Finite Group Databasebeta

← Group #13180826

Character table — Group #13180826

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122226688888888888812121818181836362222444412121616161616161616161616162424363636367272333366661818242424242424242424242424363654545454108108
order12443612122433366612121212121261288882436121236121261233366612121212121261224242424612224466121224666666121212121212612888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1
χ311-1-111-1-1-11111111-1-1-1-1-1-1-1111-1-11-111-1-111-1-1-11111111-1-1-1-1-1-1-1111-1-11-111-1-111-1-1-11111111-1-1-1-1-1-1-1111-1-11-1
χ411-1-111-1-1-11111111-1-1-1-1-1-1-11-1-111-1111-1-111-1-1-11111111-1-1-1-1-1-1-11-1-111-1111-1-111-1-1-11111111-1-1-1-1-1-1-11-1-111-11
χ52222222222-1-1-1-1-1-1-1-1-1-1-1-1220000002222222222-1-1-1-1-1-1-1-1-1-1-1-1220000002222222222-1-1-1-1-1-1-1-1-1-1-1-122000000
χ62222-1-1-1-1222-1-12-1-122-1-1-1-1-1-10000002222-1-1-1-1222-1-12-1-122-1-1-1-1-1-10000002222-1-1-1-1222-1-12-1-122-1-1-1-1-1-1000000
χ72222-1-1-1-122-12-1-12-1-1-122-1-1-1-10000002222-1-1-1-122-12-1-12-1-1-122-1-1-1-10000002222-1-1-1-122-12-1-12-1-1-122-1-1-1-1000000
χ82222-1-1-1-122-1-12-1-12-1-1-1-122-1-10000002222-1-1-1-122-1-12-1-12-1-1-1-122-1-10000002222-1-1-1-122-1-12-1-12-1-1-1-122-1-1000000
χ922-2-222-2-2-22-1-1-1-1-1-1111111-2200000022-2-222-2-2-22-1-1-1-1-1-1111111-2200000022-2-222-2-2-22-1-1-1-1-1-1111111-22000000
χ1022-2-2-1-111-222-1-12-1-1-2-211111-100000022-2-2-1-111-222-1-12-1-1-2-211111-100000022-2-2-1-111-222-1-12-1-1-2-211111-1000000
χ1122-2-2-1-111-22-12-1-12-111-2-2111-100000022-2-2-1-111-22-12-1-12-111-2-2111-100000022-2-2-1-111-22-12-1-12-111-2-2111-1000000
χ1222-2-2-1-111-22-1-12-1-121111-2-21-100000022-2-2-1-111-22-1-12-1-121111-2-21-100000022-2-2-1-111-22-1-12-1-121111-2-21-1000000
χ132-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00i2−i22−2002-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00i2−i22−2002-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00i2−i22−200
χ142-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00−i2i2−22002-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00−i2i2−22002-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00−i2i2−2200
χ152-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00i2−i2−22002-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00i2−i2−22002-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00i2−i2−2200
χ162-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00−i2i22−2002-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00−i2i22−2002-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00−i2i22−200
χ1733333333-1-1000000000000-1-11111-1-133333333-1-1000000000000-1-11111-1-133333333-1-1000000000000-1-11111-1-1
χ1833333333-1-1000000000000-1-1-1-1-1-11133333333-1-1000000000000-1-1-1-1-1-11133333333-1-1000000000000-1-1-1-1-1-111
χ1933-3-333-3-31-10000000000001-111-1-1-1133-3-333-3-31-10000000000001-111-1-1-1133-3-333-3-31-10000000000001-111-1-1-11
χ2033-3-333-3-31-10000000000001-1-1-1111-133-3-333-3-31-10000000000001-1-1-1111-133-3-333-3-31-10000000000001-1-1-1111-1
