Finite Group Databasebeta

← Group #72271468

Character table — Group #72271468

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222244444444444448888888888881616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323264646464646464646464646464
order12222222244444444444444444444444422224444444444444444444444444488888888888888882888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1
χ5111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-111111-1-111-1-111-1-1-1-1
χ7111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1111111
χ8111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-11111
χ91111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1i−ii−ii−ii−i11-1-1
χ101111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1−ii−ii−ii−ii11-1-1
χ111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1i−ii−i−ii−ii-1-111
χ121111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1−ii−iii−ii−i-1-111
χ131111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii1i−i−iii−i−ii-1-111
χ141111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i1−iii−i−iii−i-1-111
χ151111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-1i−i−ii−iii−i11-1-1
χ161111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-1−iii−ii−i−ii11-1-1
χ17222222222222222-2-222-2-222-2-2-2-222-2-222000000000000-2-222-2-20000222222-2-20000000000000000-2000000000000
χ18222222222222222-2-222-2-222-2-2-2-222-2-222000000000000-2-222-2-20000-2-2-2-2-2-22200000000000000002000000000000
χ192222222222222-2-222-2-22222-2-2-2-2-2-22222000000000000-2-2-2-22200002222-2-2220000000000000000-2000000000000
χ202222222222222-2-222-2-22222-2-2-2-2-2-22222000000000000-2-2-2-2220000-2-2-2-222-2-200000000000000002000000000000
χ2122222222222-2-2222-2222-22-222-2-2222-2-2-20000000000002-2-2-22-2000000000000000000002222000000000-2-2000000
χ2222222222222-2-2222-2222-22-222-2-2222-2-2-20000000000002-2-2-22-200000000000000000000-2-2-2-200000000022000000
χ2322222222222-2-222-2222-222-2-2-22222-22-2-2000000000000-22-2-2-2200000000000022220000000000000-2-20000000000
χ2422222222222-2-222-2222-222-2-2-22222-22-2-2000000000000-22-2-2-22000000000000-2-2-2-20000000000000220000000000
χ2522222222222-2-2-2-22-2-2-22-22-2-2-222-2-22-2-2-2000000000000-22222-20000000000002i2i−2i−2i0000000000000−2i2i0000000000
χ2622222222222-2-2-2-22-2-2-22-22-2-2-222-2-22-2-2-2000000000000-22222-2000000000000−2i−2i2i2i00000000000002i−2i0000000000
χ2722222222222-2-2-2-2-22-2-2-222-222-2-2-2-2-22-2-20000000000002-222-22000000000000000000002i2i−2i−2i000000000−2i2i000000
χ2822222222222-2-2-2-2-22-2-2-222-222-2-2-2-2-22-2-20000000000002-222-2200000000000000000000−2i−2i2i2i0000000002i−2i000000
χ29222222222-2-2222-2222-222-2222-2-22-222-2-2000000000000-222-2-2-200000000000000000000000022220000000-2-20000
χ30222222222-2-2222-2222-222-2222-2-22-222-2-2000000000000-222-2-2-2000000000000000000000000-2-2-2-20000000220000
χ31222222222-2-2222-2-2-22-2-2-2-22-2-2222-2-2-2-2-20000000000002-22-22200000000000000002i2i−2i−2i00000000000−2i2i00000000
χ32222222222-2-2222-2-2-22-2-2-2-22-2-2222-2-2-2-2-20000000000002-22-2220000000000000000−2i−2i2i2i000000000002i−2i00000000
χ33222222222-2-222-2222-2222-22-2-222-2222-2-20000000000002-2-22-2-20000000000000000222200000000000-2-200000000
