Finite Group Databasebeta

← Group #72282567

Character table — Group #72282567

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11112222224444444444444444888888888888888888888816161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222244442222224444448888222222224444444488888822444444444488881616161616161616161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ10111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ11111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ12111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ13111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ14111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ15111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ16111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ171-1-111-11-1-111-111-1-11-11-11-111-1-11111-1-1-1-1ii−i−iii−i−i1-11-11-11-1ii−i−i1-1ii−i−ii−ii−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ181-1-111-11-1-111-111-1-11-11-11-111-1-11111-1-1-1-1ii−i−iii−i−i1-11-11-11-1ii−i−i1-1ii−i−ii−ii−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ191-1-111-11-1-111-111-1-11-11-11-111-1-11111-1-1-1-1−i−iii−i−iii1-11-11-11-1−i−iii1-1−i−iii−ii−ii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ201-1-111-11-1-111-111-1-11-11-11-111-1-11111-1-1-1-1−i−iii−i−iii1-11-11-11-1−i−iii1-1−i−iii−ii−ii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ211-1-111-11-1-111-111-1-11-11-11-111-1-1-1-1-1-11111ii−i−iii−i−i1-11-11-1-11−i−iii-11−i−iiii−ii−i11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ221-1-111-11-1-111-111-1-11-11-11-111-1-1-1-1-1-11111ii−i−iii−i−i1-11-11-1-11−i−iii-11−i−iiii−ii−i-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ231-1-111-11-1-111-111-1-11-11-11-111-1-1-1-1-1-11111−i−iii−i−iii1-11-11-1-11ii−i−i-11ii−i−i−ii−ii11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ241-1-111-11-1-111-111-1-11-11-11-111-1-1-1-1-1-11111−i−iii−i−iii1-11-11-1-11ii−i−i-11ii−i−i−ii−ii-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ251-1-111-11-1-111-1-1-1111-1-11-1111-1-11111-1-1-1-1ii−i−i−i−iii1-1-11-11-11ii−i−i-11−i−iiii−i−iiii−i−i−i−iii-1-11111-1-1i−i−ii-111-1
χ261-1-111-11-1-111-1-1-1111-1-11-1111-1-11111-1-1-1-1ii−i−i−i−iii1-1-11-11-11ii−i−i-11−i−iiii−i−ii−i−iiiii−i−i11-1-1-1-111−iii−i1-1-11
χ271-1-111-11-1-111-1-1-1111-1-11-1111-1-11111-1-1-1-1−i−iiiii−i−i1-1-11-11-11−i−iii-11ii−i−i−iii−iii−i−i−i−iii11-1-1-1-111i−i−ii1-1-11
χ281-1-111-11-1-111-1-1-1111-1-11-1111-1-11111-1-1-1-1−i−iiiii−i−i1-1-11-11-11−i−iii-11ii−i−i−iii−i−i−iiiii−i−i-1-11111-1-1−iii−i-111-1
χ291-1-111-11-1-111-1-1-1111-1-11-1111-1-1-1-1-1-11111ii−i−i−i−iii1-1-11-111-1−i−iii1-1ii−i−ii−i−iiii−i−i−i−iii-1-11111-1-1−iii−i1-1-11
χ301-1-111-11-1-111-1-1-1111-1-11-1111-1-1-1-1-1-11111ii−i−i−i−iii1-1-11-111-1−i−iii1-1ii−i−ii−i−ii−i−iiiii−i−i11-1-1-1-111i−i−ii-111-1
χ311-1-111-11-1-111-1-1-1111-1-11-1111-1-1-1-1-1-11111−i−iiiii−i−i1-1-11-111-1ii−i−i1-1−i−iii−iii−iii−i−i−i−iii11-1-1-1-111−iii−i-111-1
χ321-1-111-11-1-111-1-1-1111-1-11-1111-1-1-1-1-1-11111−i−iiiii−i−i1-1-11-111-1ii−i−i1-1−i−iii−iii−i−i−iiiii−i−i-1-11111-1-1i−i−ii1-1-11
χ332222222222222222222222-2-2-2-20000000022222222-2-2-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ342222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000002222000000000000000000000000
χ35222222222222-2-2-2-222-2-2-2-2-2-2-2-2000000002222-2-2-2-2-2-22222000000000000-2-222000000000000000000000000
χ36222222222222-2-2-2-222-2-2-2-2-2-2-2-200000000-2-2-2-22222-2-2222200000000000022-2-2000000000000000000000000
χ372222222222-2-22-22-2-2-22-2-22222222-2-222-2-200000000-2-22-2-22220000-2-200000000000000000000000000000000
χ382222222222-2-22-22-2-2-22-2-222222-2-222-2-22200000000-2-22-2-22-2-200002200000000000000000000000000000000
χ392222222222-2-22-22-2-2-22-2-22-2-2-2-2000000000000000022-222-2002-22-2002-22-20000000000000000000000000000
χ402222222222-2-22-22-2-2-22-2-22-2-2-2-2000000000000000022-222-200-22-2200-22-220000000000000000000000000000
χ412222222222-2-2-22-22-2-2-222-2222222-2-222-2-200000000-2-2-222-2-2-200002200000000000000000000000000000000
χ422222222222-2-2-22-22-2-2-222-22222-2-222-2-22200000000-2-2-222-2220000-2-200000000000000000000000000000000
χ432222222222-2-2-22-22-2-2-222-2-2-2-2-20000000000000000222-2-22002-22-200-22-220000000000000000000000000000
χ442222222222-2-2-22-22-2-2-222-2-2-2-2-20000000000000000222-2-2200-22-22002-22-20000000000000000000000000000