χ214-44i−4i4-44i−4i00111-1-1-1−ii−ii−ii000000004-44i−4i4-44i−4i00111-1-1-1−ii−ii−ii000000004-44i−4i4-44i−4i00111-1-1-1−ii−ii−ii00000000
χ224-44i−4i-22−2i2i0011-2-1-12−ii−ii2i−2i000000004-44i−4i-22−2i2i0011-2-1-12−ii−ii2i−2i000000004-44i−4i-22−2i2i0011-2-1-12−ii−ii2i−2i00000000
χ234-44i−4i-22−2i2i001-21-12-1−ii2i−2i−ii000000004-44i−4i-22−2i2i001-21-12-1−ii2i−2i−ii000000004-44i−4i-22−2i2i001-21-12-1−ii2i−2i−ii00000000
χ244-44i−4i-22−2i2i00-2112-1-12i−2i−ii−ii000000004-44i−4i-22−2i2i00-2112-1-12i−2i−ii−ii000000004-44i−4i-22−2i2i00-2112-1-12i−2i−ii−ii00000000
χ254-4−4i4i4-4−4i4i00111-1-1-1i−ii−ii−i000000004-4−4i4i4-4−4i4i00111-1-1-1i−ii−ii−i000000004-4−4i4i4-4−4i4i00111-1-1-1i−ii−ii−i00000000
χ264-4−4i4i-222i−2i0011-2-1-12i−ii−i−2i2i000000004-4−4i4i-222i−2i0011-2-1-12i−ii−i−2i2i000000004-4−4i4i-222i−2i0011-2-1-12i−ii−i−2i2i00000000
χ274-4−4i4i-222i−2i001-21-12-1i−i−2i2ii−i000000004-4−4i4i-222i−2i001-21-12-1i−i−2i2ii−i000000004-4−4i4i-222i−2i001-21-12-1i−i−2i2ii−i00000000
χ284-4−4i4i-222i−2i00-2112-1-1−2i2ii−ii−i000000004-4−4i4i-222i−2i00-2112-1-1−2i2ii−ii−i000000004-4−4i4i-222i−2i00-2112-1-1−2i2ii−ii−i00000000
χ296666-3-3-3-3-2-2000000000000110000006666-3-3-3-3-2-2000000000000110000006666-3-3-3-3-2-200000000000011000000
χ3066-6-6-3-3332-2000000000000-1100000066-6-6-3-3332-2000000000000-1100000066-6-6-3-3332-2000000000000-11000000
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ32111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3311-1-111-1-1-11111111-1-1-1-1-1-1-1111-1-11-111-1-111-1-1-11111111-1-1-1-1-1-1-1111-1-11-1-1-111-1-1111-1-1-1-1-1-1-11111111-1-1-111-11
χ3411-1-111-1-1-11111111-1-1-1-1-1-1-11-1-111-1111-1-111-1-1-11111111-1-1-1-1-1-1-11-1-111-11-1-111-1-1111-1-1-1-1-1-1-11111111-111-1-11-1
χ352222222222-1-1-1-1-1-1-1-1-1-1-1-1220000002222222222-1-1-1-1-1-1-1-1-1-1-1-122000000-2-2-2-2-2-2-2-2-2-2111111111111-2-2000000
χ362222-1-1-1-1222-1-12-1-122-1-1-1-1-1-10000002222-1-1-1-1222-1-12-1-122-1-1-1-1-1-1000000-2-2-2-21111-2-2-211-211-2-2111111000000
χ372222-1-1-1-122-12-1-12-1-1-122-1-1-1-10000002222-1-1-1-122-12-1-12-1-1-122-1-1-1-1000000-2-2-2-21111-2-21-211-2111-2-21111000000
χ382222-1-1-1-122-1-12-1-12-1-1-1-122-1-10000002222-1-1-1-122-1-12-1-12-1-1-1-122-1-1000000-2-2-2-21111-2-211-211-21111-2-211000000
χ3922-2-222-2-2-22-1-1-1-1-1-1111111-2200000022-2-222-2-2-22-1-1-1-1-1-1111111-22000000-2-222-2-2222-2111111-1-1-1-1-1-12-2000000
χ4022-2-2-1-111-222-1-12-1-1-2-211111-100000022-2-2-1-111-222-1-12-1-1-2-211111-1000000-2-22211-1-12-2-211-21122-1-1-1-1-11000000
χ4122-2-2-1-111-22-12-1-12-111-2-2111-100000022-2-2-1-111-22-12-1-12-111-2-2111-1000000-2-22211-1-12-21-211-21-1-122-1-1-11000000
χ4222-2-2-1-111-22-1-12-1-121111-2-21-100000022-2-2-1-111-22-1-12-1-121111-2-21-1000000-2-22211-1-12-211-211-2-1-1-1-122-11000000
χ432-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00i2−i22−2002-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00i2−i22−200-22−2i2i-22−2i2i00111-1-1-1−ii−ii−ii00−i2i2−2200