χ34222222222-2-222-2222-2222-22-2-222-2222-2-20000000000002-2-22-2-20000000000000000-2-2-2-2000000000002200000000
χ35222222222-2-222-22-2-2-22-2-2-2222-2-2-22-2-2-2-2000000000000-22-22220000000000000000000000002i2i−2i−2i0000000−2i2i0000
χ36222222222-2-222-22-2-2-22-2-2-2222-2-2-22-2-2-2-2000000000000-22-2222000000000000000000000000−2i−2i2i2i00000002i−2i0000
χ37222222222-2-2-2-22-22-22-22-2-2-222222-22-2222-22-222-2-222-2-2-2-2-22-222-22-20000000000000000000000000000000000000
χ38222222222-2-2-2-22-22-22-22-2-2-222222-22-222-22-22-2-222-2-222-2-2-22-22-22-220000000000000000000000000000000000000
χ39222222222-2-2-2-22-2-222-2-22-2-2-2-2-2-22-2-222200000000000022-222-200000000000000000000000000000000000002-22-2
χ40222222222-2-2-2-22-2-222-2-22-2-2-2-2-2-22-2-222200000000000022-222-20000000000000000000000000000000000000-22-22
χ41222222222-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222-222000000000000222-2-2200000000000000000000000000000000000002-2-22
χ42222222222-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222-222000000000000222-2-220000000000000000000000000000000000000-222-2
χ43222222222-2-2-2-2-22-22-22-22-2-22222-22-22222-2-2222-2-2-2-222-2-22-22-22-2-220000000000000000000000000000000000000
χ44222222222-2-2-2-2-22-22-22-22-2-22222-22-2222-222-2-2-22222-2-2-2-22-22-2-222-20000000000000000000000000000000000000
χ4544444-44-4-40044004400440-4000000-4-40022222-22-22-22-2000000-2-2-2-20000000000000000000000000000000000000
χ4644444-44-4-40044004400440-4000000-4-400-2-2-2-2-22-22-22-2200000022220000000000000000000000000000000000000
χ4744444-44-4-4004400-4-400-4-40-4000000440022-2-22-22-2-22-22000000-2-2220000000000000000000000000000000000000
χ4844444-44-4-4004400-4-400-4-40-40000004400-2-222-22-222-22-200000022-2-20000000000000000000000000000000000000
χ4944444-44-4-400-4-4004-4004-404000000-44002-22-22-2-222-2-22000000-22-220000000000000000000000000000000000000
χ5044444-44-4-400-4-4004-4004-404000000-4400-22-22-222-2-222-20000002-22-20000000000000000000000000000000000000
χ5144444-44-4-400-4-400-4400-44040000004-4002-2-222-2-22-222-2000000-222-20000000000000000000000000000000000000
χ5244444-44-4-400-4-400-4400-44040000004-400-222-2-222-22-2-220000002-2-220000000000000000000000000000000000000
χ534444-44-44-4440044004400-400000-4-400002222-22-22-22-22000000-2-2-2-20000000000000000000000000000000000000
χ544444-44-44-4440044004400-400000-4-40000-2-2-2-22-22-22-22-200000022220000000000000000000000000000000000000
χ554444-44-44-44400-4-400-4-400-40000044000022-2-2-22-222-22-2000000-2-2220000000000000000000000000000000000000
χ564444-44-44-44400-4-400-4-400-400000440000-2-2222-22-2-22-2200000022-2-20000000000000000000000000000000000000
χ574444-44-44-4-4-4004-4004-400400000-4400002-22-2-222-2-222-2000000-22-220000000000000000000000000000000000000
χ584444-44-44-4-4-4004-4004-400400000-440000-22-222-2-222-2-220000002-22-20000000000000000000000000000000000000
χ594444-44-44-4-4-400-4400-44004000004-400002-2-22-222-22-2-22000000-222-20000000000000000000000000000000000000
χ604444-44-44-4-4-400-4400-44004000004-40000-222-22-2-22-222-20000002-2-220000000000000000000000000000000000000
χ614444-4-4-4-44000000000000004-44-400004-40004000000-4-400000000040000000000000000000000000000000000000
χ624444-4-4-4-44000000000000004-44-400004-4000-400000044000000000-40000000000000000000000000000000000000
