Finite Group Databasebeta

← Group #72318165

Character table — Group #72318165

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11222222244448888888888888888161616161616323232323232323232323232323232323232323232323232323232323232323232323232323232326464646464646464
order12222444422442222224444444444224444222244444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-11-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111111-11-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111111-1-11-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111
χ711111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ9111111111111111-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-1
χ10111111111111111-1-1111111-1-11111-1-1-1-1-1-1111-11-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-11-1-111
χ11111111111111111-1-1111111-1-11111-1-1-1-1-1-111-11-1111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-111-1-1-111
χ12111111111111111-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1111-1-1
χ13111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111
χ14111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1111-1-1
χ15111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-111-1-1
χ16111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-11-11-1-111
χ1722222222222222-2222-222-2-222-2-2-2-22-22-2-2-2000202000000002200000000000000000000000000-2-20000
χ1822222222222222-2222-222-2-222-2-2-2-22-22-2-2-2000-20-200000000-2-200000000000000000000000000220000
χ1922222222222222-2-2-22-222-2-2-2-2-2-2-2-2-22-222200020200000000-2-200000000000000000000000000-220000
χ2022222222222222-2-2-22-222-2-2-2-2-2-2-2-2-22-2222000-20-20000000022000000000000000000000000002-20000
χ212222222222222-2222-22-2-22222-2-2-2-2-22-22-2-20020200000002200000000000000000000000000-2-2000000
χ222222222222222-2222-22-2-22222-2-2-2-2-22-22-2-200-20-20000000-2-20000000000000000000000000022000000
χ232222222222222-22-2-2-22-2-222-2-2-2-2-2-22-22-222002020000000-2-200000000000000000000000000-22000000
χ242222222222222-22-2-2-22-2-222-2-2-2-2-2-22-22-22200-20-2000000022000000000000000000000000002-2000000
χ252222222222222-2-222-2-2-2-2-2-2222222-2-2-2-222000000000000000022220000000000000000-2-2-2-200000000
χ262222222222222-2-222-2-2-2-2-2-2222222-2-2-2-2220000000000000000-2-2-2-20000000000000000222200000000
χ272222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000022-2-20000000000000000-2-22200000000
χ282222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-20000000000000000-2-222000000000000000022-2-200000000
χ2922222-2-2-2-2-2-222222-222-2-2-2-22-222-2-22-2-222-22-200002-222-2-2000000000000000000000000000000000000
χ3022222-2-2-2-2-2-222222-222-2-2-2-22-222-2-22-2-222-2-220000-22-2-222000000000000000000000000000000000000
χ3122222-2-2-2-2-2-22222-2222-2-2-2-2-2222-2-2-222-2-222-200002-2-2-222000000000000000000000000000000000000
χ3222222-2-2-2-2-2-22222-2222-2-2-2-2-2222-2-2-222-2-22-220000-2222-2-2000000000000000000000000000000000000
χ3322222-2-2-2-2-2-2222-22-22-2-2-2222-2-2-22222-2-2-22000000000000000000000000000022-2-222-2-2000000000000
χ3422222-2-2-2-2-2-2222-22-22-2-2-2222-2-2-22222-2-2-220000000000000000000000000000-2-222-2-222000000000000
χ3522222-2-2-2-2-2-2222-2-222-2-2-222-22-2-222-2-2222-2000000000000000000000000000022-2-2-2-222000000000000
χ3622222-2-2-2-2-2-2222-2-222-2-2-222-22-2-222-2-2222-20000000000000000000000000000-2-22222-2-2000000000000
χ3722222-2-2-2-2-2-222-222-2-2222-2-22-2-2-222-2-222-220000000000000000000022-2-222-2-200000000000000000000
χ3822222-2-2-2-2-2-222-222-2-2222-2-22-2-2-222-2-222-2200000000000000000000-2-222-2-22200000000000000000000
χ3922222-2-2-2-2-2-222-22-22-2222-2-2-22-2-22222-2-22-20000000000000000000022-2-2-2-22200000000000000000000
χ4022222-2-2-2-2-2-222-22-22-2222-2-2-22-2-22222-2-22-200000000000000000000-2-22222-2-200000000000000000000
χ4122222-2-2-2-2-2-222-2-22-2-2-222222-222-2-2-222-22-2000000000000000000000000000000000000000000002i−2i2i−2i
χ4222222-2-2-2-2-2-222-2-22-2-2-222222-222-2-2-222-22-200000000000000000000000000000000000000000000−2i2i−2i2i
χ4322222-2-2-2-2-2-222-2-2-22-2-22222-2222-2-22-2-22-22000000000000000000000000000000000000000000002i−2i−2i2i
