Finite Group Databasebeta

← Group #72342586

Character table — Group #72342586

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size1111222222222222222222444444444444444444444444448888888888888888888888161616161616161616161616161616161616161616161616161616163232323232323232
order12222222444444444488882224444444444444888888888824448888888888888888888888888888881616161616161616161616161616161622228888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-11111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-11111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111-1-11111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-11111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1111-1-1111-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1111111-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ10111111-1-1111-1-1111-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1111111-1-1-1-1iiii−i−i−i−iii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ11111111-1-1111-1-1111-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1111111-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ12111111-1-1111-1-1111-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1111111-1-1-1-1−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ13111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ14111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-1-1-11111iiii−i−i−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ15111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ16111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-1-1-11111−i−i−i−iiiii−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ171111-1-1111-1-1-1-1111111111-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11-111-1-111-1-111-1-111-1-11-11-111-1-111-1-111-1-111-1-111-1-111-1-11-11-11-11-1
χ181111-1-1111-1-1-1-1111111111-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11-111-1-111-1-111-1-111-1-11-11-111-1-111-1-1-1-111-1-111-1-111-1-111-11-11-11-11
χ191111-1-1111-1-1-1-1111111111-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11-111-1-111-1-1-1-111-1-111-11-11-1-111-1-11111-1-111-1-111-1-111-1-1-11-11-11-11
χ201111-1-1111-1-1-1-1111111111-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11-111-1-111-1-1-1-111-1-111-11-11-1-111-1-111-1-111-1-111-1-111-1-1111-11-11-11-1
χ211111-1-1111-1-1-1-1111111111-1-1-11-1-111-1-111-1-11111-1-1-1-1-1-111-1-1111-1-1-111-1-11111-1-111-1-11-11-1-1-111-1-11111-1-111-1-1-1-111-1-1111-11-1-11-11
χ221111-1-1111-1-1-1-1111111111-1-1-11-1-111-1-111-1-11111-1-1-1-1-1-111-1-1111-1-1-111-1-11111-1-111-1-11-11-1-1-111-1-111-1-111-1-11111-1-111-1-1-11-111-11-1
χ231111-1-1111-1-1-1-1111111111-1-1-11-1-111-1-111-1-11111-1-1-1-1-1-111-1-1111-1-1-111-1-111-1-111-1-111-11-1111-1-111-1-111-1-111-1-1-1-111-1-111-11-111-11-1
χ241111-1-1111-1-1-1-1111111111-1-1-11-1-111-1-111-1-11111-1-1-1-1-1-111-1-1111-1-1-111-1-111-1-111-1-111-11-1111-1-111-1-1-1-111-1-11111-1-111-1-11-11-1-11-11
χ251111-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-11-111-111-1-1-1-111ii−i−i−i−iiii−i−iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ261111-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-11-111-111-1-1-1-111ii−i−i−i−iiii−i−iiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ271111-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-11-111-111-1-1-1-111−i−iiiii−i−i−iii−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ281111-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-11-111-111-1-1-1-111−i−iiiii−i−i−iii−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ291111-1-1-1-11-1-111111-1-1-1-1-1-11-1-11-1-1-1-1111111-1-111-1-11111-1-11-11-11-1-1-11111-1-1ii−i−i−i−iiii−i−ii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ301111-1-1-1-11-1-111111-1-1-1-1-1-11-1-11-1-1-1-1111111-1-111-1-11111-1-11-11-11-1-1-11111-1-1ii−i−i−i−iiii−i−ii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ311111-1-1-1-11-1-111111-1-1-1-1-1-11-1-11-1-1-1-1111111-1-111-1-11111-1-11-11-11-1-1-11111-1-1−i−iiiii−i−i−iii−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ321111-1-1-1-11-1-111111-1-1-1-1-1-11-1-11-1-1-1-1111111-1-111-1-11111-1-11-11-11-1-1-11111-1-1−i−iiiii−i−i−iii−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ33222222222222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ34222222222222222222-2-2-2-22-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ3522222222222-2-2-2-22-2-20000222-2-2-22-22-222-2-2-2-200000000002-2-22000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3622222222222-2-2-2-22-2-20000222-2-2-22-22-222-2-2-2-200000000002-2-22000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3722222222222-2-2-2-22-2-200002-2-2-2-2-22-22-2-2-222220000000000-222-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ3822222222222-2-2-2-22-2-200002-2-2-2-2-22-22-2-2-222220000000000-222-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3922222222-2-2-2-2-222-2222222200-22-2-2-2-2200000022-2-222-2-2-2-20000-220000000022-2-222-2-2-22-2200000000000000000000000000000000
