Finite Group Databasebeta

← Group #72271721

Character table — Group #72271721

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222222222224444444444448888888881212121212121616161616161616161616161616161616161616162424242424242424242424242432323232323232323248484848484896
order1222234444688666888121212122424441616161624242422224424444481212161624244848484848484848444448888161616164612121212121212224416164
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1
χ31111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ5111111111111111111111111111-1-1-1-111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-11-11-1-1-11
χ6111111111111111111111111111-1-1-1-1111111111-1-11111111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-11-11-1-1-1
χ7111111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-1-11-1111-1
χ8111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-11-1111
χ91111111111111111111111111-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-11111-111-1-111-1-11-11-1-1-1-1
χ101111111111111111111111111-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111111-1-111-1-111-11-11-1-11
χ111111111111111111111111111-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-111-1-111-1-1-11-11111
χ121111111111111111111111111-1-11111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-11-1-111-1-1111-11-111-1
χ131111111111111111111111111-1-1-1-1-1-111111-1-11111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111111-1
χ141111111111111111111111111-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-111-1-1-1-1-1-11111-1111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1111
χ151111111111111111111111111-1-1-1-1-1-1111-1-111-1-111-1-111-1-1-111-1-1-1-1-1-1111111111-1-1111111-111-1-1-1-111-1-1-1-1-1-11
χ161111111111111111111111111-1-1-1-1-1-1111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-11111-1-11111-1-1-1
χ1722222222222-2-2222-2-2-22222-2-2220000-2-2-2222222000000-22200-2-20000000020000-2-2-2-200000000000000000000
χ1822222222222-2-2222-2-2-22222-2-2220000-2-2-2-2-2-2-2-2-2000000-22200-2-200000000-20000222200000000000000000000
χ1922222222222-2-2222-2-2-22222-2-2-2-20000-2-2-222-2-2220000002-2-2002200000000-20000-2-22200000000000000000000
χ2022222222222-2-2222-2-2-22222-2-2-2-20000-2-2-2-2-222-2-20000002-2-20022000000002000022-2-200000000000000000000
χ21222222-2-2-2-2200222000-2-2-2-2002-222−2−20002-2222-200000002-22−20022−2−222−2−2-20000000022−2−200000000000002−20
χ22222222-2-2-2-2200222000-2-2-2-2002-222−2−2000-22-2-2-2200000002-22−20022−2−222−2−2200000000−2−2220000000000000−220
χ23222222-2-2-2-2200222000-2-2-2-2002-2−2−2220002-2222-200000002-2−2200−2−222−2−222-200000000−2−2220000000000000−220
χ24222222-2-2-2-2200222000-2-2-2-2002-2−2−222000-22-2-2-2200000002-2−2200−2−222−2−22220000000022−2−200000000000002−20
χ25222222-2-2-2-2200222000-2-2-2-200-2222−2−20002-2-2-22-20000000-22−220022−2−2−2−22220000000022−2−20000000000000−220
χ26222222-2-2-2-2200222000-2-2-2-200-2222−2−2000-2222-220000000-22−220022−2−2−2−222-200000000−2−22200000000000002−20
χ27222222-2-2-2-2200222000-2-2-2-200-22−2−2220002-2-2-22-20000000-222−200−2−22222−2−2200000000−2−22200000000000002−20
χ28222222-2-2-2-2200222000-2-2-2-200-22−2−222000-2222-220000000-222−200−2−22222−2−2-20000000022−2−20000000000000−220
χ2922222-12222-122-1-1-1222-1-1-1-1-1-1222222-1-1-10000002222222-1-122-1-1-1-1-1-1-1-1-1-100000000000002-1-1-1-1-1-1-1-10000000
χ3022222-12222-122-1-1-1222-1-1-1-1-1-1222222-1-1-1000000-2-2-2-2-2-22-1-122-1-1-1-1-1-1-1-1-1-10000000000000-2111111110000000
