Finite Group Databasebeta

← Group #14512489

Character table — Group #14512489

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111224444444455556688888888101012161616161616161616161616161616162424242430304040404040404040606060606060606060120120120120
order1222225101010101010104444443666666644415153030303030303030303030303030202020204412121212121212124888888888888
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
χ51111-1-1111-1-1-1-11111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-111-1-11-11-1
χ61111-1-1111-1-1-1-11111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-111-11-11
χ71111-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ81111-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111−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
χ112222-2-2222-2-2-2-22222222-1-1-11111-1-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-1-1-1-11111-2000000000000
χ122222-2-2222-2-2-2-22-2-2-2-222-1-1-11111-122-2-1-1-1-1-1-1-1-11111111122-2-2-2-21111-1-1-1-12000000000000
χ1322-2-2002-2-2000022i2i−2i−2i2-222-20000-20002222-2-2-2-2000000002-2002i−2i2i2i−2i−2i00000000000000000
χ1422-2-2002-2-2000022i2i−2i−2i2-2-1-11−i3−i3i3i31000-1-1-1-11111−i3−i3−i3−i3i3i3i3i32-2002i−2i−i−iii33−3−30000000000000
χ1522-2-2002-2-2000022i2i−2i−2i2-2-1-11i3i3−i3−i31000-1-1-1-11111i3i3i3i3−i3−i3−i3−i32-2002i−2i−i−iii−3−3330000000000000
χ1622-2-2002-2-200002−2i−2i2i2i2-222-20000-20002222-2-2-2-2000000002-200−2i2i−2i−2i2i2i00000000000000000
χ1722-2-2002-2-200002−2i−2i2i2i2-2-1-11−i3−i3i3i31000-1-1-1-11111−i3−i3−i3−i3i3i3i3i32-200−2i2iii−i−i−3−3330000000000000
χ1822-2-2002-2-200002−2i−2i2i2i2-2-1-11i3i3−i3−i31000-1-1-1-11111i3i3i3i3−i3−i3−i3−i32-200−2i2iii−i−i33−3−30000000000000
χ192-2-222-222-222-2-2-22i−2i2i−2i00-11-11-11-112i−2i0-1-11111-1-111-1-111-1-1000000i−ii−ii−ii−i01+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ202-2-222-222-222-2-2-22i−2i2i−2i00-11-11-11-112i−2i0-1-11111-1-111-1-111-1-1000000i−ii−ii−ii−i0−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ212-2-222-222-222-2-2-2−2i2i−2i2i00-11-11-11-11−2i2i0-1-11111-1-111-1-111-1-1000000−ii−ii−ii−ii01−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ222-2-222-222-222-2-2-2−2i2i−2i2i00-11-11-11-11−2i2i0-1-11111-1-111-1-111-1-1000000−ii−ii−ii−ii0−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ232-2-22-2222-2-2-222-22i−2i2i−2i00-11-1-11-111−2i2i0-1-11111-1-1-1-111-1-111000000i−ii−i−ii−ii01+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ242-2-22-2222-2-2-222-22i−2i2i−2i00-11-1-11-111−2i2i0-1-11111-1-1-1-111-1-111000000i−ii−i−ii−ii0−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ252-2-22-2222-2-2-222-2−2i2i−2i2i00-11-1-11-1112i−2i0-1-11111-1-1-1-111-1-111000000−ii−iii−ii−i01−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ262-2-22-2222-2-2-222-2−2i2i−2i2i00-11-1-11-1112i−2i0-1-11111-1-1-1-111-1-111000000−ii−iii−ii−i0−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
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
χ313333-3-3333-3-3-3-333333-1-100000000-3-310000000000000000-1-111-1-100000000111-1-111-1-1-11-11
χ323333-3-3333-3-3-3-333333-1-100000000-3-310000000000000000-1-111-1-1000000001-1-111-1-1111-11-1
χ333333-3-3333-3-3-3-33-3-3-3-3-1-1000000003310000000000000000-1-1111100000000-1ii−i−i−i−iii−iii−i
χ343333-3-3333-3-3-3-33-3-3-3-3-1-1000000003310000000000000000-1-1111100000000-1−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
χ384444-4-4-1-1-11111-1000044444-4-4-4-4400-4-1-1-1-1-1-1-1-111111111-1-11100000000000000000000000
χ394444-4-4-1-1-11111-1000044-2-2-22222-200-41−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152-1-11100000000000000000000000
χ404444-4-4-1-1-11111-1000044-2-2-22222-200-41+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152-1-11100000000000000000000000
χ4144-4-400-111−55−55-100004-444-40000-4000-1-1-1-11111−55−555−55−5-11−5500000000000000000000000
