Finite Group Databasebeta

← Group #72262619

Character table — Group #72262619

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122222224444444444888888888888888881616161616161616161616161616161616161616323232323232323232323232323232323232323232323232646464646464646464646464
order12222222222222222222222222222222444422224444444444444444244444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ9111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ10111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1
χ11111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111
χ12111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ172222222220000-2-2-2-2-2-2222-2-20000002-22-22-20022002200000000-2-2-2-2000000002i2i−2i−2i000000002i2i−2i−2i000000000000
χ182222222220000-2-2-2-2-2-2222-2-20000002-22-22-20022002200000000-2-2-2-200000000−2i−2i2i2i00000000−2i−2i2i2i000000000000
χ192222222220000-2-2-2-2-2-2222-2-20000002-22-22-200-2-200-2-2000000002222000000002i2i−2i−2i00000000−2i−2i2i2i000000000000
χ202222222220000-2-2-2-2-2-2222-2-20000002-22-22-200-2-200-2-200000000222200000000−2i−2i2i2i000000002i2i−2i−2i000000000000
χ212222222220000-2-2-2-2-2-222-22-2000000-22-22-22220022000000-2-2-2-200000000000000002i2i−2i−2i00002i−2i2i−2i000000000000
χ222222222220000-2-2-2-2-2-222-22-2000000-22-22-22220022000000-2-2-2-20000000000000000−2i−2i2i2i0000−2i2i−2i2i000000000000
χ232222222220000-2-2-2-2-2-222-22-2000000-22-22-22-2-200-2-2000000222200000000000000002i2i−2i−2i0000−2i2i−2i2i000000000000
χ242222222220000-2-2-2-2-2-222-22-2000000-22-22-22-2-200-2-200000022220000000000000000−2i−2i2i2i00002i−2i2i−2i000000000000
χ25222222222222222222222-2-22222222-2-2-2-2-2-200000000-2-2-2-200000000000000000000000022-2-22-2-22000000000000
χ26222222222222222222222-2-22222222-2-2-2-2-2-200000000-2-2-2-2000000000000000000000000-2-222-222-2000000000000
χ2722222222222-2-222-2-222-2-22-2-2222-2-2-22-2-22-220000000022-2-200000000000022-2-200000000000000002-20000000000
χ2822222222222-2-222-2-222-2-22-2-2222-2-2-22-2-22-220000000022-2-2000000000000-2-2220000000000000000-220000000000
χ2922222222222-2-222-2-222-2-2-22-2222-2-2-2-222-22-200000000-2-2220000000022-2-200000000000000000000002-200000000
χ3022222222222-2-222-2-222-2-2-22-2222-2-2-2-222-22-200000000-2-22200000000-2-2220000000000000000000000-2200000000
χ31222222222-2-22222-2-222-2-22-2-2-2-2-22222-2-22-2200000000-2-22200000000000022-2-20000000000000000-220000000000
χ32222222222-2-22222-2-222-2-22-2-2-2-2-22222-2-22-2200000000-2-222000000000000-2-22200000000000000002-20000000000
χ33222222222-2-22222-2-222-2-2-22-2-2-2-2222-222-22-20000000022-2-20000000022-2-20000000000000000000000-2200000000
χ34222222222-2-22222-2-222-2-2-22-2-2-2-2222-222-22-20000000022-2-200000000-2-22200000000000000000000002-200000000
χ35222222222-2-2-2-222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000022-2-2-222-2000000000000
χ36222222222-2-2-2-222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000-2-2222-2-22000000000000
