Finite Group Databasebeta

← Group #13146613

Character table — Group #13146613

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222299991212121212121212181818181818181818181818181818181818181818181818181818181818181818182424242436363636363636367272727272727272
order12223446661212121222223366666644444444446666121212121212121212121212121212121212121212121212444444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ511111-1-1111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111-1-1111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111-1-1111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ811111-1-1111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ91-11-11i−i1-1-1ii−i−i1-11-111-1-111-1-1i−i11-1-1ii−i−i1-11-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i1-11-1i−ii−i1-11-1i−ii−i
χ101-11-11i−i1-1-1ii−i−i1-11-111-1-111-1-1i−i11-1-1ii−i−i1-11-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i-11-11−ii−ii-11-11−ii−ii
χ111-11-11i−i1-1-1ii−i−i1-11-111-1-111-1-1i−i-1-111−i−iii1-11-1ii−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i1-1-11i−i−ii1-1-11i−i−ii
χ121-11-11i−i1-1-1ii−i−i1-11-111-1-111-1-1i−i-1-111−i−iii1-11-1ii−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i-111-1−iii−i-111-1−iii−i
χ131-11-11−ii1-1-1−i−iii1-11-111-1-111-1-1−ii11-1-1−i−iii1-11-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii1-11-1−ii−ii1-11-1−ii−ii
χ141-11-11−ii1-1-1−i−iii1-11-111-1-111-1-1−ii11-1-1−i−iii1-11-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii-11-11i−ii−i-11-11i−ii−i
χ151-11-11−ii1-1-1−i−iii1-11-111-1-111-1-1−ii-1-111ii−i−i1-11-1−i−iii-1-1-1-11111iiii−i−i−i−i−i−iii1-1-11−iii−i1-1-11−iii−i
χ161-11-11−ii1-1-1−i−iii1-11-111-1-111-1-1−ii-1-111ii−i−i1-11-1−i−iii-1-1-1-11111iiii−i−i−i−i−i−iii-111-1i−i−ii-111-1i−i−ii
χ1722222222222222-2-2-2-222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ1822222-2-2222-2-2-2-2-2-2-2-2222222222200000000-2-2-2-222220000000000000000-2-2-2-20000000000000000
χ1922-2-2200-22-200002-2-222222-2-2-2-20000002-22-22-2-2200000000000022-2-222-2-200000000000000000000
χ2022-2-2200-22-200002-2-222222-2-2-2-2000000-22-222-2-22000000000000-2-222-2-22200000000000000000000
χ2122-2-2200-22-20000-222-22222-2-2-2-2002-22-20000-222-2000022-2-222-2-20000000000000000000000000000
χ2222-2-2200-22-20000-222-22222-2-2-2-200-22-220000-222-20000-2-222-2-2220000000000000000000000000000
χ232-22-222i−2i2-2-22i2i−2i−2i-22-2222-2-222-2-2−2i2i00000000-22-22−2i−2i2i2i00000000000000002i2i−2i−2i0000000000000000
χ242-22-22−2i2i2-2-2−2i−2i2i2i-22-2222-2-222-2-22i−2i00000000-22-222i2i−2i−2i0000000000000000−2i−2i2i2i0000000000000000
χ252-2-22200-2-22000022-2-222-2-2-2-2220000002i−2i−2i2i22-2-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ262-2-22200-2-22000022-2-222-2-2-2-222000000−2i2i2i−2i22-2-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ272-2-22200-2-220000-2-22222-2-2-2-222002-2-220000-2-222000022-2-2-2-2220000000000000000000000000000
