Finite Group Databasebeta

← Group #72271728

Character table — Group #72271728

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222244444444448888888812121212121212121212121216161616161616161616161616161616161616161616161624243232323232323232484848484848484848484848
order1244222344461212666888812121244882424242422444444888844444488121216161616242448484848484848488812121212121224242224448816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-111-111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-111-111-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11-1-1111111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-111-1-1-111-1-1
χ10111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-11-111-11-1-1-1-111
χ11111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-11-1-11-111-1-111
χ12111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-1-111111-1-1
χ13111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1-111
χ14111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-11-1-11-11111-1-1
χ15111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111-111-11-1-111-1-1
χ16111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111
χ1722222222222222222-2-2-2-222222-2-2-2-2-2-222222222-2-2-2-200000000220000-2-200000000-2-200000000000000000000
χ1822222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000220000-2-2000000002200000000000000000000
χ1922222222222222222-2-2-2-2222-2-222-2-2-2-22222-2-2-2-2222200000000-2-200002200000000-2-200000000000000000000
χ2022222222222222222-2-2-2-2222-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2000022000000002200000000000000000000
χ212222222-1222-1-1-1-1-1-12222-1-1-12222-1-1-1-100000000000022222222-1-12222-1-1-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1000000000000
χ222222222-1222-1-1-1-1-1-12222-1-1-12222-1-1-1-100000000000022-2-2-2-222-1-1-2-2-2-2-1-11111111100-1-11111-1-1000000000000
χ232222222-1222-1-1-1-1-1-12222-1-1-12222-1-1-1-1000000000000-2-22222-2-2-1-1-2-2-2-2-1-1111111110011-1-1-1-111000000000000
χ242222222-1222-1-1-1-1-1-12222-1-1-12222-1-1-1-1000000000000-2-2-2-2-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10011111111000000000000
χ252222222-1222-1-1-1-1-1-12222-1-1-1-2-2-2-2-1-1-1-10000000000002222-2-2-2-21122-2-211-1-1-1-1111100-1-1-1-11111000000000000
χ262222222-1222-1-1-1-1-1-12222-1-1-1-2-2-2-2-1-1-1-100000000000022-2-222-2-211-2-222111111-1-1-1-100-1-111-1-111000000000000
χ272222222-1222-1-1-1-1-1-12222-1-1-1-2-2-2-2-1-1-1-1000000000000-2-222-2-22211-2-222111111-1-1-1-10011-1-111-1-1000000000000
χ282222222-1222-1-1-1-1-1-12222-1-1-1-2-2-2-2-1-1-1-1000000000000-2-2-2-222221122-2-211-1-1-1-11111001111-1-1-1-1000000000000
χ2922222-2-22-22-22222-2-22-22-2-22-200002-22-200002i2i−2i−2i2i2i−2i−2i0000000000002-200000022-2-20000000000000000002i−2i00
χ3022222-2-22-22-22222-2-22-22-2-22-200002-22-200002i2i−2i−2i2i2i−2i−2i000000000000-22000000-2-222000000000000000000−2i2i00
χ3122222-2-22-22-22222-2-22-22-2-22-200002-22-20000−2i−2i2i2i−2i−2i2i2i0000000000002-200000022-2-2000000000000000000−2i2i00
χ3222222-2-22-22-22222-2-22-22-2-22-200002-22-20000−2i−2i2i2i−2i−2i2i2i000000000000-22000000-2-2220000000000000000002i−2i00
χ3322222-2-22-22-22222-2-2-22-22-22-20000-22-2200002i2i−2i−2i−2i−2i2i2i00000000002-2000022-2-20000000000000000000000002i−2i
