Finite Group Databasebeta

← Group #11746798

Character table — Group #11746798

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222244444444444444488888888888888888888810101010202020204040406060606060606060
order1222366645101010121215153030303030304121220202020202060606060606060606060606044441212121226688888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-111-1-111-1-1
χ611111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111
χ711111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iii
χ811111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i
χ922222222-22222-2-222222222000-2-20000-2-2-2-20000000022-2-222-2-200000000000
χ1022222222-22222-2-222222222000-2-20000-2-2-2-200000000-2-222-2-22200000000000
χ112222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12-1-100000000
χ122222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-21100000000
χ132222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-21122-2-2-2-2-1-1-1-1111111112222-1-1-1-1-21100000000
χ142222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-21122-2-2-2-2-1-1-1-111111111-2-2-2-211112-1-100000000
χ152222-1-1-1-1-2222211-1-1-1-1-1-1-1-10−i3i3-2-200001111−i3−i3−i3−i3i3i3i3i322-2-2-1-1110−i3i300000000
χ162222-1-1-1-1-2222211-1-1-1-1-1-1-1-10−i3i3-2-200001111−i3−i3−i3−i3i3i3i3i3-2-22211-1-10i3−i300000000
χ172222-1-1-1-1-2222211-1-1-1-1-1-1-1-10i3−i3-2-200001111i3i3i3i3−i3−i3−i3−i322-2-2-1-1110i3−i300000000
χ182222-1-1-1-1-2222211-1-1-1-1-1-1-1-10i3−i3-2-200001111i3i3i3i3−i3−i3−i3−i3-2-22211-1-10−i3i300000000
χ192-22-22-22-2022-2-2002222-2-2-2-2000000000000000000000002i−2i002i−2i0001+i−1−i001−i−1+i00
χ202-22-22-22-2022-2-2002222-2-2-2-2000000000000000000000002i−2i002i−2i000−1−i1+i00−1+i1−i00
χ212-22-22-22-2022-2-2002222-2-2-2-200000000000000000000000−2i2i00−2i2i0001−i−1+i001+i−1−i00
χ222-22-22-22-2022-2-2002222-2-2-2-200000000000000000000000−2i2i00−2i2i000−1+i1−i00−1−i1+i00
χ232-2-222-2-2202-22-20022-2-222-2-20000000000000000000002i−2i002i−2i00000001−i−1+i001+i−1−i
χ242-2-222-2-2202-22-20022-2-222-2-20000000000000000000002i−2i002i−2i0000000−1+i1−i00−1−i1+i
χ252-2-222-2-2202-22-20022-2-222-2-2000000000000000000000−2i2i00−2i2i00000001+i−1−i001−i−1+i
χ262-2-222-2-2202-22-20022-2-222-2-2000000000000000000000−2i2i00−2i2i0000000−1−i1+i00−1+i1−i
χ27444444444-1-1-1-144-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000
χ28444444444-1-1-1-144-1-1-1-1-1-1-1-1-4-4-4-1-11111-1-1-1-1111111110000000000000000000
χ2944444444-4-1-1-1-1-4-4-1-1-1-1-1-1-1-100011−5−5551111−5−555−5−5550000000000000000000
χ3044444444-4-1-1-1-1-4-4-1-1-1-1-1-1-1-10001155−5−5111155−5−555−5−50000000000000000000
χ314444-2-2-2-24-1-1-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1524-2-2-1-1-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1520000000000000000000
χ324444-2-2-2-24-1-1-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-422-1-111111−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i1520000000000000000000
χ334444-2-2-2-24-1-1-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1524-2-2-1-1-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1520000000000000000000
χ344444-2-2-2-24-1-1-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-422-1-111111+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i1520000000000000000000
χ354444-2-2-2-2-4-1-1-1-1221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1520−2i32i31155−5−5−1+i152−1+i152−1−i152−1−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+ζ580000000000000000000
χ364444-2-2-2-2-4-1-1-1-1221−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15202i3−2i311−5−555−1+i152−1+i152−1−i152−1−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−ζ580000000000000000000
χ374444-2-2-2-2-4-1-1-1-1221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1520−2i32i311−5−555−1−i152−1−i152−1+i152−1+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+ζ460000000000000000000
