ζ28ζ6−ζ12−ζ14−ζ28ζ6+ζ12−ζ14+ζ28−ζ6−ζ12+ζ14−ζ28ζ4−ζ22+ζ36+ζ38−ζ4+ζ22−ζ36−ζ38ζ4+ζ22+ζ36−ζ38−ζ4−ζ22−ζ36+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000000000000000000
χ344444-4-400-1-1-1-11−55−5512-20−ζ4−ζ22−ζ36+ζ38ζ4+ζ22+ζ36−ζ38−ζ4+ζ22−ζ36−ζ38ζ4−ζ22+ζ36+ζ38ζ6−ζ12−ζ14−ζ28−ζ6+ζ12+ζ14+ζ28−ζ6−ζ12+ζ14−ζ28ζ6+ζ12−ζ14+ζ28−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000000000000
χ354444-4-400-1-1-1-11−55−5512-20−ζ4+ζ22−ζ36−ζ38ζ4−ζ22+ζ36+ζ38−ζ4−ζ22−ζ36+ζ38ζ4+ζ22+ζ36−ζ38−ζ6−ζ12+ζ14−ζ28ζ6+ζ12−ζ14+ζ28ζ6−ζ12−ζ14−ζ28−ζ6+ζ12+ζ14+ζ28ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000000000000
χ364444-4-400-1-1-1-11−55−551-220ζ4−ζ22+ζ36+ζ38−ζ4+ζ22−ζ36−ζ38ζ4+ζ22+ζ36−ζ38−ζ4−ζ22−ζ36+ζ38ζ6+ζ12−ζ14+ζ28−ζ6−ζ12+ζ14−ζ28−ζ6+ζ12+ζ14+ζ28ζ6−ζ12−ζ14−ζ28ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000000000000000000
χ374444-4-400-1-1-1-11−55−551-220ζ4+ζ22+ζ36−ζ38−ζ4−ζ22−ζ36+ζ38ζ4−ζ22+ζ36+ζ38−ζ4+ζ22−ζ36−ζ38−ζ6+ζ12+ζ14+ζ28ζ6−ζ12−ζ14−ζ28ζ6+ζ12−ζ14+ζ28−ζ6−ζ12+ζ14−ζ28−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000000000000000000
χ3844-4-4-440044-4-4-400004000000000000000000000000000002-20000
χ3944-4-4-440044-4-4-40000400000000000000000000000000000-220000
χ404-44i−4i00004-44i−4i0000000000000000000002-22i−2ii2−i22−2i2−i22−200000000
χ414-44i−4i00004-44i−4i0000000000000000000002-22i−2i−i2i2−22−i2i2−2200000000
χ424-44i−4i00004-44i−4i000000000000000000000-22−2i2i2−2−i2i2−22i2−i200000000
χ434-44i−4i00004-44i−4i000000000000000000000-22−2i2i−22i2−i22−2−i2i200000000
χ444-4−4i4i00004-4−4i4i0000000000000000000002-2−2i2ii2−i2−22i2−i2−2200000000
χ454-4−4i4i00004-4−4i4i0000000000000000000002-2−2i2i−i2i22−2−i2i22−200000000
χ464-4−4i4i00004-4−4i4i000000000000000000000-222i−2i2−2i2−i2−22−i2i200000000
χ474-4−4i4i00004-4−4i4i000000000000000000000-222i−2i−22−i2i22−2i2−i200000000
χ4888-8-88-88-8-2-222-2-2-222200000000000000000000000000000000000
χ4988-8-88-8-88-2-222-222-2-2200000000000000000000000000000000000
χ5088-8-8-8800-2-222225−25−2525-200000000000000000000000000000000000
χ5188-8-8-8800-2-2222−252525−25-200000000000000000000000000000000000
χ5216-1616i−16i0000-44−4i4i00000000000000000000000000000000000000000
χ5316-16−16i16i0000-444i−4i00000000000000000000000000000000000000000

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