χ3422222-2-22-22-22222-2-2-22-22-22-20000-22-2200002i2i−2i−2i−2i−2i2i2i0000000000-220000-2-222000000000000000000000000−2i2i
χ3522222-2-22-22-22222-2-2-22-22-22-20000-22-220000−2i−2i2i2i2i2i−2i−2i00000000002-2000022-2-2000000000000000000000000−2i2i
χ3622222-2-22-22-22222-2-2-22-22-22-20000-22-220000−2i−2i2i2i2i2i−2i−2i0000000000-220000-2-2220000000000000000000000002i−2i
χ3722-2-2-22-2222-22-2-2-22-222-2-222-20000-2-22200002i−2i2i−2i2i−2i2i−2i0000002i−2i0000000000000000000000002i−2i200-200000000
χ3822-2-2-22-2222-22-2-2-22-222-2-222-20000-2-22200002i−2i2i−2i2i−2i2i−2i000000−2i2i000000000000000000000000−2i2i-200200000000
χ3922-2-2-22-2222-22-2-2-22-222-2-222-20000-2-2220000−2i2i−2i2i−2i2i−2i2i0000002i−2i0000000000000000000000002i−2i-200200000000
χ4022-2-2-22-2222-22-2-2-22-222-2-222-20000-2-2220000−2i2i−2i2i−2i2i−2i2i000000−2i2i000000000000000000000000−2i2i200-200000000
χ4122-2-2-22-2222-22-2-2-22-2-2-22222-2000022-2-200002i−2i2i−2i−2i2i−2i2i2-20000000000000000000000002-20000000000002i−2i0000
χ4222-2-2-22-2222-22-2-2-22-2-2-22222-2000022-2-200002i−2i2i−2i−2i2i−2i2i-22000000000000000000000000-22000000000000−2i2i0000
χ4322-2-2-22-2222-22-2-2-22-2-2-22222-2000022-2-20000−2i2i−2i2i2i−2i2i−2i2-20000000000000000000000002-2000000000000−2i2i0000
χ4422-2-2-22-2222-22-2-2-22-2-2-22222-2000022-2-20000−2i2i−2i2i2i−2i2i−2i-22000000000000000000000000-220000000000002i−2i0000
χ4522-2-2-2-222-2222-2-2-2-222-2-22-2220000-222-200002-2-222-2-22002-20000000000000000000000002-2000000200-2000000
χ4622-2-2-2-222-2222-2-2-2-222-2-22-2220000-222-200002-2-222-2-2200-22000000000000000000000000-22000000-2002000000
χ4722-2-2-2-222-2222-2-2-2-222-2-22-2220000-222-20000-222-2-222-2002-20000000000000000000000002-2000000-2002000000
χ4822-2-2-2-222-2222-2-2-2-222-2-22-2220000-222-20000-222-2-222-200-22000000000000000000000000-22000000200-2000000
χ4922-2-2-2-222-2222-2-2-2-22-222-2-22200002-2-2200002-2-22-222-200002-20000000000000000000000002-2000200-20000000
χ5022-2-2-2-222-2222-2-2-2-22-222-2-22200002-2-2200002-2-22-222-20000-22000000000000000000000000-22000-20020000000
χ5122-2-2-2-222-2222-2-2-2-22-222-2-22200002-2-220000-222-22-2-2200002-20000000000000000000000002-2000-20020000000
χ5222-2-2-2-222-2222-2-2-2-22-222-2-22200002-2-220000-222-22-2-220000-22000000000000000000000000-22000200-20000000
χ534444444-2444-2-2-2-2-2-2-4-4-4-4-2-2-244-4-4222200000000000000000000-2-2000022000000000000000000000000000000
χ544444444-2444-2-2-2-2-2-2-4-4-4-4-2-2-2-4-444222200000000000000000000220000-2-2000000000000000000000000000000
χ5544444-4-4-2-44-4-2-2-2-2224-44-42-220000-22-220000000000000000000000004-4000000-2-2220000000000000000000000
χ5644444-4-4-2-44-4-2-2-2-2224-44-42-220000-22-22000000000000000000000000-4400000022-2-20000000000000000000000
χ5744444-4-4-2-44-4-2-2-2-222-44-442-2200002-22-200000000000000000000004-40000-2-22200000000000000000000000000
χ5844444-4-4-2-44-4-2-2-2-222-44-442-2200002-22-20000000000000000000000-44000022-2-200000000000000000000000000
χ594444-44-44-4-44444-44-40000-4-44004-40000000000000000000000000000004-4000000000000000000000000000000
χ604444-44-44-4-44444-44-40000-4-4400-44000000000000000000000000000000-44000000000000000000000000000000
