Finite Group Databasebeta

← Group #119702

Character table — Group #119702

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444488888888888888882222444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ101111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ111111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ121111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ131111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ141111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ151111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ161111-1-1-1-1-1-1-11111-1111-1-1-11111-1-1-11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ172222222222222222222222-2-2-2-2-2-2-222-2-2-2-2-200000000000000002222-2-2-2-200000000000000000000000000000000
χ182222222222222222222222-2-2-2-2-2-2-222-2-2-2-2-20000000000000000-2-2-2-2222200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-22222222-2-22-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-22222222-2-22-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ232222-2-2-2-2-2-2-22222-2222-2-2-2-2-2-2-22222-22-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ242222-2-2-2-2-2-2-22222-2222-2-2-2-2-2-2-22222-22-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
χ252222-2-2-2-2-2-2-22222-2-2-2-22222222-2-2-2-22-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ262222-2-2-2-2-2-2-22222-2-2-2-22222222-2-2-2-22-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ272222-2-2-2-2-2-2-22222-2-2-2-2222-2-2-2-2222-22222-2-200000000000000000000000022-2-2-2-222000000000000000000000000
χ282222-2-2-2-2-2-2-22222-2-2-2-2222-2-2-2-2222-22222-2-2000000000000000000000000-2-22222-2-2000000000000000000000000
χ29222-22222-2-2-22-2-2-2-222-222-20000000-2-20000022−2−222−2−222−2−222−2−22-22-200002−22−22−22−2000000000000000000000000
χ30222-22222-2-2-22-2-2-2-222-222-20000000-2-20000022−2−222−2−222−2−222−2−2-22-220000−22−22−22−22000000000000000000000000
χ31222-22222-2-2-22-2-2-2-222-222-20000000-2-200000−2−222−2−222−2−222−2−2222-22-20000−22−22−22−22000000000000000000000000
χ32222-22222-2-2-22-2-2-2-222-222-20000000-2-200000−2−222−2−222−2−222−2−222-22-2200002−22−22−22−2000000000000000000000000
χ33222-22222-2-2-22-2-2-2-2-2-22-2-220000000220000022−2−2−2−22222−2−2−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ34222-22222-2-2-22-2-2-2-2-2-22-2-220000000220000022−2−2−2−22222−2−2−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ35222-22222-2-2-22-2-2-2-2-2-22-2-2200000002200000−2−22222−2−2−2−22222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ36222-22222-2-2-22-2-2-2-2-2-22-2-2200000002200000−2−22222−2−2−2−22222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ37222-2-2-2-2-22222-2-2-2222-2-2-220000000-2200000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-2-220000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ38222-2-2-2-2-22222-2-2-2222-2-2-220000000-2200000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-222-20000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ39222-2-2-2-2-22222-2-2-2222-2-2-220000000-2200000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-2-220000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ40222-2-2-2-2-22222-2-2-2222-2-2-220000000-2200000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-222-20000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ41222-2-2-2-2-22222-2-2-22-2-2222-200000002-200000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200002i−2i−2i2i−222−22−2−22000000000000000000000000
χ42222-2-2-2-2-22222-2-2-22-2-2222-200000002-200000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000−2i2i2i−2i2−2−22−222−2000000000000000000000000
χ43222-2-2-2-2-22222-2-2-22-2-2222-200000002-200000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200002i−2i−2i2i2−2−22−222−2000000000000000000000000
χ44222-2-2-2-2-22222-2-2-22-2-2222-200000002-200000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000−2i2i2i−2i−222−22−2−22000000000000000000000000
χ4522-2222-2-222-2-2-22-2-200000022-2-2-22-2002000000002-22-200002-22-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ4622-2222-2-222-2-2-22-2-200000022-2-2-22-2002000000002-22-200002-22-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ4722-2222-2-222-2-2-22-2-200000022-2-2-22-200200000000-22-220000-22-220000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ4822-2222-2-222-2-2-22-2-200000022-2-2-22-200200000000-22-220000-22-220000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ4922-22-2-222-2-22-2-22-2200000022-2-22-2200-2000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ5022-22-2-222-2-22-2-22-2200000022-2-22-2200-2000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ5122-22-2-222-2-22-2-22-2200000022-2-22-2200-200000000−2i2i−2i2i00002i−2i2i−2i0000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ5222-22-2-222-2-22-2-22-2200000022-2-22-2200-200000000−2i2i−2i2i00002i−2i2i−2i0000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ532-22-22-22-22-22-2-222-20000002-22-222-200-200002i−2i2i−2i00002i−2i2i−2i000000000000000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ542-22-22-22-22-22-2-222-20000002-22-222-200-200002i−2i2i−2i00002i−2i2i−2i00000000000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ552-22-22-22-22-22-2-222-20000002-22-222-200-20000−2i2i−2i2i0000−2i2i−2i2i000000000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ562-22-22-22-22-22-2-222-20000002-22-222-200-20000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ572-22-2-22-22-22-2-2-22220000002-22-2-2-2200200002-22-20000-22-22000000000000000000002−22−2−22−222−22−2−22−2200000000
χ582-22-2-22-22-22-2-2-22220000002-22-2-2-2200200002-22-20000-22-2200000000000000000000−22−222−22−2−22−222−22−200000000
χ592-22-2-22-22-22-2-2-22220000002-22-2-2-220020000-22-2200002-22-2000000000000000000002−22−2−22−22−22−222−22−200000000
χ602-22-2-22-22-22-2-2-22220000002-22-2-2-220020000-22-2200002-22-200000000000000000000−22−222−22−22−22−2−22−2200000000
χ612-2-2-22-2-222-2-2222-222-222-222-2-22-222-2-2-22-22-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ622-2-2-22-2-222-2-2222-222-222-222-2-22-222-2-2-22-22-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ632-2-2-22-2-222-2-2222-222-222-22-222-22-2-2-2-22-22-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ642-2-2-22-2-222-2-2222-222-222-22-222-22-2-2-2-22-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ652-2-2-22-2-222-2-2222-22-22-2-22-22-2-22-22222-2-22-2200000000000000000000000000000000000000002-2-222-2-2200000000
χ662-2-2-22-2-222-2-2222-22-22-2-22-22-2-22-22222-2-22-220000000000000000000000000000000000000000-222-2-222-200000000
χ672-2-2-22-2-222-2-2222-22-22-2-22-2-222-22-2-22222-22-200000000000000000000000000000000000000000000000000002-22-2
χ682-2-2-22-2-222-2-2222-22-22-2-22-2-222-22-2-22222-22-20000000000000000000000000000000000000000000000000000-22-22
χ692-2-2-2-222-2-222222-2-22-22-22-22-2-222-2-2-2222-2-22000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ702-2-2-2-222-2-222222-2-22-22-22-22-2-222-2-2-2222-2-2200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ712-2-2-2-222-2-222222-2-22-22-22-2-222-2-222-22-2-222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ722-2-2-2-222-2-222222-2-22-22-22-2-222-2-222-22-2-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ732-2-2-2-222-2-222222-2-2-22-22-222-2-222-2-22-22-222-200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ742-2-2-2-222-2-222222-2-2-22-22-222-2-222-2-22-22-222-20000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ752-2-2-2-222-2-222222-2-2-22-22-22-222-2-2222-2-22-2-2200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ762-2-2-2-222-2-222222-2-2-22-22-22-222-2-2222-2-22-2-220000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ7744-4444-4-444-4-4-44-4-4000000-4-4444-4400-4000000000000000000000000000000000000000000000000000000000000
χ7844-44-4-444-4-44-4-44-44000000-4-444-44-4004000000000000000000000000000000000000000000000000000000000000
χ7944-4-444-4-4-4-44-44-44400000000000000000000000022−22−2222000022−22−22220000000000000000000000000000000000000000
χ8044-4-444-4-4-4-44-44-444000000000000000000000000−222222−220000−222222−220000000000000000000000000000000000000000
χ8144-4-4-4-44444-4-44-44-40000000000000000000000002i2−2i2−2i22i20000−2i22i22i2−2i20000000000000000000000000000000000000000
χ8244-4-4-4-44444-4-44-44-4000000000000000000000000−2i22i22i2−2i200002i2−2i2−2i22i20000000000000000000000000000000000000000
χ834-4444-44-4-44-4-44-4-44000000000000000000002i2−2i2−2i22i200002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ844-4444-44-4-44-4-44-4-4400000000000000000000−2i22i22i2−2i20000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ854-444-44-444-44-44-4-4-40000000000000000000022−22−22220000−222222−2200000000000000000000000000000000000000000000
χ864-444-44-444-44-44-4-4-400000000000000000000−222222−22000022−22−222200000000000000000000000000000000000000000000
χ874-44-44-44-44-44-4-444-4000000-44-44-4-44004000000000000000000000000000000000000000000000000000000000000
χ884-44-4-44-44-44-4-4-4444000000-44-4444-400-4000000000000000000000000000000000000000000000000000000000000
χ894-4-444-4-44-4444-4-44-44-4-44-4-40000000440000000000000000000000000000000000000000000000000000000000000
χ904-4-444-4-44-4444-4-44-4-444-4440000000-4-40000000000000000000000000000000000000000000000000000000000000
χ914-4-44-444-44-4-44-4-4444-4-4-44400000004-40000000000000000000000000000000000000000000000000000000000000
χ924-4-44-444-44-4-44-4-444-4444-4-40000000-440000000000000000000000000000000000000000000000000000000000000

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