χ282-2-22200-2-220000-2-22222-2-2-2-22200-222-20000-2-2220000-2-22222-2-20000000000000000000000000000
χ294444444444444400001-21-21-21-200000000000000000000000000000000001-21-20022002200-1-100-1-1
χ304444444444444400001-21-21-21-200000000000000000000000000000000001-21-200-2-200-2-200110011
χ31444444444444440000-21-21-21-210000000000000000000000000000000000-21-2122002200-1-100-1-100
χ32444444444444440000-21-21-21-210000000000000000000000000000000000-21-21-2-200-2-20011001100
χ3344444-4-4444-4-4-4-400001-21-21-21-20000000000000000000000000000000000-12-12002200-2-200-1-10011
χ3444444-4-4444-4-4-4-400001-21-21-21-20000000000000000000000000000000000-12-1200-2-20022001100-1-1
χ3544444-4-4444-4-4-4-40000-21-21-21-2100000000000000000000000000000000002-12-12200-2-200-1-1001100
χ3644444-4-4444-4-4-4-40000-21-21-21-2100000000000000000000000000000000002-12-1-2-20022001100-1-100
χ374-44-444i−4i4-4-44i4i−4i−4i00001-2-121-2-120000000000000000000000000000000000i−2i−i2i002-2002i−2i00-1100−ii
χ384-44-444i−4i4-4-44i4i−4i−4i00001-2-121-2-120000000000000000000000000000000000i−2i−i2i00-2200−2i2i001-100i−i
χ394-44-444i−4i4-4-44i4i−4i−4i0000-212-1-212-10000000000000000000000000000000000−2ii2i−i2-2002i−2i00-1100−ii00
χ404-44-444i−4i4-4-44i4i−4i−4i0000-212-1-212-10000000000000000000000000000000000−2ii2i−i-2200−2i2i001-100i−i00
χ414-44-44−4i4i4-4-4−4i−4i4i4i00001-2-121-2-120000000000000000000000000000000000−i2ii−2i002-200−2i2i00-1100i−i
χ424-44-44−4i4i4-4-4−4i−4i4i4i00001-2-121-2-120000000000000000000000000000000000−i2ii−2i00-22002i−2i001-100−ii
χ434-44-44−4i4i4-4-4−4i−4i4i4i0000-212-1-212-100000000000000000000000000000000002i−i−2ii2-200−2i2i00-1100i−i00
χ444-44-44−4i4i4-4-4−4i−4i4i4i0000-212-1-212-100000000000000000000000000000000002i−i−2ii-22002i−2i001-100−ii00
χ456666-366-3-3-3-3-3-3-32222000000002200000000-1-1-1-1-1-1-1-13−33−33−33−33−33−33−33−300000000000000000000
χ466666-366-3-3-3-3-3-3-32222000000002200000000-1-1-1-1-1-1-1-1−33−33−33−33−33−33−33−3300000000000000000000
χ476666-366-3-3-3-3-3-3-3-2-2-2-200000000-2-22222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ486666-366-3-3-3-3-3-3-3-2-2-2-200000000-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000000
χ496666-3-6-6-3-3-33333222200000000-2-200000000-1-1-1-111113−33−33−33−3−33−33−33−3300000000000000000000
χ506666-3-6-6-3-3-33333222200000000-2-200000000-1-1-1-11111−33−33−33−333−33−33−33−300000000000000000000
χ516666-3-6-6-3-3-33333-2-2-2-200000000222222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ526666-3-6-6-3-3-33333-2-2-2-20000000022-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000
χ5366-6-6-3003-3333−3333−332-2-2200000000002-22-20000-111-13−33−3-1-111-1-1113−3−333−3−3300000000000000000000
χ5466-6-6-3003-3333−3333−332-2-220000000000-22-220000-111-13−33−311-1-111-1-1−333−3−333−300000000000000000000
χ5566-6-6-3003-3333−3333−33-222-2000000000000002-22-21-1-11−33−33−333−3−333−3-1-111-1-11100000000000000000000
