Finite Group Databasebeta

← Group #14512499

Character table — Group #14512499

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111224444444455556688888888101012161616161616161616161616161616162424242430304040404040404040606060606060606060120120120120
order1222445101010202020204444443666121212122221515303030303030606060606060606010102020226666121212124444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-11111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111-1-1-1-11111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-11-11-1
χ61111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-111-11-11
χ71111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11ii−i−i−i−iiii−i−ii
χ81111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11−i−iiiii−i−i−iii−i
χ922222222222222222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12000000000000
χ1022222222222222-2-2-2-222-1-1-1-1-1-1-1-1-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-211111111-2000000000000
χ112222-2-22222-2-2-2-2222222-1-1-1-11111-2-2-2-1-1-1-1-1-1-1-111111111-2-222221111-1-1-1-1-2000000000000
χ122222-2-22222-2-2-2-2-2-2-2-222-1-1-1-1111122-2-1-1-1-1-1-1-1-111111111-2-222-2-2-1-1-1-111112000000000000
χ1322-2-22i−2i22-2-22i2i−2i−2i2i2i−2i−2i00-11-11ii−i−i2-20-1-111-1-111iiii−i−i−i−i00000011-1-1ii−i−i01+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ1422-2-22i−2i22-2-22i2i−2i−2i2i2i−2i−2i00-11-11ii−i−i2-20-1-111-1-111iiii−i−i−i−i00000011-1-1ii−i−i0−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ1522-2-22i−2i22-2-22i2i−2i−2i−2i−2i2i2i00-11-11ii−i−i-220-1-111-1-111iiii−i−i−i−i000000-1-111−i−iii01−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ1622-2-22i−2i22-2-22i2i−2i−2i−2i−2i2i2i00-11-11ii−i−i-220-1-111-1-111iiii−i−i−i−i000000-1-111−i−iii0−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ1722-2-2−2i2i22-2-2−2i−2i2i2i2i2i−2i−2i00-11-11−i−iii-220-1-111-1-111−i−i−i−iiiii000000-1-111ii−i−i01+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ1822-2-2−2i2i22-2-2−2i−2i2i2i2i2i−2i−2i00-11-11−i−iii-220-1-111-1-111−i−i−i−iiiii000000-1-111ii−i−i0−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ1922-2-2−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i00-11-11−i−iii2-20-1-111-1-111−i−i−i−iiiii00000011-1-1−i−iii01−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ2022-2-2−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i00-11-11−i−iii2-20-1-111-1-111−i−i−i−iiiii00000011-1-1−i−iii0−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ212-2-22002-2-2200002-22-22-22-2-22000000022-2-2-2-22200000000002-22-200002-22-20000000000000
χ222-2-22002-2-2200002-22-22-2-111-1−i3i3−i3i3000-1-11111-1-1−i3−i3i3i3−i3−i3i3i3002-22-2−i3i3−i3i3-11-110000000000000
χ232-2-22002-2-2200002-22-22-2-111-1i3−i3i3−i3000-1-11111-1-1i3i3−i3−i3i3i3−i3−i3002-22-2i3−i3i3−i3-11-110000000000000
χ242-2-22002-2-220000-22-222-22-2-22000000022-2-2-2-22200000000002-2-220000-22-220000000000000
χ252-2-22002-2-220000-22-222-2-111-1−i3i3−i3i3000-1-11111-1-1−i3−i3i3i3−i3−i3i3i3002-2-22i3−i3i3−i31-11-10000000000000
χ262-2-22002-2-220000-22-222-2-111-1i3−i3i3−i3000-1-11111-1-1i3i3−i3−i3i3i3−i3−i3002-2-22−i3i3−i3i31-11-10000000000000
χ27333333333333333333-1-10000000033-10000000000000000-1-1-1-1-1-100000000-111111111-1-1-1-1
χ28333333333333333333-1-10000000033-10000000000000000-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-11111
χ2933333333333333-3-3-3-3-1-100000000-3-3-10000000000000000-1-1-1-111000000001iiii−i−i−i−i−i−iii
χ3033333333333333-3-3-3-3-1-100000000-3-3-10000000000000000-1-1-1-111000000001−i−i−i−iiiiiii−i−i
χ313333-3-33333-3-3-3-33333-1-100000000-3-31000000000000000011-1-1-1-100000000111-1-111-1-1-11-11
χ323333-3-33333-3-3-3-33333-1-100000000-3-31000000000000000011-1-1-1-1000000001-1-111-1-1111-11-1
χ333333-3-33333-3-3-3-3-3-3-3-3-1-100000000331000000000000000011-1-11100000000-1ii−i−i−i−iii−iii−i
χ343333-3-33333-3-3-3-3-3-3-3-3-1-100000000331000000000000000011-1-11100000000-1−i−iiiii−i−ii−i−ii
χ35444444-1-1-1-1-1-1-1-100004444444444004-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ36444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-20041−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-1-1-1-100000000000000000000000
χ37444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-20041+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-1-1-1-100000000000000000000000
