Finite Group Databasebeta

← Group #14313296

Character table — Group #14313296

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1122244444444448888888810101010161616161616161620202020202024242424242440404040404040404040404040404848120120120120120120
order12236224566610101061010121530303044121210203030303060602441212122410101010688881224242424242424242020244444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1ii−i−i-1iiii−i−i−i−i11-1-1ii−i−i
χ611111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1−i−iii-1−i−i−i−iiiii11-1-1−i−iii
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i-1-111−i−iii
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiii-1-111ii−i−i
χ9111111-1-111-1-1111111-111111111-1-111-1-1-1-1-11-11-1-11-11111-1i−ii−i1ii−i−iii−i−i-1-11-1i−ii−i
χ10111111-1-111-1-1111111-111111111-1-111-1-1-1-1-11-11-1-11-11111-1−ii−ii1−i−iii−i−iii-1-11-1−ii−ii
χ11111111-1-111-1-1111111-111111111-1-111-1-1-1-1-11-11-1-1-11-1-1-1-1-1i−ii−i1ii−i−iii−i−i11-11−ii−ii
χ12111111-1-111-1-1111111-111111111-1-111-1-1-1-1-11-11-1-1-11-1-1-1-1-1−ii−ii1−i−iii−i−iii11-11i−ii−i
χ13111111-1-111-1-1111111-11111-1-1-1-1-1-111-1-1-1-11-11-1111-1111111-1-11-111-1-1-1-111-1-1-111-1-11
χ14111111-1-111-1-1111111-11111-1-1-1-1-1-111-1-1-1-11-11-1111-111111-111-1-1-1-11111-1-1-1-1-11-111-1
χ15111111-1-111-1-1111111-11111-1-1-1-1-1-111-1-1-1-11-11-111-11-1-1-1-111-1-11-111-1-1-1-111111-1-111-1
χ16111111-1-111-1-1111111-11111-1-1-1-1-1-111-1-1-1-11-11-111-11-1-1-1-11-111-1-1-1-11111-1-1111-11-1-11
χ1722222-22-22222222-2-2-2-2222222222-2-2-222-2-2-2-22222000000-20000-20000000000000000
χ1822222-22-22222222-2-2-2-22222-2-2-2-22-2-2-222-2-222-2-2-2-20000002000020000000000000000
χ1922222-2-2222-2-2222-2-2-2222222222-22-2-2-2-2222-2-22-2-200000020000-20000000000000000
χ2022222-2-2222-2-2222-2-2-222222-2-2-2-2-22-2-2-2-222-222-222000000-2000020000000000000000
χ21222-1-12222-1-1-1222-122-1-1-1-1-122-1-122-1-1-1-1-1-1222-1-1-1000000-12222-1-1-1-1-1-1-1-1-100000000
χ22222-1-12222-1-1-1222-122-1-1-1-1-122-1-122-1-1-1-1-1-1222-1-1-1000000-1-2-2-2-2-11111111100000000
χ23222-1-12222-1-1-1222-122-1-1-1-1-1-2-21122-1-1-1-1-1-1-2-2-211100000012i2i−2i−2i1−i−i−i−iiiii00000000
χ24222-1-12222-1-1-1222-122-1-1-1-1-1-2-21122-1-1-1-1-1-1-2-2-21110000001−2i−2i2i2i1iiii−i−i−i−i00000000
χ25222-1-12-2-22-111222-1221-1-1-1-122-1-1-2-2-1-11111-22-2-11100000012i−2i2i−2i-1−i−iii−i−iii00000000
χ26222-1-12-2-22-111222-1221-1-1-1-122-1-1-2-2-1-11111-22-2-1110000001−2i2i−2i2i-1ii−i−iii−i−i00000000
χ27222-1-12-2-22-111222-1221-1-1-1-1-2-211-2-2-1-111112-221-1-1000000-12-2-221-1-11111-1-100000000
χ28222-1-12-2-22-111222-1221-1-1-1-1-2-211-2-2-1-111112-221-1-1000000-1-222-2111-1-1-1-11100000000
χ29222-1-1-22-22-1-1-12221-2-21-1-1-1-122-1-12-211-1-111-2-22-1-1-1000000100001−i3i3−i3i3−i3i3−i3i300000000
χ30222-1-1-22-22-1-1-12221-2-21-1-1-1-122-1-12-211-1-111-2-22-1-1-1000000100001i3−i3i3−i3i3−i3i3−i300000000
χ31222-1-1-22-22-1-1-12221-2-21-1-1-1-1-2-2112-211-1-11122-2111000000-10000-13−33−3−33−3300000000
χ32222-1-1-22-22-1-1-12221-2-21-1-1-1-1-2-2112-211-1-11122-2111000000-10000-1−33−333−33−300000000
χ33222-1-1-2-222-1112221-2-2-1-1-1-1-122-1-1-221111-1-12-2-2-111000000-1000013−3−333−3−3300000000
χ34222-1-1-2-222-1112221-2-2-1-1-1-1-122-1-1-221111-1-12-2-2-111000000-100001−333−3−333−300000000