χ384444-2-2-2-2-4-1-1-1-1221+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15202i3−2i31155−5−5−1−i152−1−i152−1+i152−1+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−ζ460000000000000000000
χ3944-4-444-4-404-4-440044-4-4-4-4440000000000000000000000000000000000000000
χ4044-4-444-4-40-111-100-1-11111-1-1000−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−55−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ580000000000000000000
χ4144-4-444-4-40-111-100-1-11111-1-1000−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−55−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ580000000000000000000
χ4244-4-444-4-40-111-100-1-11111-1-10005−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ585−55−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ580000000000000000000
χ4344-4-444-4-40-111-100-1-11111-1-10005−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ585−55−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ580000000000000000000
χ4444-4-4-2-22204-4-44−2i32i3-2-22222-2-2000000000−2i32i32i3−2i3000000000000000000000000000
χ4544-4-4-2-22204-4-442i3−2i3-2-22222-2-20000000002i3−2i3−2i32i3000000000000000000000000000
χ4644-4-4-2-2220-111-1−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520005−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ580000000000000000000
χ4744-4-4-2-2220-111-1−2i32i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1520005−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ580000000000000000000
χ4844-4-4-2-2220-111-1−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ460000000000000000000
χ4944-4-4-2-2220-111-1−2i32i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152000−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ58−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ460000000000000000000
χ5044-4-4-2-2220-111-12i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ46−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ580000000000000000000
χ5144-4-4-2-2220-111-12i3−2i31−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152000−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ14+ζ22−ζ26+ζ58ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ46ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ580000000000000000000
χ5244-4-4-2-2220-111-12i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520005−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58−ζ2−ζ34+ζ38+ζ46ζ2+ζ34−ζ38−ζ46−ζ14+ζ22+ζ26−ζ58ζ14−ζ22−ζ26+ζ58−ζ14−ζ22+ζ26+ζ58ζ14+ζ22−ζ26−ζ58ζ2−ζ34−ζ38+ζ46−ζ2+ζ34+ζ38−ζ460000000000000000000
χ5344-4-4-2-2220-111-12i3−2i31+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1520005−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58−ζ2+ζ34−ζ38+ζ46ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ14+ζ22−ζ26+ζ58ζ2+ζ34−ζ38−ζ46−ζ2−ζ34+ζ38+ζ46ζ14−ζ22−ζ26+ζ58−ζ14+ζ22+ζ26−ζ58ζ14+ζ22−ζ26−ζ58−ζ14−ζ22+ζ26+ζ58−ζ2+ζ34+ζ38−ζ46ζ2−ζ34−ζ38+ζ460000000000000000000
χ544-44-4-22-22044-4-400-2-2-2-22222000000000000000000000004i−4i00−2i2i00000000000
χ554-44-4-22-22044-4-400-2-2-2-2222200000000000000000000000−4i4i002i−2i00000000000
χ564-4-44-222-204-44-400-2-222-2-2220000000000000000000004i−4i00−2i2i0000000000000
χ574-4-44-222-204-44-400-2-222-2-222000000000000000000000−4i4i002i−2i0000000000000
χ588-88-88-88-80-2-22200-2-2-2-222220000000000000000000000000000000000000000
χ598-88-8-44-440-2-222001−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i150000000000000000000000000000000000000000
χ608-88-8-44-440-2-222001+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i150000000000000000000000000000000000000000
χ618-8-888-8-880-22-2200-2-222-2-2220000000000000000000000000000000000000000
χ628-8-88-444-40-22-22001−i151+i15−1+i15−1−i151−i151+i15−1+i15−1−i150000000000000000000000000000000000000000
χ638-8-88-444-40-22-22001+i151−i15−1−i15−1+i151+i151−i15−1−i15−1+i150000000000000000000000000000000000000000

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