χ45222222-2-2-2-2-2-2222222-2-2-2-20000000000002-22-22-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ46222222-2-2-2-2-2-2222222-2-2-2-20000000000002-22-22-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ47222222-2-2-2-2-2-2222222-2-2-2-2000000000000-22-22-22-220000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ48222222-2-2-2-2-2-2222222-2-2-2-2000000000000-22-22-22-220000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ49222222-2-2-2-2-2-2-2-2-2-22222220000000000002-22-2-22-2200000000000000000000002−22−2−22−222−22−2−22−2200000000
χ50222222-2-2-2-2-2-2-2-2-2-22222220000000000002-22-2-22-220000000000000000000000−22−222−22−2−22−222−22−200000000
χ51222222-2-2-2-2-2-2-2-2-2-2222222000000000000-22-222-22-200000000000000000000002−22−2−22−22−22−222−22−200000000
χ52222222-2-2-2-2-2-2-2-2-2-2222222000000000000-22-222-22-20000000000000000000000−22−222−22−22−22−2−22−2200000000
χ532-2-222-22-2-222-222-2-22-22-22-2-2-222000000002i2i−2i−2i2i2i−2i−2i-22-22-22000000000000−2i2i−2i2i000000000000000000000000
χ542-2-222-22-2-222-222-2-22-22-22-2-2-22200000000−2i−2i2i2i−2i−2i2i2i-22-22-220000000000002i−2i2i−2i000000000000000000000000
χ552-2-222-22-2-222-2-2-2222-2-22-22-2-222000000002i2i−2i−2i−2i−2i2i2i-222-22-2000000000000−2i2i2i−2i000000000000000000000000
χ562-2-222-22-2-222-2-2-2222-2-22-22-2-22200000000−2i−2i2i2i2i2i−2i−2i-222-22-20000000000002i−2i−2i2i000000000000000000000000
χ572-2-222-22-2-22-222-2-22-2222-2-222-2-222-2-2-2-22200000000-2222-2-22-20000-2200000000000000000000000000000000
χ582-2-222-22-2-22-222-2-22-2222-2-222-2-2-2-22222-2-200000000-2222-2-2-2200002-200000000000000000000000000000000
χ592-2-222-22-2-22-222-2-22-2222-2-2-2-22200000000000000002-2-2-222002i−2i−2i2i002i−2i−2i2i0000000000000000000000000000
χ602-2-222-22-2-22-222-2-22-2222-2-2-2-22200000000000000002-2-2-22200−2i2i2i−2i00−2i2i2i−2i0000000000000000000000000000
χ612-2-222-22-2-22-22-222-2-22-2-22222-2-222-2-2-2-22200000000-22-2-222-2200002-200000000000000000000000000000000
χ622-2-222-22-2-22-22-222-2-22-2-22222-2-2-2-22222-2-200000000-22-2-2222-20000-2200000000000000000000000000000000
χ632-2-222-22-2-22-22-222-2-22-2-222-2-22200000000000000002-222-2-2002i−2i−2i2i00−2i2i2i−2i0000000000000000000000000000
χ642-2-222-22-2-22-22-222-2-22-2-222-2-22200000000000000002-222-2-200−2i2i2i−2i002i−2i−2i2i0000000000000000000000000000
χ652-2-222-2-222-2-2222-2-22-2-22-220000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000i2−i2−i2i2i2−i2−i2i2−222−2−222−200000000
χ662-2-222-2-222-2-2222-2-22-2-22-220000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000−i2i2i2−i2−i2i2i2−i22−2−222−2−2200000000
χ672-2-222-2-222-2-2222-2-22-2-22-22000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000i2−i2−i2i2i2−i2−i2i22−2−222−2−2200000000
χ682-2-222-2-222-2-2222-2-22-2-22-22000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−2−222−200000000
χ692-2-222-2-222-2-22-2-2222-22-22-20000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ702-2-222-2-222-2-22-2-2222-22-22-20000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ712-2-222-2-222-2-22-2-2222-22-22-2000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ722-2-222-2-222-2-22-2-2222-22-22-2000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ73444444-4-4-4-4444-44-4-4-4-444-4000000000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-444-44-44-4-44-4-44000000000000000000000000000000000000000000000000000000000000000000
χ754444-4-4-44-440000000000004-44-4004-4004-4000000000000000000000000000000000000000000000000000000
χ764444-4-4-44-440000000000004-44-400-4400-44000000000000000000000000000000000000000000000000000000
χ774444-4-4-44-44000000000000-44-444-4004-400000000000000000000000000000000000000000000000000000000
χ784444-4-4-44-44000000000000-44-44-4400-4400000000000000000000000000000000000000000000000000000000
χ794-4-444-4-444-44-44-4-44-44-4-444000000000000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-444-44-4-444-4-4444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ814-4-44-44-4-4440000000000004-4-44004-400-44000000000000000000000000000000000000000000000000000000
χ824-4-44-44-4-4440000000000004-4-4400-44004-4000000000000000000000000000000000000000000000000000000
χ834-4-44-44-4-444000000000000-444-44-400-4400000000000000000000000000000000000000000000000000000000
χ844-4-44-44-4-444000000000000-444-4-44004-400000000000000000000000000000000000000000000000000000000
χ858888-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ871616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8816-1616-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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