Finite Group Databasebeta

← Group #14313209

Character table — Group #14313209

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size112222222444444444444444444444444444444448888888888888888888888888888888888888888882020202040404040404040404040120120120120120120120120
order1222236662256666661010101010101015153030303030303030303030303030441010101012121212202020202020202030303030303030306060606060606060606060606060606022442466661212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iii
χ811111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−i
χ911-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-11-1111-1-1-1i−ii−ii−ii−i
χ1011-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-11-1111-1-1-1−ii−ii−ii−ii
χ1111-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-11-1-1-11111-1-111-1-11
χ1211-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1111-111-1-111-1
χ1311-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-111-1-1-11-111i−ii−i−ii−ii
χ1411-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-111-1-1-11-111−ii−iii−ii−i
χ1511-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111-1-1111-11-1-11-1-11-111-1
χ1611-1-1111111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111-1-1111-11-1-1-111-11-1-11
χ17222222222-2-22-2-222-2-22-2-2-2-2222222-2-2-2-2-2-2-2-2222200-2-222000000000000-2-2-2-22222000000000000000022-2-2002200-2-20000000000
χ18222222222-2-22-2-222-2-22-2-2-2-2222222-2-2-2-2-2-2-2-2222200-2-222000000000000-2-2-2-222220000000000000000-2-22200-2-200220000000000
χ1922222-1-1-1-1222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ2022222-1-1-1-1222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ2122222-1-1-1-1222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222221111-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-1-111-1-11100000000
χ2222222-1-1-1-1222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222221111-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-22211-1-111-1-100000000
χ2322222-1-1-1-1-2-2211-1-1112-2-2-2-222-1-1-1-111111111-1-1-1-100-2-222−i3i3−i3i3000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-2-200-1-1−i3i311−i3i300000000
χ2422222-1-1-1-1-2-2211-1-1112-2-2-2-222-1-1-1-111111111-1-1-1-100-2-222−i3i3−i3i3000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-2-2220011i3−i3-1-1i3−i300000000
χ2522222-1-1-1-1-2-2211-1-1112-2-2-2-222-1-1-1-111111111-1-1-1-100-2-222i3−i3i3−i3000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-2-200-1-1i3−i311i3−i300000000
χ2622222-1-1-1-1-2-2211-1-1112-2-2-2-222-1-1-1-111111111-1-1-1-100-2-222i3−i3i3−i3000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-2220011−i3i3-1-1−i3i300000000
χ2722-2-222222-222-2-2-2-2222222222222222222222222200-2-2-2-2000000000000-2-2-2-2-2-2-2-200000000000000002-2-22002-200-220000000000
χ2822-2-222222-222-2-2-2-2222222222222222222222222200-2-2-2-2000000000000-2-2-2-2-2-2-2-20000000000000000-222-200-22002-20000000000
χ2922-2-22-1-1-1-12-22-1-111112-2-2-2-222-1-1-1-111111111-1-1-1-12-222-2-2-1-1112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111112-22-22-2-11-1-1-111100000000
χ3022-2-22-1-1-1-12-22-1-111112-2-2-2-222-1-1-1-111111111-1-1-1-12-222-2-2-1-1112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111-22-22-221-1111-1-1-100000000
χ3122-2-22-1-1-1-12-22-1-111112-2-2-2-222-1-1-1-111111111-1-1-1-1-2222-2-211-1-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-12-22-2-22-1111-11-1-100000000
χ3222-2-22-1-1-1-12-22-1-111112-2-2-2-222-1-1-1-111111111-1-1-1-1-2222-2-211-1-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1-22-222-21-1-1-11-11100000000
χ3322-2-22-1-1-1-1-2221111-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2−i3i3i3−i30000000011111111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-2200-11−i3i31-1i3−i300000000
χ3422-2-22-1-1-1-1-2221111-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2−i3i3i3−i30000000011111111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-2001-1i3−i3-11−i3i300000000