χ614444-44-4-2-4-44-2-2-22-22000022-2004-4000000000000000000000000000000-226−66−66−66−60000000000000000000000
χ624444-44-4-2-4-44-2-2-22-22000022-2004-4000000000000000000000000000000-22−66−66−66−660000000000000000000000
χ634444-44-4-2-4-44-2-2-22-22000022-200-440000000000000000000000000000002-26−66−6−66−660000000000000000000000
χ644444-44-4-2-4-44-2-2-22-22000022-200-440000000000000000000000000000002-2−66−666−66−60000000000000000000000
χ654444-4-4444-4-4444-4-4400004-4-44-4000000000000000000000000004-4000000000000000000000000000000000000
χ664444-4-4444-4-4444-4-4400004-4-4-4400000000000000000000000000-44000000000000000000000000000000000000
χ674444-4-44-24-4-4-2-2-222-20000-2224-400000000000000000000000000-220000006−6−666−6−660000000000000000000000
χ684444-4-44-24-4-4-2-2-222-20000-2224-400000000000000000000000000-22000000−666−6−666−60000000000000000000000
χ694444-4-44-24-4-4-2-2-222-20000-222-44000000000000000000000000002-20000006−6−66−666−60000000000000000000000
χ704444-4-44-24-4-4-2-2-222-20000-222-44000000000000000000000000002-2000000−666−66−6−660000000000000000000000
χ7144-4-44444-4-4-44-4-44440000-4-4-40000000044-4-4000000000000000000000000000000000000000000000000000000
χ7244-4-44444-4-4-44-4-44440000-4-4-400000000-4-444000000000000000000000000000000000000000000000000000000
χ7344-4-44-4-444-444-4-44-4-400004-44000000000000000000000000000000000000000000004i−4i00000000000000000000
χ7444-4-44-4-444-444-4-44-4-400004-4400000000000000000000000000000000000000000000−4i4i00000000000000000000
χ7544-4-4-44-4-244-4-2222-2244-4-4-2-22000022-2-20000000000000000004i−4i000000000000000000000000−2i2i000000000000
χ7644-4-4-44-4-244-4-2222-2244-4-4-2-22000022-2-2000000000000000000−4i4i0000000000000000000000002i−2i000000000000
χ7744-4-4-44-4-244-4-2222-22-4-444-2-220000-2-2220000000000004-4000000000000000000000000-22000000000000000000
χ7844-4-4-44-4-244-4-2222-22-4-444-2-220000-2-222000000000000-440000000000000000000000002-2000000000000000000
χ7944-4-4-4-44-2-444-22222-24-4-442-2-200002-2-22000000000000004-4000000000000000000000000-220000000000000000
χ8044-4-4-4-44-2-444-22222-24-4-442-2-200002-2-2200000000000000-440000000000000000000000002-20000000000000000
χ8144-4-4-4-44-2-444-22222-2-444-42-2-20000-222-200000000000000004-4000000000000000000000000-2200000000000000
χ8244-4-4-4-44-2-444-22222-2-444-42-2-20000-222-20000000000000000-440000000000000000000000002-200000000000000
χ8388-8-8888-4-8-8-8-444-4-4-40000444000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-8-8-48-88-444-4440000-44-4000000000000000000000000000000000000000000000000000000000000000000
χ858-88i−8i0008000-88i−8i0000000000000000004-44i−4i000000000000000000000000000000000000000000000000000000
χ868-88i−8i0008000-88i−8i000000000000000000-44−4i4i000000000000000000000000000000000000000000000000000000
χ878-8−8i8i0008000-8−8i8i0000000000000000004-4−4i4i000000000000000000000000000000000000000000000000000000
χ888-8−8i8i0008000-8−8i8i000000000000000000-444i−4i000000000000000000000000000000000000000000000000000000
χ8916-1616i−16i000-80008−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9016-16−16i16i000-800088i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000

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