χ35222-1-1-2-222-1112221-2-2-1-1-1-1-1-2-211-221111-1-1-2221-1-100000010000-1−i3i3i3−i3i3−i3−i3i300000000
χ36222-1-1-2-222-1112221-2-2-1-1-1-1-1-2-211-221111-1-1-2221-1-100000010000-1i3−i3−i3i3−i3i3i3−i300000000
χ3744444444-1444-1-1-14-1-14-1-1-1-10000-1-1-1-1-1-1-1-100000044-1-1-1-100000000000000-1-1000000
χ3844444444-1444-1-1-14-1-14-1-1-1-10000-1-1-1-1-1-1-1-1000000-4-411110000000000000011000000
χ39444444-4-4-14-4-4-1-1-14-1-1-4-1-1-1-1000011-1-111110000004-4-1-1-1-10000000000000011000000
χ40444444-4-4-14-4-4-1-1-14-1-1-4-1-1-1-1000011-1-11111000000-44111100000000000000-1-1000000
χ4144444-44-4-1444-1-1-1-411-4-1-1-1-10000-1111-1-11100000000−5−55500000000000000−55000000
χ4244444-44-4-1444-1-1-1-411-4-1-1-1-10000-1111-1-1110000000055−5−5000000000000005−5000000
χ4344444-4-44-14-4-4-1-1-1-4114-1-1-1-100001-11111-1-100000000−5−555000000000000005−5000000
χ4444444-4-44-14-4-4-1-1-1-4114-1-1-1-100001-11111-1-10000000055−5−500000000000000−55000000
χ4544-4440004-4004-4-400004-4-444-44400000000000-4000000000000000000000000000000
χ4644-4440004-4004-4-400004-4-44-44-4-4000000000004000000000000000000000000000000
χ4744-4-2-200042−2i32i34-4-40000-222-24-4-2-20000−2i32i3000002−2i32i30000000000000000000000000000
χ4844-4-2-200042−2i32i34-4-40000-222-2-44220000−2i32i300000-22i3−2i30000000000000000000000000000
χ4944-4-2-2000422i3−2i34-4-40000-222-24-4-2-200002i3−2i30000022i3−2i30000000000000000000000000000
χ5044-4-2-2000422i3−2i34-4-40000-222-2-442200002i3−2i300000-2−2i32i30000000000000000000000000000
χ51888-4-4888-2-4-4-4-2-2-2-4-2-2-411110000-2-21111110000000000000000000000000000000000
χ52888-4-48-8-8-2-444-2-2-2-4-2-24111100002211-1-1-1-10000000000000000000000000000000000
χ53888-4-4-88-8-2-4-4-4-2-2-2422411110000-22-1-111-1-10000000000000000000000000000000000
χ54888-4-4-8-88-2-444-2-2-2422-4111100002-2-1-1-1-1110000000000000000000000000000000000
χ5588-888000-2-800-2220−25250-222-2000000−252500000000000000000000000000000000000000
χ5688-888000-2-800-222025−250-222-200000025−2500000000000000000000000000000000000000
χ5788-8-4-4000-24−4i34i3-2220−252501-1-110000005−5i3−i3−i15i150000000000000000000000000000000000
χ5888-8-4-4000-24−4i34i3-222025−2501-1-11000000−55i3−i3i15−i150000000000000000000000000000000000
χ5988-8-4-4000-244i3−4i3-2220−252501-1-110000005−5−i3i3i15−i150000000000000000000000000000000000
χ6088-8-4-4000-244i3−4i3-222025−2501-1-11000000−55−i3i3−i15i150000000000000000000000000000000000
χ618-808-80008000-8000000800-80000000000000000000000000000000000000000000000
χ628-808-8000-20002−25250000-2−2525200000000000000000000−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ580000000000000000000000
χ638-808-8000-20002−25250000-2−25252000000000000000000002ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ580000000000000000000000
χ648-808-8000-2000225−250000-225−252000000000000000000002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ460000000000000000000000
χ658-808-8000-2000225−250000-225−25200000000000000000000−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ460000000000000000000000
χ668-80-440008000-8000000-40040043−43000000000000000000000000000000000000000000
χ678-80-440008000-8000000-400400−4343000000000000000000000000000000000000000000
χ6816-160-88000-40004−45450000225−25-20000000000000000000000000000000000000000000000
χ6916-160-88000-4000445−4500002−2525-20000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.