χ5666-6-6-3003-3333−3333−33-222-200000000000000-22-221-1-11−33−333−3−333−3−3311-1-111-1-100000000000000000000
χ5766-6-6-3003-33−3333−33332-2-2200000000002-22-20000-111-1−33−33-1-111-1-111−333−3−333−300000000000000000000
χ5866-6-6-3003-33−3333−33332-2-220000000000-22-220000-111-1−33−3311-1-111-1-13−3−333−3−3300000000000000000000
χ5966-6-6-3003-33−3333−3333-222-2000000000000002-22-21-1-113−33−33−3−333−3−33-1-111-1-11100000000000000000000
χ6066-6-6-3003-33−3333−3333-222-200000000000000-22-221-1-113−33−3−333−3−333−311-1-111-1-100000000000000000000
χ616-66-6-36i−6i-333−3i−3i3i3i2-22-2000000002i−2i00000000-11-11−i−iii3−33−3−33−33i3−i3i3−i3−i3i3−i3i300000000000000000000
χ626-66-6-36i−6i-333−3i−3i3i3i2-22-2000000002i−2i00000000-11-11−i−iii−33−333−33−3−i3i3−i3i3i3−i3i3−i300000000000000000000
χ636-66-6-36i−6i-333−3i−3i3i3i-22-2200000000−2i2i22-2-22i2i−2i−2i1-11-1ii−i−i-1-1-1-11111−i−i−i−iiiii00000000000000000000
χ646-66-6-36i−6i-333−3i−3i3i3i-22-2200000000−2i2i-2-222−2i−2i2i2i1-11-1ii−i−i1111-1-1-1-1iiii−i−i−i−i00000000000000000000
χ656-66-6-3−6i6i-3333i3i−3i−3i2-22-200000000−2i2i00000000-11-11ii−i−i3−33−3−33−33−i3i3−i3i3i3−i3i3−i300000000000000000000
χ666-66-6-3−6i6i-3333i3i−3i−3i2-22-200000000−2i2i00000000-11-11ii−i−i−33−333−33−3i3−i3i3−i3−i3i3−i3i300000000000000000000
χ676-66-6-3−6i6i-3333i3i−3i−3i-22-22000000002i−2i22-2-2−2i−2i2i2i1-11-1−i−iii-1-1-1-11111iiii−i−i−i−i00000000000000000000
χ686-66-6-3−6i6i-3333i3i−3i−3i-22-22000000002i−2i-2-2222i2i−2i−2i1-11-1−i−iii1111-1-1-1-1−i−i−i−iiiii00000000000000000000
χ696-6-66-30033-3−3i33i33i3−3i322-2-200000000002-2-220000-1-111−i3i3i3−i3-1-11111-1-1−i3i3i3−i3i3−i3−i3i300000000000000000000
χ706-6-66-30033-3−3i33i33i3−3i322-2-20000000000-222-20000-1-111−i3i3i3−i311-1-1-1-111i3−i3−i3i3−i3i3i3−i300000000000000000000
χ716-6-66-30033-3−3i33i33i3−3i3-2-222000000000000002i−2i−2i2i11-1-1i3−i3−i3i33−3−33−333−3−i−iiiii−i−i00000000000000000000
χ726-6-66-30033-3−3i33i33i3−3i3-2-22200000000000000−2i2i2i−2i11-1-1i3−i3−i3i3−333−33−3−33ii−i−i−i−iii00000000000000000000
χ736-6-66-30033-33i3−3i3−3i33i322-2-200000000002-2-220000-1-111i3−i3−i3i3-1-11111-1-1i3−i3−i3i3−i3i3i3−i300000000000000000000
χ746-6-66-30033-33i3−3i3−3i33i322-2-20000000000-222-20000-1-111i3−i3−i3i311-1-1-1-111−i3i3i3−i3i3−i3−i3i300000000000000000000
χ756-6-66-30033-33i3−3i3−3i33i3-2-222000000000000002i−2i−2i2i11-1-1−i3i3i3−i3−333−33−3−33−i−iiiii−i−i00000000000000000000
χ766-6-66-30033-33i3−3i3−3i33i3-2-22200000000000000−2i2i2i−2i11-1-1−i3i3i3−i33−3−33−333−3ii−i−i−i−iii00000000000000000000
χ7788-8-8800-88-8000000002-42-4-24-24000000000000000000000000000000000000000000000000000000
χ7888-8-8800-88-800000000-42-424-24-2000000000000000000000000000000000000000000000000000000
χ798-8-88800-8-88000000002-4-24-242-4000000000000000000000000000000000000000000000000000000
χ808-8-88800-8-8800000000-424-24-2-42000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).