χ4022222222-2-2-2-2-222-2222222200-22-2-2-2-2200000022-2-222-2-2-2-20000-2200000000-2-222-2-2222-22-200000000000000000000000000000000
χ4122222222-2-2-2-2-222-222-2-2-2-2200-22-2-2-2-22000000-2-222-2-2222200002-2000000000000000000002-22-22-22-2000000000000000000000000
χ4222222222-2-2-2-2-222-222-2-2-2-2200-22-2-2-2-22000000-2-222-2-2222200002-200000000000000000000-22-22-22-22000000000000000000000000
χ43222222-2-222222-2-22220000-222-2-2-2-22-222222220000000000-2-2-2-20000000000000000000000000000002−22−2−22−222−22−2−22−2200000000
χ44222222-2-222222-2-22220000-222-2-2-2-22-222222220000000000-2-2-2-2000000000000000000000000000000−22−222−22−2−22−222−22−200000000
χ45222222-2-222222-2-22220000-2-2-2-2-2-2-22-22-2-2-2-2-2-2000000000022220000000000000000000000000000002−22−2−22−22−22−222−22−200000000
χ46222222-2-222222-2-22220000-2-2-2-2-2-2-22-22-2-2-2-2-2-200000000002222000000000000000000000000000000−22−222−22−22−22−2−22−2200000000
χ47222222-2-2222-2-2222-2-22222-222222-2-2-2-222-2-2-2-2-2-2-2-2222222-222-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ48222222-2-2222-2-2222-2-22222-2-2-2222-2-2-2-2-2-22222-2-2-2-22222222-2-22-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ49222222-2-2-2-2-22222-2-2-22222-200-22-2222-2000000-2-22222-2-2-2-200002-2000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ50222222-2-2-2-2-22222-2-2-22222-200-22-2222-2000000-2-22222-2-2-2-200002-200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ51222222-2-2-2-2-22222-2-2-2-2-2-2-2-200-22-2222-200000022-2-2-2-222220000-22000000002i2i−2i−2i−2i−2i2i2i−2i2i2i−2i00000000000000000000000000000000
χ52222222-2-2-2-2-22222-2-2-2-2-2-2-2-200-22-2222-200000022-2-2-2-222220000-2200000000−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i00000000000000000000000000000000
χ532222-2-2222-2-222-2-22-2-20000-222-2222-2-22-2-2-2-22200000000002-22-2000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ542222-2-2222-2-222-2-22-2-20000-222-2222-2-22-2-2-2-22200000000002-22-2000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ552222-2-2222-2-222-2-22-2-20000-2-2-2-2222-2-222222-2-20000000000-22-22000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ562222-2-2222-2-222-2-22-2-20000-2-2-2-2222-2-222222-2-20000000000-22-22000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ572222-2-2222-2-2-2-222222-2-2-2-2-2222-2-222-2-2-2-222-2-2-2-2222222-2-222-2-2-22-2-222-2-22200000000000000000000000000000000000000000000
χ582222-2-2222-2-2-2-222222-2-2-2-2-2-2-22-2-222-2-222-2-222-2-2222222-2-2-2-222-2222-2-222-2-200000000000000000000000000000000000000000000
χ592222-2-222-2222222-2222222-200-2-22-2-22-20000002222-2-222-2-20000-2-20000000022222222-2-2-2-200000000000000000000000000000000
χ602222-2-222-2222222-2222222-200-2-22-2-22-20000002222-2-222-2-20000-2-200000000-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ612222-2-222-2222222-222-2-2-2-2-200-2-22-2-22-2000000-2-2-2-222-2-222000022000000000000000000002-2-222-2-22000000000000000000000000
χ622222-2-222-2222222-222-2-2-2-2-200-2-22-2-22-2000000-2-2-2-222-2-22200002200000000000000000000-222-2-222-2000000000000000000000000
χ632222-2-2-2-22-2-222222-2-222222222-2-2-2-222-2-2-2-222-2-222-2-2-2-222-22-22-22-2-22222-2-200000000000000000000000000000000000000000000
χ642222-2-2-2-22-2-222222-2-222222-2-22-2-2-2-2222222-2-2-2-222-2-2-2-2222-22-2-2222-2-2-2-22200000000000000000000000000000000000000000000
χ652222-2-2-2-22-2-2-2-2-2-22220000222-222-222-2-2-222-2-20000000000-2-2220000000000000000000000000000002−2−22−222−22−2−22−222−200000000
χ662222-2-2-2-22-2-2-2-2-2-22220000222-222-222-2-2-222-2-20000000000-2-222000000000000000000000000000000−222−22−2−22−222−22−2−2200000000
χ672222-2-2-2-22-2-2-2-2-2-222200002-2-2-222-222-222-2-222000000000022-2-20000000000000000000000000000002−2−22−222−2−222−22−2−2200000000
χ682222-2-2-2-22-2-2-2-2-2-222200002-2-2-222-222-222-2-222000000000022-2-2000000000000000000000000000000−222−22−2−222−2−22−222−200000000