χ37222-2-22-2-22000022-2-2-2-22-2222000000-2-2-2-222002-2002-20000000022-2-20000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ38222-2-22-2-22000022-2-2-2-22-2222000000-2-2-2-222002-2002-20000000022-2-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ39222-2-22-2-22000022-2-2-2-22-2222000000-2-2-2-22200-2200-2200000000-2-2220000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ40222-2-22-2-22000022-2-2-2-22-2222000000-2-2-2-22200-2200-2200000000-2-222000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ41222-2-22-2-22000022-2-2-2-22-2-2-220000002222-2-22-2002-200000022-2-20000000000002i−2i2i−2i00002i−2i−2i2i0000000000000000
χ42222-2-22-2-22000022-2-2-2-22-2-2-220000002222-2-22-2002-200000022-2-2000000000000−2i2i−2i2i0000−2i2i2i−2i0000000000000000
χ43222-2-22-2-22000022-2-2-2-22-2-2-220000002222-2-2-2200-22000000-2-2220000000000002i−2i2i−2i0000−2i2i2i−2i0000000000000000
χ44222-2-22-2-22000022-2-2-2-22-2-2-220000002222-2-2-2200-22000000-2-222000000000000−2i2i−2i2i00002i−2i−2i2i0000000000000000
χ45222-2-22-2-222222-2-222222-22-2-22-2-22-2-2-22-222-22-22-22-22-22-22-2-2-222-2-222000000000000000000000000000000000000
χ46222-2-22-2-222222-2-222222-22-2-22-2-22-2-2-22-222-2-22-22-22-222-22-222-2-222-2-2000000000000000000000000000000000000
χ47222-2-22-2-222222-2-222222-2-22-22-2-22-2-22-22-2-2200000000-22-2200000000000000002-2-222-2-2200000000000000000000
χ48222-2-22-2-222222-2-222222-2-22-22-2-22-2-22-22-2-2200000000-22-220000000000000000-222-2-222-200000000000000000000
χ49222-2-22-2-2222-2-2-2-2-2-222-222222-2-2-222-2-222-2-2000000002-2-22000000000000000000000000000000000000002i−2i002i−2i
χ50222-2-22-2-2222-2-2-2-2-2-222-222222-2-2-222-2-222-2-2000000002-2-2200000000000000000000000000000000000000−2i2i00−2i2i
χ51222-2-22-2-2222-2-2-2-2-2-222-22-2-222-2-2-22222-2-22200000000-222-20000000000000000000000000000000000002-2002-200
χ52222-2-22-2-2222-2-2-2-2-2-222-22-2-222-2-2-22222-2-22200000000-222-2000000000000000000000000000000000000-2200-2200
χ53222-2-22-2-22-2-222-2-2-2-222-22222-2222-2-2-2-222-2-200000000-222-2000000000000000000000000000000000000002i−2i00−2i2i
χ54222-2-22-2-22-2-222-2-2-2-222-22222-2222-2-2-2-222-2-200000000-222-200000000000000000000000000000000000000−2i2i002i−2i
χ55222-2-22-2-22-2-222-2-2-2-222-22-2-22-2222-2-222-2-222000000002-2-220000000000000000000000000000000000002-200-2200
χ56222-2-22-2-22-2-222-2-2-2-222-22-2-22-2222-2-222-2-222000000002-2-22000000000000000000000000000000000000-22002-200
χ57222-2-22-2-22-2-2-2-2-2-222222-22-2-2-222-222-22-222-22-2-222-2-22-22-22-2-22222-2-2000000000000000000000000000000000000
χ58222-2-22-2-22-2-2-2-2-2-222222-22-2-2-222-222-22-222-2-222-2-222-2-22-2222-2-2-2-222000000000000000000000000000000000000
χ59222-2-22-2-22-2-2-2-2-2-222222-2-22-2-222-2222-22-2-22000000002-22-200000000000000002-2-22-222-200000000000000000000
χ60222-2-22-2-22-2-2-2-2-2-222222-2-22-2-222-2222-22-2-22000000002-22-20000000000000000-222-22-2-2200000000000000000000
χ614444444440000-4-444-4-4-4-444400000044-4-4-4-400000000000000000000000000000000000000000000000000000000
χ624444444440000-4-444-4-4-4-4-4-44000000-4-4444400000000000000000000000000000000000000000000000000000000
χ63444-4-44-4-4400004444-4-4-444-4-4000000-444-4-4400000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4400004444-4-4-44-44-40000004-4-444-400000000000000000000000000000000000000000000000000000000
