Finite Group Databasebeta

← Group #72271754

Character table — Group #72271754

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1122222222244444444444448888816161616161616161616161616161616161616161616162424242424242424242432323232323232323248484848484848484896
order122223444466668888121212122424442424242222448121216161616242448484848484848484444444488466661212121224888161616168
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-11-1111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1111-11-1-1-1111-1-1-1-1-1-1-1
χ411111111111111111111111111111111-11-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-11111111
χ511111111111111111111111111111-1-1-11-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-11-1111-1-1111-1-1-1-11
χ611111111111111111111111111111-1-1-11-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-11-111111-1-1-11111-1
χ711111111111111111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1
χ811111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11
χ9111111111111111111111111-1-111111-11-11-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-111-11-11-1-1-1-11-1-111-1-11
χ10111111111111111111111111-1-111111-11-11-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-111-11-11-1-111-111-1-111-1
χ11111111111111111111111111-1-111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1111-1-1-1-111-1-1111-1-111-1
χ12111111111111111111111111-1-111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-111-1-11
χ13111111111111111111111111-1-1111-1-11111-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1111
χ14111111111111111111111111-1-1111-1-11111-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1
χ15111111111111111111111111-1-1111-1-11-11-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-11-1111111111-1-1-1
χ16111111111111111111111111-1-1111-1-11-11-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111111-1-11-11-111-1-1-1-1-1-1-1111
χ1722222222222222-2-2-2-22222-2-222-2-2-2000000-2220000-2-20000000022220000-2-200000000000-20000000
χ1822222222222222-2-2-2-22222-2-222-2-2-2000000-2220000-2-200000000-2-2-2-20000220000000000020000000
χ1922222222222222-2-2-2-22222-2-2-2-2-2-2-20000002-2-20000220000000022-2-200002200000000000-20000000
χ2022222222222222-2-2-2-22222-2-2-2-2-2-2-20000002-2-200002200000000-2-2220000-2-20000000000020000000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-122-1-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-100000000002-1-1-1-1-1-1-1-10000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-122-1-1-1222-22-22-1-1-2-2-2-2-1-1111111110000000000-2-1-1-11-11110000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-122-1-1-1-2-2-22-222-1-1-2-2-2-2-1-11111111100000000002111-11-1-1-10000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-122-1-1-1-2-2-2-2-2-22-1-12222-1-1-1-1-1-1-1-1-1-10000000000-2111111110000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-1-1-122-22-22-211-2-222111111-1-1-1-10000000000-2-1-11-11-1110000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-1-1-122-2-2-2-2-21122-2-211-1-1-1-1111100000000002-1-11111-1-10000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-1-1-1-2-22222-21122-2-211-1-1-1-111110000000000-211-1-1-1-1110000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-1-1-1-2-22-22-2-211-2-222111111-1-1-1-10000000000211-11-11-1-10000000000
χ29222-2-2222-2-222-2-2-22-222-22-22200-2-2200020-20000000000000000000002i2i−2i−2i00000020-200000002i−2i000
χ30222-2-2222-2-222-2-2-22-222-22-22200-2-2200020-2000000000000000000000−2i−2i2i2i00000020-20000000−2i2i000
χ31222-2-2222-2-222-2-2-22-222-22-22200-2-22000-2020000000000000000000002i2i−2i−2i000000-2020000000−2i2i000
χ32222-2-2222-2-222-2-2-22-222-22-22200-2-22000-202000000000000000000000−2i−2i2i2i000000-20200000002i−2i000
χ3322-22-22-222-22-2-2222-2-2-222-222002-2-20000000002-2000022-2-2000000002i−2i2i−2i000000000000002i−2i00000
χ3422-22-22-222-22-2-2222-2-2-222-222002-2-20000000002-2000022-2-200000000−2i2i−2i2i00000000000000−2i2i00000
χ3522-22-22-222-22-2-2222-2-2-222-222002-2-2000000000-220000-2-222000000002i−2i2i−2i00000000000000−2i2i00000
χ3622-22-22-222-22-2-2222-2-2-222-222002-2-2000000000-220000-2-22200000000−2i2i−2i2i000000000000002i−2i00000
χ3722-2-222-22-222-22-22-2-22-2-222-2-2002-222-2000000000000000000000002-200002-202-20000002-200000000
χ3822-2-222-22-222-22-22-2-22-2-222-2-2002-222-200000000000000000000000-220000-2202-2000000-2200000000