χ3122222-12222-122-1-1-1222-1-1-1-1-1-122-2-2-2-2-1-1-100000022-2-2-2-22-1-1-2-2-1-11111111100000000000002-1-1-1-111110000000
χ3222222-12222-122-1-1-1222-1-1-1-1-1-122-2-2-2-2-1-1-1000000-2-222222-1-1-2-2-1-1111111110000000000000-21111-1-1-1-10000000
χ3322222-12222-122-1-1-1222-1-1-1-1-1-1-2-22222-1-1-10000002222-2-2-211-2-211-1-1-1-111110000000000000-2-1-111-1-1110000000
χ3422222-12222-122-1-1-1222-1-1-1-1-1-1-2-22222-1-1-1000000-2-2-2-222-211-2-211-1-1-1-111110000000000000211-1-111-1-10000000
χ3522222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-100000022-2-222-21122111111-1-1-1-10000000000000-2-1-11111-1-10000000
χ3622222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1000000-2-222-2-2-21122111111-1-1-1-10000000000000211-1-1-1-1110000000
χ37222-2-222-2-222-2-2-22-222-22-22-2-2-2002i−2i2i−2i2-2200000000000000000002i−2i2i−2i000002i2i−2i−2i0000000000000000020-20000
χ38222-2-222-2-222-2-2-22-222-22-22-2-2-2002i−2i2i−2i2-2200000000000000000002i−2i2i−2i00000−2i−2i2i2i00000000000000000-2020000
χ39222-2-222-2-222-2-2-22-222-22-22-2-2-200−2i2i−2i2i2-220000000000000000000−2i2i−2i2i000002i2i−2i−2i00000000000000000-2020000
χ40222-2-222-2-222-2-2-22-222-22-22-2-2-200−2i2i−2i2i2-220000000000000000000−2i2i−2i2i00000−2i−2i2i2i0000000000000000020-20000
χ4122-22-22-22-222-2-22-2-22-22-222-2-2-200000022-20000002-2000000000000000000002i−2i2i−2i00002i−2i2i−2i02-20000000000000
χ4222-22-22-22-222-2-22-2-22-22-222-2-2-200000022-20000002-200000000000000000000−2i2i−2i2i0000−2i2i−2i2i02-20000000000000
χ4322-22-22-22-222-2-22-2-22-22-222-2-2-200000022-2000000-22000000000000000000002i−2i2i−2i0000−2i2i−2i2i0-220000000000000
χ4422-22-22-22-222-2-22-2-22-22-222-2-2-200000022-2000000-2200000000000000000000−2i2i−2i2i00002i−2i2i−2i0-220000000000000
χ4522-2-222-2-222222-2-222-2-2-2-222220000002-2-22-200-22002-20000000000000000002-2-222-2000000000002-2000000000
χ4622-2-222-2-222222-2-222-2-2-2-222220000002-2-22-200-2200-22000000000000000000-222-22-200000000000-22000000000
χ4722-2-222-2-222222-2-222-2-2-2-222220000002-2-2-22002-2002-2000000000000000000-222-2-22000000000002-2000000000
χ4822-2-222-2-222222-2-222-2-2-2-222220000002-2-2-22002-200-220000000000000000002-2-22-2200000000000-22000000000
χ4922-2-222-2-2222-2-2-2-22-222-2-222-2-2000000-2222-200-2200002-200000000000000000000-2200000000000002-2020-2000
χ5022-2-222-2-2222-2-2-2-22-222-2-222-2-2000000-2222-200-220000-2200000000000000000000-220000000000000-220-202000
χ5122-2-222-2-2222-2-2-2-22-222-2-222-2-2000000-222-22002-200002-2000000000000000000002-200000000000002-20-202000
χ5222-2-222-2-2222-2-2-2-22-222-2-222-2-2000000-222-22002-20000-22000000000000000000002-20000000000000-22020-2000
χ5344444-24444-2-4-4-2-2-2-4-4-4-2-2-2-222440000222000000000000-4-2-200220000000000000000000000000000000000000
χ5444444-24444-2-4-4-2-2-2-4-4-4-2-2-2-222-4-4000022200000000000042200-2-20000000000000000000000000000000000000
χ5544444-2-4-4-4-4-200-2-2-20002222004-42222−22−220000000000000000-2222−2200−2−222−2−22200000000000000000000000000000
χ5644444-2-4-4-4-4-200-2-2-20002222004-4−22−2222220000000000000000-22−22220022−2−222−2−200000000000000000000000000000
χ5744444-2-4-4-4-4-200-2-2-2000222200-442222−22−2200000000000000002-2−222200−2−22222−2−200000000000000000000000000000
χ5844444-2-4-4-4-4-200-2-2-2000222200-44−22−22222200000000000000002-222−220022−2−2−2−22200000000000000000000000000000
χ59444-4-444-4-44444-44-4-4-444-44-444000000-44-400000000000000000000000000000000000000000000000000000000
