Finite Group Databasebeta

← Group #11746799

Character table — Group #11746799

Order 960.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size112222244444444444444488888888888888888888820202020202020204040120120120120
order1223666451010101212151530303030303041212202020202020606060606060606060606060224412121212664444
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii
χ51111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-11-1
χ61111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-11
χ71111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1i−i−ii
χ81111111111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1−iii−i
χ92222222-22222-2-222222222000-2-20000-2-2-2-2000000002-20000002-20000
χ102222222-22222-2-222222222000-2-20000-2-2-2-200000000-22000000-220000
χ11222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-10000
χ12222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111110000
χ13222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-21122-2-2-2-2-1-1-1-11111111122-2-21111-1-10000
χ14222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-21122-2-2-2-2-1-1-1-111111111-2-222-1-1-1-1110000
χ15222-1-1-1-1-2222211-1-1-1-1-1-1-1-10−i3i3-2-200001111−i3−i3−i3−i3i3i3i3i32-200−i3−i3i3i3-110000
χ16222-1-1-1-1-2222211-1-1-1-1-1-1-1-10−i3i3-2-200001111−i3−i3−i3−i3i3i3i3i3-2200i3i3−i3−i31-10000
χ17222-1-1-1-1-2222211-1-1-1-1-1-1-1-10i3−i3-2-200001111i3i3i3i3−i3−i3−i3−i32-200i3i3−i3−i3-110000
χ18222-1-1-1-1-2222211-1-1-1-1-1-1-1-10i3−i3-2-200001111i3i3i3i3−i3−i3−i3−i3-2200−i3−i3i3i31-10000
χ1944444444-1-1-1-144-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2044444444-1-1-1-144-1-1-1-1-1-1-1-1-4-4-4-1-11111-1-1-1-11111111100000000000000
χ214444444-4-1-1-1-1-4-4-1-1-1-1-1-1-1-100011−5−5551111−5−555−5−55500000000000000
χ224444444-4-1-1-1-1-4-4-1-1-1-1-1-1-1-10001155−5−5111155−5−555−5−500000000000000
χ23444-2-2-2-24-1-1-1-1-2-21−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−i15200000000000000
χ24444-2-2-2-24-1-1-1-1-2-21−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+i15200000000000000
χ25444-2-2-2-24-1-1-1-1-2-21+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+i15200000000000000
χ26444-2-2-2-24-1-1-1-1-2-21+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−i15200000000000000
χ27444-2-2-2-2-4-1-1-1-1221−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+ζ5800000000000000
χ28444-2-2-2-2-4-1-1-1-1221−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−ζ5800000000000000
χ29444-2-2-2-2-4-1-1-1-1221+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+ζ4600000000000000
χ30444-2-2-2-2-4-1-1-1-1221+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−ζ4600000000000000
χ3144-444-4-404-4-440044-4-4-4-44400000000000000000000000000000000000
χ3244-444-4-40-111-100-1-11111-1-1000−55ζ2−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+ζ5800000000000000
χ3344-444-4-40-111-100-1-11111-1-1000−55−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−ζ5800000000000000
χ3444-444-4-40-111-100-1-11111-1-10005−5ζ2+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−ζ5800000000000000
χ3544-444-4-40-111-100-1-11111-1-10005−5−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+ζ5800000000000000
χ3644-4-2-22204-4-44−2i32i3-2-22222-2-2000000000−2i32i32i3−2i30000000000000000000000
χ3744-4-2-22204-4-442i3−2i3-2-22222-2-20000000002i3−2i3−2i32i30000000000000000000000
χ3844-4-2-2220-111-1−2i32i31−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+ζ5800000000000000
χ3944-4-2-2220-111-1−2i32i31−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−ζ5800000000000000
χ4044-4-2-2220-111-1−2i32i31+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−ζ4600000000000000
χ4144-4-2-2220-111-1−2i32i31+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+ζ4600000000000000
χ4244-4-2-2220-111-12i3−2i31−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−ζ5800000000000000
χ4344-4-2-2220-111-12i3−2i31−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+ζ5800000000000000
χ4444-4-2-2220-111-12i3−2i31+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−ζ4600000000000000
χ4544-4-2-2220-111-12i3−2i31+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+ζ4600000000000000
χ464-404-4000400-400440000-4-4000000000000000000000002i−2i2i−2i2i−2i000000
χ474-404-4000400-400440000-4-400000000000000000000000−2i2i−2i2i−2i2i000000
χ484-40-22−2i32i30400-400-2-2−2i32i3−2i32i322000000000000000000000002i−2i−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43000000
χ494-40-22−2i32i30400-400-2-2−2i32i3−2i32i32200000000000000000000000−2i2i2ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ43000000
χ504-40-222i3−2i30400-400-2-22i3−2i32i3−2i322000000000000000000000002i−2i−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59000000
χ514-40-222i3−2i30400-400-2-22i3−2i32i3−2i32200000000000000000000000−2i2i2ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ59000000
χ528-808-8000-2−2525200-2-2−252525−252200000000000000000000000000000000000
χ538-808-8000-225−25200-2-225−25−25252200000000000000000000000000000000000
χ548-80-44−4i34i30-2−25252001+i151−i152ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ462ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ58−1−i15−1+i1500000000000000000000000000000000000
χ558-80-44−4i34i30-225−252001−i151+i152ζ14−2ζ22+2ζ26−2ζ58−2ζ14+2ζ22−2ζ26+2ζ582ζ2−2ζ34+2ζ38−2ζ46−2ζ2+2ζ34−2ζ38+2ζ46−1+i15−1−i1500000000000000000000000000000000000
χ568-80-444i3−4i30-2−25252001−i151+i15−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−1+i15−1−i1500000000000000000000000000000000000
χ578-80-444i3−4i30-225−252001+i151−i15−2ζ2+2ζ34−2ζ38+2ζ462ζ2−2ζ34+2ζ38−2ζ46−2ζ14+2ζ22−2ζ26+2ζ582ζ14−2ζ22+2ζ26−2ζ58−1−i15−1+i1500000000000000000000000000000000000

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