Finite Group Databasebeta

← Group #13014303

Character table — Group #13014303

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111224444448888881616161616161616161616161616162020202040404040404040404040808080808080
order124424245102020101010202020888404040404040404040404040224444444444888816161616
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
χ51111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ61111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
χ71111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ81111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ9222222222222222222-200-2-2-2-200000000222200000000-2-2000000
χ10222222222222222222-200-2-2-2-200000000-2-2-2-20000000022000000
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
χ1944444444-1-1-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
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
χ23444444-4-444444-4-4-4-4400000000000000000000000000000000000
χ24444444-4-4-1-1-1-1-11111-100055−5−5−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
χ25444444-4-4-1-1-1-1-11111-100055−5−5ζ6−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
χ26444444-4-4-1-1-1-1-11111-1000−5−555ζ6−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
χ27444444-4-4-1-1-1-1-11111-1000−5−555−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
χ284444-4-4004444-40000-402-200002-22-22-22-200000000000000000000
χ294444-4-4004444-40000-40-220000-22-22-22-2200000000000000000000
χ304444-4-400-1-1-1-115−55−5102-2−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−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+ζ2800000000000000000000
χ314444-4-400-1-1-1-115−55−5102-2ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−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+ζ2800000000000000000000
χ324444-4-400-1-1-1-115−55−510-22−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ4+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−ζ2800000000000000000000
χ334444-4-400-1-1-1-115−55−510-22ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ4−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−ζ2800000000000000000000
χ344444-4-400-1-1-1-11−55−55102-2ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−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−ζ3800000000000000000000
χ354444-4-400-1-1-1-11−55−55102-2−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−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+ζ3800000000000000000000
χ364444-4-400-1-1-1-11−55−5510-22ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−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+ζ3800000000000000000000
χ374444-4-400-1-1-1-11−55−5510-22−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6+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−ζ3800000000000000000000
χ3844-4-4-440044-4-4-400004000000000000000000000000000002i−2i0000
χ3944-4-4-440044-4-4-40000400000000000000000000000000000−2i2i0000
χ404-44i−4i00004-44i−4i0000000000000000000002-22i−2i1+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ414-44i−4i00004-44i−4i0000000000000000000002-22i−2i−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ424-44i−4i00004-44i−4i000000000000000000000-22−2i2i1−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ434-44i−4i00004-44i−4i000000000000000000000-22−2i2i−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ444-4−4i4i00004-4−4i4i0000000000000000000002-2−2i2i1−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ454-4−4i4i00004-4−4i4i0000000000000000000002-2−2i2i−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ464-4−4i4i00004-4−4i4i000000000000000000000-222i−2i1+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ474-4−4i4i00004-4−4i4i000000000000000000000-222i−2i−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
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.