χ3922-2-222-22-222-22-22-2-22-2-222-2-2002-22-22000000000000000000000002-200002-20-22000000-2200000000
χ4022-2-222-22-222-22-22-2-22-2-222-2-2002-22-2200000000000000000000000-220000-220-220000002-200000000
χ4122-2-222-22-222-22-2-222-2-2-2222200-22-20020-2000000000000000000002-22-2-22-2200020-20000000000000
χ4222-2-222-22-222-22-2-222-2-2-2222200-22-20020-200000000000000000000-22-222-22-200020-20000000000000
χ4322-2-222-22-222-22-2-222-2-2-2222200-22-200-202000000000000000000002-2-222-2-22000-2020000000000000
χ4422-2-222-22-222-22-2-222-2-2-2222200-22-200-20200000000000000000000-222-2-222-2000-2020000000000000
χ45444444-4-4-4-444440000-4-4-4-4004-400000000004-40000000000000000000000000000000000000000000
χ46444444-4-4-4-444440000-4-4-4-400-440000000000-440000000000000000000000000000000000000000000
χ4744444-24444-2-2-2-2-4-4-4-4-2-2-2-22244222000000-4-2-20000220000000000000000000000000000000000000
χ4844444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-42220000004220000-2-20000000000000000000000000000000000000
χ4944444-2-4-4-4-4-2-2-2-200002222004-40000000000-22000000i6−i6i6−i6i6i6−i6−i600000000000000000000000000000
χ5044444-2-4-4-4-4-2-2-2-200002222004-40000000000-22000000−i6i6−i6i6−i6−i6i6i600000000000000000000000000000
χ5144444-2-4-4-4-4-2-2-2-20000222200-4400000000002-2000000i6−i6i6−i6−i6−i6i6i600000000000000000000000000000
χ5244444-2-4-4-4-4-2-2-2-20000222200-4400000000002-2000000−i6i6−i6i6i6i6−i6−i600000000000000000000000000000
χ53444-4-4444-4-444-4-44-44-44-44-4-4-40044-40000000000000000000000000000000000000000000000000000
χ54444-4-44-4-44444-4-40000-44-440000000000000000000000000000000000000000000000000000000022−220
χ55444-4-44-4-44444-4-40000-44-4400000000000000000000000000000000000000000000000000000000−22220
χ56444-4-4-244-4-4-2-2224-44-4-22-222200-2-22000000000000000000000000000000000000000023−230000000000
χ57444-4-4-244-4-4-2-2224-44-4-22-222200-2-220000000000000000000000000000000000000000−23230000000000
χ58444-4-4-244-4-4-2-222-44-44-22-22-2-20022-200040-40000000000000000000000000000000-202000000000000
χ59444-4-4-244-4-4-2-222-44-44-22-22-2-20022-2000-404000000000000000000000000000000020-2000000000000
χ6044-44-444-4-444-4-4400004-4-4400000000000000000022−2200000022−2222−2200000000000000000000000000000
χ6144-44-444-4-444-4-4400004-4-44000000000000000000−2222000000−2222−222200000000000000000000000000000
χ6244-44-44-444-44-4-44-4-444-444-4-4-400-4440000000000000000000000000000000000000000000000000000
χ6344-44-4-24-4-44-222-20000-222-200000000000000000022−22−2i32i3i6−i6−i6i6−22−2200000000000000000000000000000
χ6444-44-4-24-4-44-222-20000-222-200000000000000000022−222i3−2i3−i6i6i6−i6−22−2200000000000000000000000000000
χ6544-44-4-24-4-44-222-20000-222-2000000000000000000−2222−2i32i3−i6i6i6−i62−22−200000000000000000000000000000
χ6644-44-4-24-4-44-222-20000-222-2000000000000000000−22222i3−2i3i6−i6−i6i62−22−200000000000000000000000000000
χ6744-44-4-2-444-4-222-244-4-42-2-22-2-200-2220000000004-40000-2-222000000000000000000000000000000000
χ6844-44-4-2-444-4-222-244-4-42-2-22-2-200-222000000000-44000022-2-2000000000000000000000000000000000
χ6944-44-4-2-444-4-222-2-4-4442-2-2222002-2-20000000000000000000−2i32i32i3−2i300000000000000000000000000000
χ7044-44-4-2-444-4-222-2-4-4442-2-2222002-2-200000000000000000002i3−2i3−2i32i300000000000000000000000000000
χ7144-4-4444-44-44-44-4000044-4-40000000000000000000000000000004-4000000000000000000000000000
χ7244-4-4444-44-44-44-4000044-4-4000000000000000000000000000000-44000000000000000000000000000
χ7344-4-44-2-44-44-22-224-4-4422-2-22200-22-24-400000000000000000000000000000000-220000000000000000
χ7444-4-44-2-44-44-22-224-4-4422-2-22200-22-2-44000000000000000000000000000000002-20000000000000000
χ7544-4-44-2-44-44-22-22-444-422-2-2-2-2002-220040-40000000000000000000000000000000-2020000000000000
χ7644-4-44-2-44-44-22-22-444-422-2-2-2-2002-2200-404000000000000000000000000000000020-20000000000000
χ77888-8-8-4-8-888-4-44400004-44-400000000000000000000000000000000000000000000000000000000000
χ7888-8-88-48-88-8-44-440000-4-44400000000000000000000000000000000000000000000000000000000000
χ7916-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000
χ8016-16000-800008000000000004i6−4i6000000000000000000000000000000000000000000000000000000000
χ8116-16000-80000800000000000−4i64i6000000000000000000000000000000000000000000000000000000000

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