χ442-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00−i2i2−22002-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00−i2i2−2200-22−2i2i-22−2i2i00111-1-1-1−ii−ii−ii00i2−i22−200
χ452-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00i2−i2−22002-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00i2−i2−2200-222i−2i-222i−2i00111-1-1-1i−ii−ii−i00−i2i22−200
χ462-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00−i2i22−2002-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00−i2i22−200-222i−2i-222i−2i00111-1-1-1i−ii−ii−i00i2−i2−2200
χ4733333333-1-1000000000000-1-11111-1-133333333-1-1000000000000-1-11111-1-1-3-3-3-3-3-3-3-31100000000000011-1-1-1-111
χ4833333333-1-1000000000000-1-1-1-1-1-11133333333-1-1000000000000-1-1-1-1-1-111-3-3-3-3-3-3-3-311000000000000111111-1-1
χ4933-3-333-3-31-10000000000001-111-1-1-1133-3-333-3-31-10000000000001-111-1-1-11-3-333-3-333-11000000000000-11-1-1111-1
χ5033-3-333-3-31-10000000000001-1-1-1111-133-3-333-3-31-10000000000001-1-1-1111-1-3-333-3-333-11000000000000-1111-1-1-11
χ514-44i−4i4-44i−4i00111-1-1-1−ii−ii−ii000000004-44i−4i4-44i−4i00111-1-1-1−ii−ii−ii00000000-44−4i4i-44−4i4i00-1-1-1111i−ii−ii−i00000000
χ524-44i−4i-22−2i2i0011-2-1-12−ii−ii2i−2i000000004-44i−4i-22−2i2i0011-2-1-12−ii−ii2i−2i00000000-44−4i4i2-22i−2i00-1-1211-2i−ii−i−2i2i00000000
χ534-44i−4i-22−2i2i001-21-12-1−ii2i−2i−ii000000004-44i−4i-22−2i2i001-21-12-1−ii2i−2i−ii00000000-44−4i4i2-22i−2i00-12-11-21i−i−2i2ii−i00000000
χ544-44i−4i-22−2i2i00-2112-1-12i−2i−ii−ii000000004-44i−4i-22−2i2i00-2112-1-12i−2i−ii−ii00000000-44−4i4i2-22i−2i002-1-1-211−2i2ii−ii−i00000000
χ554-4−4i4i4-4−4i4i00111-1-1-1i−ii−ii−i000000004-4−4i4i4-4−4i4i00111-1-1-1i−ii−ii−i00000000-444i−4i-444i−4i00-1-1-1111−ii−ii−ii00000000
χ564-4−4i4i-222i−2i0011-2-1-12i−ii−i−2i2i000000004-4−4i4i-222i−2i0011-2-1-12i−ii−i−2i2i00000000-444i−4i2-2−2i2i00-1-1211-2−ii−ii2i−2i00000000
χ574-4−4i4i-222i−2i001-21-12-1i−i−2i2ii−i000000004-4−4i4i-222i−2i001-21-12-1i−i−2i2ii−i00000000-444i−4i2-2−2i2i00-12-11-21−ii2i−2i−ii00000000
χ584-4−4i4i-222i−2i00-2112-1-1−2i2ii−ii−i000000004-4−4i4i-222i−2i00-2112-1-1−2i2ii−ii−i00000000-444i−4i2-2−2i2i002-1-1-2112i−2i−ii−ii00000000
χ596666-3-3-3-3-2-2000000000000110000006666-3-3-3-3-2-200000000000011000000-6-6-6-6333322000000000000-1-1000000
χ6066-6-6-3-3332-2000000000000-1100000066-6-6-3-3332-2000000000000-11000000-6-66633-3-3-220000000000001-1000000
χ61222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ62222222222222222222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000000000000000000000
χ6322-2-222-2-2-22222222-2-2-2-2-2-2-2222-2-22-2-1-111-1-1111-1-1-1-1-1-1-11111111-1-1-111-11000000000000000000000000000000
χ6422-2-222-2-2-22222222-2-2-2-2-2-2-22-2-222-22-1-111-1-1111-1-1-1-1-1-1-11111111-111-1-11-1000000000000000000000000000000
χ654444444444-2-2-2-2-2-2-2-2-2-2-2-244000000-2-2-2-2-2-2-2-2-2-2111111111111-2-2000000000000000000000000000000000000
χ664444-2-2-2-2444-2-24-2-244-2-2-2-2-2-2000000-2-2-2-21111-2-2-211-211-2-2111111000000000000000000000000000000000000