χ6544-44-4-44-4400444-4004-400000000-44-40000002222-2-2-2-200002-22-22-22-2000000000000000000000000000000000000
χ6644-44-4-44-4400444-4004-400000000-44-4000000-2-2-2-222220000-22-22-22-22000000000000000000000000000000000000
χ6744-44-4-44-4400-4-44-4004-4000000004-4400000022-2-2-2-22200002-22-2-22-22000000000000000000000000000000000000
χ6844-44-4-44-4400-4-44-4004-4000000004-44000000-2-22222-2-20000-22-222-22-2000000000000000000000000000000000000
χ6944-44-4-44-444400-4400-4400000-44-40000000002222-2-2-2-20000-22-22-22-22000000000000000000000000000000000000
χ7044-44-4-44-444400-4400-4400000-44-4000000000-2-2-2-2222200002-22-22-22-2000000000000000000000000000000000000
χ7144-44-4-44-44-4-400-4400-44000004-4400000000022-2-2-2-2220000-22-222-22-2000000000000000000000000000000000000
χ7244-44-4-44-44-4-400-4400-44000004-44000000000-2-22222-2-200002-22-2-22-22000000000000000000000000000000000000
χ7344-4-44-4-4440044-44004-400000000-4-440000002-22-2-22-220000-222-2-222-2000000000000000000000000000000000000
χ7444-4-44-4-4440044-44004-400000000-4-44000000-22-222-22-200002-2-222-2-22000000000000000000000000000000000000
χ7544-4-44-4-44400-4-4-44004-40000000044-40000002-2-22-222-20000-222-22-2-22000000000000000000000000000000000000
χ7644-4-44-4-44400-4-4-44004-40000000044-4000000-222-22-2-2200002-2-22-222-2000000000000000000000000000000000000
χ7744-4-44-4-44444004-400-4400000-4-440000000002-22-2-22-2200002-2-222-2-22000000000000000000000000000000000000
χ7844-4-44-4-44444004-400-4400000-4-44000000000-22-222-22-20000-222-2-222-2000000000000000000000000000000000000
χ7944-4-44-4-444-4-4004-400-440000044-40000000002-2-22-222-200002-2-22-222-2000000000000000000000000000000000000
χ8044-4-44-4-444-4-4004-400-440000044-4000000000-222-22-2-220000-222-22-2-22000000000000000000000000000000000000
χ8188888-8-8-8-80000000000000000000000000000000000000000000000000004i−4i000000000000000000000000000000
χ8288888-8-8-8-8000000000000000000000000000000000000000000000000000−4i4i000000000000000000000000000000
χ83888-8-8-888-8000000000000000000000000000000000000000000000000000004-40000000000000000000000000000
χ84888-8-8-888-800000000000000000000000000000000000000000000000000000-440000000000000000000000000000
χ8588-88-88-88-8000000000000000000000000000000000000000000000004-40000000000000000000000000000000000
χ8688-88-88-88-800000000000000000000000000000000000000000000000-440000000000000000000000000000000000
χ8788-8-8888-8-800000000000000000000000000000000000000000000000004-400000000000000000000000000000000
χ8888-8-8888-8-80000000000000000000000000000000000000000000000000-4400000000000000000000000000000000
χ8916-1600000008-88-8008-8000000000000000000000000000000000000000000000000000000000000000000000000000
χ9016-1600000008-8-8800-88000000000000000000000000000000000000000000000000000000000000000000000000000
χ9116-160000000-888-800-88000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-160000000-88-88008-8000000000000000000000000000000000000000000000000000000000000000000000000000

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