χ4422222-2-2-2-2-2-222-2-2-22-2-22222-2222-2-22-2-22-2200000000000000000000000000000000000000000000−2i2i2i−2i
χ45222-2-222-2-22-22-22-200-222-22-2002-22-20000000000000000000000002i−2i2-22-2000000002i−2i2i−2i002i−2i00000000
χ46222-2-222-2-22-22-22-200-222-22-2002-22-20000000000000000000000002i−2i-22-2200000000−2i2i−2i2i002i−2i00000000
χ47222-2-222-2-22-22-22-200-222-22-2002-22-2000000000000000000000000−2i2i2-22-200000000−2i2i−2i2i00−2i2i00000000
χ48222-2-222-2-22-22-22-200-222-22-2002-22-2000000000000000000000000−2i2i-22-22000000002i−2i2i−2i00−2i2i00000000
χ49222-2-222-2-22-22-2-22002-2-22-22002-22-20000000000000000000000002i−2i00002i−2i2i−2i2-22-2000000−2i2i00000000
χ50222-2-222-2-22-22-2-22002-2-22-22002-22-20000000000000000000000002i−2i0000−2i2i−2i2i-22-22000000−2i2i00000000
χ51222-2-222-2-22-22-2-22002-2-22-22002-22-2000000000000000000000000−2i2i00002i−2i2i−2i-22-220000002i−2i00000000
χ52222-2-222-2-22-22-2-22002-2-22-22002-22-2000000000000000000000000−2i2i0000−2i2i−2i2i2-22-20000002i−2i00000000
χ53222-2-2-2-222-222-22200-2-2-222-200-222-200000000000000000000002-20000002i−2i−2i2i00002i−2i−2i2i2-20000000000
χ54222-2-2-2-222-222-22200-2-2-222-200-222-200000000000000000000002-2000000−2i2i2i−2i0000−2i2i2i−2i2-20000000000
χ55222-2-2-2-222-222-22200-2-2-222-200-222-20000000000000000000000-220000002i−2i−2i2i0000−2i2i2i−2i-220000000000
χ56222-2-2-2-222-222-22200-2-2-222-200-222-20000000000000000000000-22000000−2i2i2i−2i00002i−2i−2i2i-220000000000
χ57222-2-2-2-222-222-2-2-200222-2-2200-222-200000000000000000000002-2002-2-220000-222-20000-220000000000
χ58222-2-2-2-222-222-2-2-200222-2-2200-222-200000000000000000000002-200-222-200002-2-220000-220000000000
χ59222-2-2-2-222-222-2-2-200222-2-2200-222-20000000000000000000000-22002-2-2200002-2-2200002-20000000000
χ60222-2-2-2-222-222-2-2-200222-2-2200-222-20000000000000000000000-2200-222-20000-222-200002-20000000000
χ61444444444-4-4-4-4004-4000000-440000000000220000-2-22-22-2000000000000000000000000000000000000
χ62444444444-4-4-4-4004-4000000-440000000000-2-2000022-22-22000000000000000000000000000000000000
χ63444444444-4-4-4-400-440000004-40000000000220000-2-2-22-22000000000000000000000000000000000000
χ64444444444-4-4-4-400-440000004-40000000000-2-20000222-22-2000000000000000000000000000000000000
χ6544444-4-4-4-444-4-40044000000-4-400000000002-20000-222-2-22000000000000000000000000000000000000
χ6644444-4-4-4-444-4-40044000000-4-40000000000-2200002-2-222-2000000000000000000000000000000000000
χ6744444-4-4-4-444-4-400-4-40000004400000000002-20000-22-222-2000000000000000000000000000000000000
χ6844444-4-4-4-444-4-400-4-4000000440000000000-2200002-22-2-22000000000000000000000000000000000000
χ69444-4-444-4-44-44-44400-4-44-4-4400-44-44000000000000000000000000000000000000000000000000000000
χ70444-4-444-4-44-44-4-4-40044-444-400-44-44000000000000000000000000000000000000000000000000000000
χ71444-4-4-4-444-444-44-400-44-44-44004-4-44000000000000000000000000000000000000000000000000000000
χ72444-4-4-4-444-444-4-44004-44-44-4004-4-44000000000000000000000000000000000000000000000000000000
χ73888-8-888-8-8-88-880000000000000000000000000000000000000000000000000000000000000000000000
χ74888-8-8-8-8888-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ7588-88-88-88-800000000000000000000000000000000000000004-400000000000000000000000000000000
χ7688-88-88-88-80000000000000000000000000000000000000000-4400000000000000000000000000000000
χ7788-88-8-88-880000000000000000000000000000040-4000000000000000000000000000000000000000000
χ7888-88-8-88-8800000000000000000000000000000-404000000000000000000000000000000000000000000
χ7988-8-888-8-88000000000000000000000000000040-40000000000000000000000000000000000000000000
χ8088-8-888-8-880000000000000000000000000000-4040000000000000000000000000000000000000000000
χ8188-8-88-888-8000000000000000000000000000000000000004-40000000000000000000000000000000000
χ8288-8-88-888-800000000000000000000000000000000000000-440000000000000000000000000000000000
χ8332-32000000000000000000000000000000000000000000000000000000000000000000000000000000000

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