Finite Group Databasebeta

← Group #72262347

Character table — Group #72262347

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222244444888888888888881616161616161616161616161616163232323232323232323232326464646464646464646464646464646464646464
order12222222222222222222222444422222224444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ9111111111111111-1-1-1-111-1-1-1-1-1-111-111-1-111-111-1-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111111-1-1-1-111-1-1-1-1-1-111-111-1-111-111-1-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111111-1-1-1-111-1-1-1-1-1-111-111-1-111-111-1-1-1-1-1-1-111-1-11111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ12111111111111111-1-1-1-111-1-1-1-1-1-111-111-1-111-111-1-1-1-1-1-1-111-1-11111-1-111−i−iiiii−i−iii−i−i−i−iii
χ13111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-111-11111-1-111-1-1-1-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ14111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-111-11111-1-111-1-1-1-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ15111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-111-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ16111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-111-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ17222222222222222222222-2-22222-2-2-22222-2-2-22222-20000-2-2-2-2000000000000000000000000
χ18222222222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200002222000000000000000000000000
χ19222222222222222-2-2-2-22222-2-2-2-2-2-2222-2-2-2-2222-2-220000-2-222000000000000000000000000
χ20222222222222222-2-2-2-22222-2-2-2-2-2-22-2-222-2-22-2-2222000022-2-2000000000000000000000000
χ212222222222222-2-22222-2-222-2-2-2-22220000-2-2-20000-20000000000000000000000002i−2i2i−2i0000
χ222222222222222-2-22222-2-222-2-2-2-22220000-2-2-20000-2000000000000000000000000−2i2i−2i2i0000
χ232222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2000022200002000000000000000000002i−2i2i−2i00000000
χ242222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-200002220000200000000000000000000−2i2i−2i2i00000000
χ252222222222222-2-2-2-2-2-2-2-2222222-2-22000022-20000-2000000000000000000002-2-2200000000
χ262222222222222-2-2-2-2-2-2-2-2222222-2-22000022-20000-200000000000000000000-222-200000000
χ272222222222222-2-2-2-2-2-2-2-2-2-2222222-20000-2-22000020000000000000000000000002-2-220000
χ282222222222222-2-2-2-2-2-2-2-2-2-2222222-20000-2-2200002000000000000000000000000-222-20000
χ292222-2-2-2-222-22-22222-2-2-2-22222-2-22-2-200002-220000-20000000000002i−2i2i−2i0000000000000000
χ302222-2-2-2-222-22-22222-2-2-2-22222-2-22-2-200002-220000-2000000000000−2i2i−2i2i0000000000000000
χ312222-2-2-2-222-22-22222-2-2-2-2-2-222-2-2-2220000-22-2000022i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ322222-2-2-2-222-22-22222-2-2-2-2-2-222-2-2-2220000-22-200002−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ332222-2-2-2-222-22-222-2-222-2-222-2-222-22-20000-2220000-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ342222-2-2-2-222-22-222-2-222-2-222-2-222-22-20000-2220000-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ352222-2-2-2-222-22-222-2-222-2-2-2-2-2-2222-2200002-2-2000020000000000002i−2i−2i2i0000000000000000
χ362222-2-2-2-222-22-222-2-222-2-2-2-2-2-2222-2200002-2-200002000000000000−2i2i2i−2i0000000000000000
χ372222-2-2-2-222-22-2-2-222-2-22222-2-2222-2-20000-22-20000200000000000000002-22-2000000000000
χ382222-2-2-2-222-22-2-2-222-2-22222-2-2222-2-20000-22-2000020000000000000000-22-22000000000000
χ392222-2-2-2-222-22-2-2-222-2-222-2-2-2-222-22200002-220000-200000000000000000000000000002i−2i2i−2i
χ402222-2-2-2-222-22-2-2-222-2-222-2-2-2-222-22200002-220000-20000000000000000000000000000−2i2i−2i2i
χ412222-2-2-2-222-22-2-2-2-2-222222222-2-2-22-200002-2-20000200000000000000000000000000002-2-22
χ422222-2-2-2-222-22-2-2-2-2-222222222-2-2-22-200002-2-2000020000000000000000000000000000-222-2
χ432222-2-2-2-222-22-2-2-2-2-22222-2-222-2-22-220000-2220000-200000000000000002i−2i−2i2i000000000000
χ442222-2-2-2-222-22-2-2-2-2-22222-2-222-2-22-220000-2220000-20000000000000000−2i2i2i−2i000000000000
χ4544444444-4-4-44-44-400004-4000000000004400000-4-4000000000000000000000000000000000
χ4644444444-4-4-44-44-400004-400000000000-4-40000044000000000000000000000000000000000
χ4744444444-4-4-44-4-440000-440000000004400000-4-400000000000000000000000000000000000
χ4844444444-4-4-44-4-440000-44000000000-4-4000004400000000000000000000000000000000000
χ49444444-4-44-44-4-400000000004-44-40000000000000002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ50444444-4-44-44-4-400000000004-44-4000000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ51444444-4-44-44-4-40000000000-44-440000000000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ52444444-4-44-44-4-40000000000-44-44000000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ534444-4-4444-4-4-4400000000004-4-440000000000000002-2-2200002-2-2200000000000000000000
χ544444-4-4444-4-4-4400000000004-4-44000000000000000-222-20000-222-200000000000000000000
χ554444-4-4444-4-4-440000000000-444-40000000000000002-2-220000-222-200000000000000000000
χ564444-4-4444-4-4-440000000000-444-4000000000000000-222-200002-2-2200000000000000000000
χ574444-4-4-4-4-4-44444-40000-440000000000000000000000000004-4000000000000000000000000
χ584444-4-4-4-4-4-44444-40000-44000000000000000000000000000-44000000000000000000000000
χ594444-4-4-4-4-4-4444-4400004-400000000000000000000000004-400000000000000000000000000
χ604444-4-4-4-4-4-4444-4400004-40000000000000000000000000-4400000000000000000000000000
χ61888888-8-8-88-8-880000000000000000000000000000000000000000000000000000000000000
χ628888-8-888-888-8-80000000000000000000000000000000000000000000000000000000000000
χ638-8-88008-800000004-44-40000000000000000004-44-4000000000000000000000000000000000
χ648-8-88008-800000004-44-4000000000000000000-44-44000000000000000000000000000000000
χ658-8-88008-80000000-44-440000000000000000004-4-44000000000000000000000000000000000
χ668-8-88008-80000000-44-44000000000000000000-444-4000000000000000000000000000000000
χ678-8-8800-8800000004-4-44000000000004-44-40000000000000000000000000000000000000000
χ688-8-8800-8800000004-4-4400000000000-44-440000000000000000000000000000000000000000
χ698-8-8800-880000000-444-4000000000004-4-440000000000000000000000000000000000000000
χ708-8-8800-880000000-444-400000000000-444-40000000000000000000000000000000000000000
χ711616-16-16000000000000000008-8000000000000000000000000000000000000000000000000000
χ721616-16-1600000000000000000-88000000000000000000000000000000000000000000000000000
χ7316-1616-1616-1600000000000000000000000000000000000000000000000000000000000000000000
χ7416-1616-16-161600000000000000000000000000000000000000000000000000000000000000000000

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