χ4244-4-400-111−55−55-100004-4-2-22−2i3−2i32i32i320001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58-11−5500000000000000000000000
χ4344-4-400-111−55−55-100004-4-2-222i32i3−2i3−2i320001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46-11−5500000000000000000000000
χ4444-4-400-1115−55−5-100004-444-40000-4000-1-1-1-111115−55−5−55−55-115−500000000000000000000000
χ4544-4-400-1115−55−5-100004-4-2-22−2i3−2i32i32i320001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46-115−500000000000000000000000
χ4644-4-400-1115−55−5-100004-4-2-222i32i3−2i3−2i320001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58-115−500000000000000000000000
χ474-44-4004-440000-44-4-44001-1-1−i3i3i3−i3100011-1-111-1-1−i3−i3i3i3i3i3−i3−i3000000-111-1−i3i3i3−i30000000000000
χ484-44-4004-440000-44-4-44001-1-1i3−i3−i3i3100011-1-111-1-1i3i3−i3−i3−i3−i3i3i3000000-111-1i3−i3−i3i30000000000000
χ494-44-4004-440000-44-4-4400-2220000-2000-2-222-2-222000000000000002-2-2200000000000000000
χ504-44-4004-440000-4-444-4001-1-1−i3i3i3−i3100011-1-111-1-1−i3−i3i3i3i3i3−i3−i30000001-1-11i3−i3−i3i30000000000000
χ514-44-4004-440000-4-444-4001-1-1i3−i3−i3i3100011-1-111-1-1i3i3−i3−i3−i3−i3i3i30000001-1-11−i3i3i3−i30000000000000
χ524-44-4004-440000-4-444-400-2220000-2000-2-222-2-22200000000000000-222-200000000000000000
χ534-4-444-444-444-4-4-44i−4i4i−4i001-11-11-11-14i−4i011-1-1-1-111-1-111-1-111000000−ii−ii−ii−ii0000000000000
χ544-4-444-444-444-4-4-4−4i4i−4i4i001-11-11-11-1−4i4i011-1-1-1-111-1-111-1-111000000i−ii−ii−ii−i0000000000000
χ554-4-44-4444-4-4-444-44i−4i4i−4i001-111-11-1-1−4i4i011-1-1-1-11111-1-111-1-1000000−ii−iii−ii−i0000000000000
χ564-4-44-4444-4-4-444-4−4i4i−4i4i001-111-11-1-14i−4i011-1-1-1-11111-1-111-1-1000000i−ii−i−ii−ii0000000000000
χ5766-6-6006-6-6000066i6i−6i−6i-22000000000000000000000000000-2200−2i2i000000000000000000000
χ5866-6-6006-6-600006−6i−6i6i6i-22000000000000000000000000000-22002i−2i000000000000000000000
χ598-88-800-22-2−252525−2520000002-2-2−2i32i32i3−2i32000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58000000000000000000000000000
χ608-88-800-22-2−252525−2520000002-2-22i3−2i3−2i32i32000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46000000000000000000000000000
χ618-88-800-22-2−252525−252000000-4440000-400011-1-111-1-1−555−55−5−55000000000000000000000000000
χ628-88-800-22-225−25−252520000002-2-2−2i32i32i3−2i32000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46000000000000000000000000000
χ638-88-800-22-225−25−252520000002-2-22i3−2i3−2i32i32000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58000000000000000000000000000
χ648-88-800-22-225−25−25252000000-4440000-400011-1-111-1-15−5−55−555−5000000000000000000000000000
χ658-8-888-8-2-22-2-22220000002-22-22-22-2000−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152000000000000000000000000000
χ668-8-888-8-2-22-2-22220000002-22-22-22-2000−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152000000000000000000000000000
χ678-8-888-8-2-22-2-2222000000-44-44-44-4400011-1-1-1-111-1-111-1-111000000000000000000000000000
χ688-8-88-88-2-2222-2-220000002-222-22-2-2000−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152000000000000000000000000000
χ698-8-88-88-2-2222-2-220000002-222-22-2-2000−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152000000000000000000000000000
χ708-8-88-88-2-2222-2-22000000-44-4-44-44400011-1-1-1-11111-1-111-1-1000000000000000000000000000
χ71121212121212-3-3-3-3-3-3-3-30000-4-40000000000-40000000000000000111100000000000000000000000
χ7212121212-12-12-3-3-33333-30000-4-400000000004000000000000000011-1-100000000000000000000000
χ731212-12-1200-333−3535−3535-30000-440000000000000000000000000001-15−500000000000000000000000
χ741212-12-1200-33335−3535−35-30000-440000000000000000000000000001-1−5500000000000000000000000

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