χ634444-4-4-4-44000000000000004-4-440000-44040000-4-4000000000004000000000000000000000000000000000000000
χ644444-4-4-4-44000000000000004-4-440000-440-400004400000000000-4000000000000000000000000000000000000000
χ654444-4-4-4-4400000000000000-444-40000-444000-4-400000000000040000000000000000000000000000000000000000
χ664444-4-4-4-4400000000000000-444-40000-44-400044000000000000-40000000000000000000000000000000000000000
χ674444-4-4-4-4400000000000000-44-4400004-400400000-4-40000000000400000000000000000000000000000000000000
χ684444-4-4-4-4400000000000000-44-4400004-400-400000440000000000-400000000000000000000000000000000000000
χ6944-4-40-40404-4004-400-440000000000000000000000000000000000002i2i−2i−2i2i−2i002i−2i2i−2i00002-22-200000000000000000
χ7044-4-40-40404-4004-400-440000000000000000000000000000000000002i2i−2i−2i2i−2i00−2i2i−2i2i0000-22-2200000000000000000
χ7144-4-40-40404-4004-400-44000000000000000000000000000000000000−2i−2i2i2i−2i2i002i−2i2i−2i0000-22-2200000000000000000
χ7244-4-40-40404-4004-400-44000000000000000000000000000000000000−2i−2i2i2i−2i2i00−2i2i−2i2i00002-22-200000000000000000
χ7344-4-40-40404-400-44004-40000000000000000000000000000000000002i2i−2i−2i−2i2i002-2-220000−2i2i2i−2i00000000000000000
χ7444-4-40-40404-400-44004-40000000000000000000000000000000000002i2i−2i−2i−2i2i00-222-200002i−2i−2i2i00000000000000000
χ7544-4-40-40404-400-44004-4000000000000000000000000000000000000−2i−2i2i2i2i−2i002-2-2200002i−2i−2i2i00000000000000000
χ7644-4-40-40404-400-44004-4000000000000000000000000000000000000−2i−2i2i2i2i−2i00-222-20000−2i2i2i−2i00000000000000000
χ774-44-4-40400004-4004-400-4400000000000000000000000000000000002i−2i2i−2i002i−2i00002i−2i2i−2i00002-22-20000000000000
χ784-44-4-40400004-4004-400-4400000000000000000000000000000000002i−2i2i−2i002i−2i0000−2i2i−2i2i0000-22-220000000000000
χ794-44-4-40400004-4004-400-440000000000000000000000000000000000−2i2i−2i2i00−2i2i00002i−2i2i−2i0000-22-220000000000000
χ804-44-4-40400004-4004-400-440000000000000000000000000000000000−2i2i−2i2i00−2i2i0000−2i2i−2i2i00002-22-20000000000000
χ814-44-4-40400004-400-44004-400000000000000000000000000000000002i−2i2i−2i00−2i2i00002-2-220000−2i2i2i−2i0000000000000
χ824-44-4-40400004-400-44004-400000000000000000000000000000000002i−2i2i−2i00−2i2i0000-222-200002i−2i−2i2i0000000000000
χ834-44-4-40400004-400-44004-40000000000000000000000000000000000−2i2i−2i2i002i−2i00002-2-2200002i−2i−2i2i0000000000000
χ844-44-4-40400004-400-44004-40000000000000000000000000000000000−2i2i−2i2i002i−2i0000-222-20000−2i2i2i−2i0000000000000
χ8588-8-80-8080-88008800-8-80000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-80-8080-8800-8-800880000000000000000000000000000000000000000000000000000000000000000000000000
χ878-88-8-8080000-88008800-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8-8080000-8800-8-8008800000000000000000000000000000000000000000000000000000000000000000000000
χ891616-16-160160-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9016-1616-16160-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9116-16-16160000000000000000000000000000000000000000000000000004-4-44000000000000000000000000000000000
χ9216-16-1616000000000000000000000000000000000000000000000000000-444-4000000000000000000000000000000000

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