χ692222-2-2-2-2-222-2-222-2-2-22222200-2-2222-22000000-2-2-2-2-2-222-2-2000022000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ702222-2-2-2-2-222-2-222-2-2-22222200-2-2222-22000000-2-2-2-2-2-222-2-200002200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ712222-2-2-2-2-222-2-222-2-2-2-2-2-2-2200-2-2222-22000000222222-2-2220000-2-2000000002i2i2i2i−2i−2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ722222-2-2-2-2-222-2-222-2-2-2-2-2-2-2200-2-2222-22000000222222-2-2220000-2-200000000−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ7344444444-4-4-444-4-4-4-4-400004004-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-4-4-4-4-4-4-4440000-4004-444-44400000000000000000000000000000000000000000000000000000000000000000000000000
χ754444-4-444-444-4-4-4-4-4-4-40000-40044-4-444400000000000000000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-4-44444-4-4-444000040044-44-4-4-400000000000000000000000000000000000000000000000000000000000000000000000000
χ7744-4-4004-4000004-404-444-4-400000000000000004-40000000000000000000000004i−4i004i−4i000000000000000000000000000000000000
χ7844-4-4004-4000004-404-444-4-400000000000000004-4000000000000000000000000−4i4i00−4i4i000000000000000000000000000000000000
χ7944-4-4004-4000004-404-4-4-4440000000000000000-4400000000000000000000004-4004-400000000000000000000000000000000000000
χ8044-4-4004-4000004-404-4-4-4440000000000000000-440000000000000000000000-4400-4400000000000000000000000000000000000000
χ8144-4-400-44000004-40-4444-4-40000000000000000-4400000000000000000000004i−4i00−4i4i00000000000000000000000000000000000000
χ8244-4-400-44000004-40-4444-4-40000000000000000-440000000000000000000000−4i4i004i−4i00000000000000000000000000000000000000
χ8344-4-400-44000004-40-44-4-44400000000000000004-40000000000000000000000004-400-44000000000000000000000000000000000000
χ8444-4-400-44000004-40-44-4-44400000000000000004-4000000000000000000000000-44004-4000000000000000000000000000000000000
χ854-44-44-40044-40000-40022−2222−220000000000004i−4i4i−4i000022−2222−2222−220000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ864-44-44-40044-40000-40022−2222−22000000000000−4i4i−4i4i000022−2222−2222−22000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ874-44-44-40044-40000-400−2222−22220000000000004i−4i4i−4i0000−2222−2222−2222000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ884-44-44-40044-40000-400−2222−2222000000000000−4i4i−4i4i0000−2222−2222−22220000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ894-44-44-400-4-44000040022−2222−2204-400000004-40000000022−22−2222−2222000000000022−2222−2200000000000000000000000000000000000000000000
χ904-44-44-400-4-44000040022−2222−220-440000000-440000000022−22−2222−22220000000000−2222−222200000000000000000000000000000000000000000000
χ914-44-44-400-4-440000400−2222−222204-400000004-400000000−222222−2222−220000000000−2222−222200000000000000000000000000000000000000000000
χ924-44-44-400-4-440000400−2222−22220-440000000-4400000000−222222−2222−22000000000022−2222−2200000000000000000000000000000000000000000000
χ934-44-4-44004-440000-40022−2222−220000000000004i−4i−4i4i0000−2222−222222−220000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ944-44-4-44004-440000-40022−2222−22000000000000−4i4i4i−4i0000−2222−222222−22000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ954-44-4-44004-440000-400−2222−22220000000000004i−4i−4i4i000022−2222−22−2222000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ964-44-4-44004-440000-400−2222−2222000000000000−4i4i4i−4i000022−2222−22−22220000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ974-44-4-4400-44-4000040022−2222−2204-40000000-4400000000−222222−22−2222000000000022−22−222200000000000000000000000000000000000000000000
χ984-44-4-4400-44-4000040022−2222−220-4400000004-400000000−222222−22−22220000000000−222222−2200000000000000000000000000000000000000000000
χ994-44-4-4400-44-40000400−2222−222204-40000000-440000000022−22−222222−220000000000−222222−2200000000000000000000000000000000000000000000
χ1004-44-4-4400-44-40000400−2222−22220-4400000004-40000000022−22−222222−22000000000022−22−222200000000000000000000000000000000000000000000
χ10188-8-8008-800000-880-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-800-8800000-8808-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-8800000008-80000042−42−424200000000000000000042−420000000000000000000000000000000000000000000000000000000000000000
χ1048-8-8800000008-800000−424242−42000000000000000000−42420000000000000000000000000000000000000000000000000000000000000000
χ1058-8-880000000-880000042−42−4242000000000000000000−42420000000000000000000000000000000000000000000000000000000000000000
χ1068-8-880000000-8800000−424242−4200000000000000000042−420000000000000000000000000000000000000000000000000000000000000000

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