χ674444-2-2-2-244-24-2-24-2-2-244-2-2-2-2000000-2-2-2-21111-2-21-211-2111-2-21111000000000000000000000000000000000000
χ684444-2-2-2-244-2-24-2-24-2-2-2-244-2-2000000-2-2-2-21111-2-211-211-21111-2-211000000000000000000000000000000000000
χ6944-4-444-4-4-44-2-2-2-2-2-2222222-44000000-2-222-2-2222-2111111-1-1-1-1-1-12-2000000000000000000000000000000000000
χ7044-4-4-2-222-444-2-24-2-2-4-422222-2000000-2-22211-1-12-2-211-21122-1-1-1-1-11000000000000000000000000000000000000
χ7144-4-4-2-222-44-24-2-24-222-4-4222-2000000-2-22211-1-12-21-211-21-1-122-1-1-11000000000000000000000000000000000000
χ7244-4-4-2-222-44-2-24-2-242222-4-42-2000000-2-22211-1-12-211-211-2-1-1-1-122-11000000000000000000000000000000000000
χ734-44i−4i4-44i−4i00-2-2-22222i−2i2i−2i2i−2i002i2−2i222−2200-22−2i2i-22−2i2i00111-1-1-1−ii−ii−ii00−i2i2−2200000000000000000000000000000000
χ744-44i−4i4-44i−4i00-2-2-22222i−2i2i−2i2i−2i00−2i22i2−222200-22−2i2i-22−2i2i00111-1-1-1−ii−ii−ii00i2−i22−200000000000000000000000000000000
χ754-4−4i4i4-4−4i4i00-2-2-2222−2i2i−2i2i−2i2i002i2−2i2−222200-222i−2i-222i−2i00111-1-1-1i−ii−ii−i00−i2i22−200000000000000000000000000000000
χ764-4−4i4i4-4−4i4i00-2-2-2222−2i2i−2i2i−2i2i00−2i22i222−2200-222i−2i-222i−2i00111-1-1-1i−ii−ii−i00i2−i2−2200000000000000000000000000000000
χ7766666666-2-2000000000000-2-22222-2-2-3-3-3-3-3-3-3-31100000000000011-1-1-1-111000000000000000000000000000000
χ7866666666-2-2000000000000-2-2-2-2-2-222-3-3-3-3-3-3-3-311000000000000111111-1-1000000000000000000000000000000
χ7966-6-666-6-62-20000000000002-222-2-2-22-3-333-3-333-11000000000000-11-1-1111-1000000000000000000000000000000
χ8066-6-666-6-62-20000000000002-2-2-2222-2-3-333-3-333-11000000000000-1111-1-1-11000000000000000000000000000000
χ818-88i−8i8-88i−8i00222-2-2-2−2i2i−2i2i−2i2i00000000-44−4i4i-44−4i4i00-1-1-1111i−ii−ii−i00000000000000000000000000000000000000
χ828-88i−8i-44−4i4i0022-4-2-24−2i2i−2i2i4i−4i00000000-44−4i4i2-22i−2i00-1-1211-2i−ii−i−2i2i00000000000000000000000000000000000000
χ838-88i−8i-44−4i4i002-42-24-2−2i2i4i−4i−2i2i00000000-44−4i4i2-22i−2i00-12-11-21i−i−2i2ii−i00000000000000000000000000000000000000
χ848-88i−8i-44−4i4i00-4224-2-24i−4i−2i2i−2i2i00000000-44−4i4i2-22i−2i002-1-1-211−2i2ii−ii−i00000000000000000000000000000000000000
χ858-8−8i8i8-8−8i8i00222-2-2-22i−2i2i−2i2i−2i00000000-444i−4i-444i−4i00-1-1-1111−ii−ii−ii00000000000000000000000000000000000000
χ868-8−8i8i-444i−4i0022-4-2-242i−2i2i−2i−4i4i00000000-444i−4i2-2−2i2i00-1-1211-2−ii−ii2i−2i00000000000000000000000000000000000000
χ878-8−8i8i-444i−4i002-42-24-22i−2i−4i4i2i−2i00000000-444i−4i2-2−2i2i00-12-11-21−ii2i−2i−ii00000000000000000000000000000000000000
χ888-8−8i8i-444i−4i00-4224-2-2−4i4i2i−2i2i−2i00000000-444i−4i2-2−2i2i002-1-1-2112i−2i−ii−ii00000000000000000000000000000000000000
χ8912121212-6-6-6-6-4-400000000000022000000-6-6-6-6333322000000000000-1-1000000000000000000000000000000000000
χ901212-12-12-6-6664-4000000000000-22000000-6-66633-3-3-220000000000001-1000000000000000000000000000000000000

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