χ60444-4-44-444-4400-44-4000-44-440000−2i22i22i2−2i20000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ61444-4-44-444-4400-44-4000-44-4400002i2−2i2−2i22i200000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ62444-4-4-24-4-44-2442-22-4-44-22-22-2-20000002-220000000000000000000000023−2323−2300000000000000000000000000000
χ63444-4-4-24-4-44-2442-22-4-44-22-22-2-20000002-2200000000000000000000000−2323−232300000000000000000000000000000
χ64444-4-4-24-4-44-2-4-42-2244-4-22-2222004i−4i4i−4i-22-20000000000000000000−2i2i−2i2i000000000000000000000000000000000
χ65444-4-4-24-4-44-2-4-42-2244-4-22-222200−4i4i−4i4i-22-200000000000000000002i−2i2i−2i000000000000000000000000000000000
χ66444-4-4-2-444-4-2002-220002-22-20000−2i22i22i2−2i200000000000000000000−2i32i3i2−i2−i2i26−6−6600000000000000000000000000000
χ67444-4-4-2-444-4-2002-220002-22-20000−2i22i22i2−2i2000000000000000000002i3−2i3i2−i2−i2i2−666−600000000000000000000000000000
χ68444-4-4-2-444-4-2002-220002-22-200002i2−2i2−2i22i200000000000000000000−2i32i3−i2i2i2−i2−666−600000000000000000000000000000
χ69444-4-4-2-444-4-2002-220002-22-200002i2−2i2−2i22i2000000000000000000002i3−2i3−i2i2i2−i26−6−6600000000000000000000000000000
χ7044-44-444-44-44004-4-40004-4-4400000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ7144-44-444-44-44004-4-40004-4-44000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ7244-44-44-44-444444-4-4-44-4-444-444000000-4-4400000000000000000000000000000000000000000000000000000000
χ7344-44-4-2-44-44-244-222-44-42-2-22-2-200000022-2000000000000000000000000000000000000000000023−2300000000000
χ7444-44-4-2-44-44-244-222-44-42-2-22-2-200000022-20000000000000000000000000000000000000000000−232300000000000
χ7544-44-4-2-44-44-2-4-4-2224-442-2-2222000000-2-220000004-4000000000000000000000000000000000-220000000000000
χ7644-44-4-2-44-44-2-4-4-2224-442-2-2222000000-2-22000000-440000000000000000000000000000000002-20000000000000
χ7744-4-44444-4-4400-4-4400044-4-4000000000004400-4-400000000000000000000000000000000000000000000000000
χ7844-4-44444-4-4400-4-4400044-4-400000000000-4-4004400000000000000000000000000000000000000000000000000
χ7944-4-44-2-4-444-24422-24-4-422-2-2-2-2000000-222000000004-400000000000000000000000000000000000-22000000000
χ8044-4-44-2-4-444-24422-24-4-422-2-2-2-2000000-22200000000-44000000000000000000000000000000000002-2000000000
χ8144-4-44-2-4-444-2-4-422-2-44422-2-2220000002-2-200000000004-400000000000000000000000000000000000-220000000
χ8244-4-44-2-4-444-2-4-422-2-44422-2-2220000002-2-20000000000-44000000000000000000000000000000000002-20000000
χ8388-88-8-48-88-8-400-444000-444-40000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-488-8-8-40044-4000-4-4440000000000000000000000000000000000000000000000000000000000000000000
χ858-800080000-8−4i24i20000000000−4i24i2000000000004-4000000000000000000000000000000−2i22i200000000000000000000
χ868-800080000-8−4i24i20000000000−4i24i200000000000-440000000000000000000000000000002i2−2i200000000000000000000
χ878-800080000-84i2−4i200000000004i2−4i2000000000004-40000000000000000000000000000002i2−2i200000000000000000000
χ888-800080000-84i2−4i200000000004i2−4i200000000000-44000000000000000000000000000000−2i22i200000000000000000000
χ8916-16000-800008−8i28i200000000004i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ9016-16000-8000088i2−8i20000000000−4i24i200000000000000000000000000000000000000000000000000000000000000000

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