χ3522-2-22-1-1-1-1-2221111-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2i3−i3−i3i30000000011111111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-2200-11i3−i31-1−i3i300000000
χ3622-2-22-1-1-1-1-2221111-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2i3−i3−i3i30000000011111111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-2001-1−i3i3-11i3−i300000000
χ3744444444444-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3844444444444-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-1-1-1-1-4-4-4-411111111-1-1-1-1-1-1-1-111111111111111110000000000000000000000
χ39444444444-4-4-1-4-444-4-4-11111-1-1-1-1-1-111111111-1-1-1-10011-1-10000−5−555−5−5551111-1-1-1-1−5−555−5−555−5−555−5−5550000000000000000000000
χ40444444444-4-4-1-4-444-4-4-11111-1-1-1-1-1-111111111-1-1-1-10011-1-1000055−5−555−5−51111-1-1-1-155−5−555−5−555−5−555−5−50000000000000000000000
χ4144444-2-2-2-244-1-2-2-2-2-2-2-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521+i1521+i15244-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1520000000000000000000000
χ4244444-2-2-2-244-1-2-2-2-2-2-2-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521+i1521+i152-4-4-1-1-1-12222111111111−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i1520000000000000000000000
χ4344444-2-2-2-244-1-2-2-2-2-2-2-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521−i1521−i15244-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1520000000000000000000000
χ4444444-2-2-2-244-1-2-2-2-2-2-2-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521−i1521−i152-4-4-1-1-1-12222111111111+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i1520000000000000000000000
χ4544444-2-2-2-2-4-4-122-2-222-11111-1-11−i1521+i1521−i1521+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1521−i1521−i1521+i1521+i1520011-1-1−2i32i3−2i32i355−5−555−5−5−1+i152−1+i152−1−i152−1−i1521−i1521−i1521+i1521+i152ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ580000000000000000000000
χ4644444-2-2-2-2-4-4-122-2-222-11111-1-11−i1521+i1521−i1521+i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1521−i1521−i1521+i1521+i1520011-1-12i3−2i32i3−2i3−5−555−5−555−1+i152−1+i152−1−i152−1−i1521−i1521−i1521+i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ580000000000000000000000
χ4744444-2-2-2-2-4-4-122-2-222-11111-1-11+i1521−i1521+i1521−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1521+i1521+i1521−i1521−i1520011-1-1−2i32i3−2i32i3−5−555−5−555−1−i152−1−i152−1+i152−1+i1521+i1521+i1521−i1521−i152ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ460000000000000000000000
χ4844444-2-2-2-2-4-4-122-2-222-11111-1-11+i1521−i1521+i1521−i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1521+i1521+i1521−i1521−i1520011-1-12i3−2i32i3−2i355−5−555−5−5−1−i152−1−i152−1+i152−1+i1521+i1521+i1521−i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ2−ζ34+ζ38−ζ460000000000000000000000
χ49444-4-44-4-44004004-40040000-4-4444400000000-4-4-4-400004-400000000000000004-44-400000000000000000000000000000000000000
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χ1048-8000-44i3−4i3400-200000022ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ5825−251+i151−i15−1−i15−1+i15−2ζ2−2ζ34+2ζ38+2ζ462ζ2+2ζ34−2ζ38−2ζ462ζ2−2ζ34−2ζ38+2ζ46−2ζ2+2ζ34+2ζ38−2ζ46−2ζ14−2ζ22+2ζ26+2ζ582ζ14+2ζ22−2ζ26−2ζ58−2ζ14+2ζ22+2ζ26−2ζ582ζ14−2ζ22−2ζ26+2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ580000000000000000000000000000000000000000000000000000000000000000
χ1058-8000-44i3−4i3400-20000002−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ5825−251+i151−i15−1−i15−1+i152ζ2+2ζ34−2ζ38−2ζ46−2ζ2−2ζ34+2ζ38+2ζ46−2ζ2+2ζ34+2ζ38−2ζ462ζ2−2ζ34−2ζ38+2ζ462ζ14+2ζ22−2ζ26−2ζ58−2ζ14−2ζ22+2ζ26+2ζ582ζ14−2ζ22−2ζ26+2ζ58−2ζ14+2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ580000000000000000000000000000000000000000000000000000000000000000

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