χ384444-4-4-1-1-1-111110000444444-4-4-4-400-4-1-1-1-1-1-1-1-11111111111-1-100000000000000000000000
χ394444-4-4-1-1-1-11111000044-2-2-2-2222200-41−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15211-1-100000000000000000000000
χ404444-4-4-1-1-1-11111000044-2-2-2-2222200-41+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15211-1-100000000000000000000000
χ4144-4-44i−4i44-4-44i4i−4i−4i4i4i−4i−4i001-11-1−i−iii4-4011-1-111-1-1−i−i−i−iiiii000000-1-111−i−iii0000000000000
χ4244-4-44i−4i44-4-44i4i−4i−4i−4i−4i4i4i001-11-1−i−iii-44011-1-111-1-1−i−i−i−iiiii00000011-1-1ii−i−i0000000000000
χ4344-4-4−4i4i44-4-4−4i−4i4i4i4i4i−4i−4i001-11-1ii−i−i-44011-1-111-1-1iiii−i−i−i−i00000011-1-1−i−iii0000000000000
χ4444-4-4−4i4i44-4-4−4i−4i4i4i−4i−4i4i4i001-11-1ii−i−i4-4011-1-111-1-1iiii−i−i−i−i000000-1-111ii−i−i0000000000000
χ454-44-4004-44-400004i−4i−4i4i0011-1-13−3−330001111-1-1-1-133−3−3−3−333000000−i3i3i3−i3−iii−i0000000000000
χ464-44-4004-44-400004i−4i−4i4i0011-1-1−333−30001111-1-1-1-1−3−33333−3−3000000i3−i3−i3i3−iii−i0000000000000
χ474-44-4004-44-400004i−4i−4i4i00-2-2220000000-2-2-2-222220000000000000000002i−2i−2i2i0000000000000
χ484-44-4004-44-40000−4i4i4i−4i0011-1-13−3−330001111-1-1-1-133−3−3−3−333000000i3−i3−i3i3i−i−ii0000000000000
χ494-44-4004-44-40000−4i4i4i−4i0011-1-1−333−30001111-1-1-1-1−3−33333−3−3000000−i3i3i3−i3i−i−ii0000000000000
χ504-44-4004-44-40000−4i4i4i−4i00-2-2220000000-2-2-2-22222000000000000000000−2i2i2i−2i0000000000000
χ514-4-4400-111-1−55−5500004-44-4-440000000-1-11111-1-1−555−5−555−5−55-1100000000000000000000000
χ524-4-4400-111-1−55−5500004-4-222-2−2i32i3−2i32i30001+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−55-1100000000000000000000000
χ534-4-4400-111-1−55−5500004-4-222-22i3−2i32i3−2i30001−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−55-1100000000000000000000000
χ544-4-4400-111-15−55−500004-44-4-440000000-1-11111-1-15−5−555−5−555−5-1100000000000000000000000
χ554-4-4400-111-15−55−500004-4-222-2−2i32i3−2i32i30001−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ465−5-1100000000000000000000000
χ564-4-4400-111-15−55−500004-4-222-22i3−2i32i3−2i30001+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ585−5-1100000000000000000000000
χ576-6-66006-6-6600006-66-6-2200000000000000000000000000000-22-22000000000000000000000
χ586-6-66006-6-660000-66-66-2200000000000000000000000000000-222-2000000000000000000000
χ5988-8-88i−8i-2-222−2i−2i2i2i0000002-22-2−2i−2i2i2i000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59000000000000000000000000000
χ6088-8-88i−8i-2-222−2i−2i2i2i0000002-22-2−2i−2i2i2i000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47000000000000000000000000000
χ6188-8-88i−8i-2-222−2i−2i2i2i000000-44-444i4i−4i−4i00011-1-111-1-1−i−i−i−iiiii000000000000000000000000000
χ6288-8-8−8i8i-2-2222i2i−2i−2i0000002-22-22i2i−2i−2i000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59000000000000000000000000000
χ6388-8-8−8i8i-2-2222i2i−2i−2i0000002-22-22i2i−2i−2i000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47000000000000000000000000000
χ6488-8-8−8i8i-2-2222i2i−2i−2i000000-44-44−4i−4i4i4i00011-1-111-1-1iiii−i−i−i−i000000000000000000000000000
χ658-88-800-22-22−2i52i52i5−2i500000022-2-223−23−2323000−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59000000000000000000000000000
χ668-88-800-22-22−2i52i52i5−2i500000022-2-2−232323−23000−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47000000000000000000000000000
χ678-88-800-22-22−2i52i52i5−2i5000000-4-44400000001111-1-1-1-1−i5i5i5−i5i5−i5−i5i5000000000000000000000000000
χ688-88-800-22-222i5−2i5−2i52i500000022-2-223−23−2323000−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47000000000000000000000000000
χ698-88-800-22-222i5−2i5−2i52i500000022-2-2−232323−23000−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59000000000000000000000000000
χ708-88-800-22-222i5−2i5−2i52i5000000-4-44400000001111-1-1-1-1i5−i5−i5i5−i5i5i5−i5000000000000000000000000000
χ71121212121212-3-3-3-3-3-3-3-30000-4-40000000000-40000000000000000111100000000000000000000000
χ7212121212-12-12-3-3-3-333330000-4-4000000000040000000000000000-1-11100000000000000000000000
χ7312-12-121200-333-3−3535−35350000-440000000000000000000000000005−51-100000000000000000000000
χ7412-12-121200-333-335−3535−350000-44000000000000000000000000000−551-100000000000000000000000

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