Finite Group Databasebeta

← Group #239591

Character table — Group #239591

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444224488888888888888882244444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ17222222222222222222-2-22222-2-2-2-222-2-2-2-2-2-200000000000000000022220000-2-2-2-200000000000000000000000000
χ18222222222222222222-2-22222-2-2-2-222-2-2-2-2-2-2000000000000000000-2-2-2-20000222200000000000000000000000000
χ192222222222222222-2-222-2-2-2-22222-2-222-2-2-2-20000000000000000220000-2-2-2-2000022000000000000000000000000
χ202222222222222222-2-222-2-2-2-22222-2-222-2-2-2-20000000000000000-2-2000022220000-2-2000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000002-200002-2
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000-220000-22
χ2322222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222-2-222-2-200000000000000000022-2-20000-2-22200000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222-2-222-2-2000000000000000000-2-222000022-2-200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-20000000000000000220000-2-2220000-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-20000000000000000-2-2000022-2-2000022000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2220000000000000000000000000000000000000000000000002-20000-22
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222000000000000000000000000000000000000000000000000-2200002-2
χ2922-22-22-2-22i2i2i2i−2i−2i−2i−2i002-200002i2i−2i−2i002-20000i2i2i2i2−i2−i2−i2−i22222−2−2−2−20000002i−2i2-200000022−2−2i2i2−i2−i20000000000000000
χ3022-22-22-2-22i2i2i2i−2i−2i−2i−2i002-200002i2i−2i−2i002-20000i2i2i2i2−i2−i2−i2−i22222−2−2−2−2000000−2i2i-22000000−2−222−i2−i2i2i20000000000000000
χ3122-22-22-2-22i2i2i2i−2i−2i−2i−2i002-200002i2i−2i−2i002-20000−i2−i2−i2−i2i2i2i2i2−2−2−2−222220000002i−2i2-2000000−2−222−i2−i2i2i20000000000000000
χ3222-22-22-2-22i2i2i2i−2i−2i−2i−2i002-200002i2i−2i−2i002-20000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222000000−2i2i-2200000022−2−2i2i2−i2−i20000000000000000
χ3322-22-22-2-2−2i−2i−2i−2i2i2i2i2i002-20000−2i−2i2i2i002-20000i2i2i2i2−i2−i2−i2−i2−2−2−2−222220000002i−2i-2200000022−2−2−i2−i2i2i20000000000000000
χ3422-22-22-2-2−2i−2i−2i−2i2i2i2i2i002-20000−2i−2i2i2i002-20000i2i2i2i2−i2−i2−i2−i2−2−2−2−22222000000−2i2i2-2000000−2−222i2i2−i2−i20000000000000000
χ3522-22-22-2-2−2i−2i−2i−2i2i2i2i2i002-20000−2i−2i2i2i002-20000−i2−i2−i2−i2i2i2i2i22222−2−2−2−20000002i−2i-22000000−2−222i2i2−i2−i20000000000000000
χ3622-22-22-2-2−2i−2i−2i−2i2i2i2i2i002-20000−2i−2i2i2i002-20000−i2−i2−i2−i2i2i2i2i22222−2−2−2−2000000−2i2i2-200000022−2−2−i2−i2i2i20000000000000000
χ3722-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2002i2i−2i−2i00002-200000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000002-22i−2i000000000022−2−2i2i2−i2−i200000000
χ3822-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2002i2i−2i−2i00002-200000022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000-22−2i2i0000000000−2−222−i2−i2i2i200000000
χ3922-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2002i2i−2i−2i00002-2000000−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000002-22i−2i0000000000−2−222−i2−i2i2i200000000
χ4022-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2002i2i−2i−2i00002-2000000−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000-22−2i2i000000000022−2−2i2i2−i2−i200000000
χ4122-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-200−2i−2i2i2i00002-200000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000002-2−2i2i000000000022−2−2−i2−i2i2i200000000
χ4222-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-200−2i−2i2i2i00002-200000022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000-222i−2i0000000000−2−222i2i2−i2−i200000000
χ4322-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-200−2i−2i2i2i00002-2000000−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000002-2−2i2i0000000000−2−222i2i2−i2−i200000000
χ4422-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-200−2i−2i2i2i00002-2000000−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000-222i−2i000000000022−2−2−i2−i2i2i200000000
χ452-222-2-22-22i−2i2i−2i2i−2i2i−2i00-2200002i−2i2i−2i002-200002−22−22−22−2i2−i2i2−i2i2−i2i2−i22-20000000000002i−2i2−22−2i2−i2i2−i20000000000000000
χ462-222-2-22-22i−2i2i−2i2i−2i2i−2i00-2200002i−2i2i−2i002-200002−22−22−22−2i2−i2i2−i2i2−i2i2−i2-22000000000000−2i2i−22−22−i2i2−i2i20000000000000000
χ472-222-2-22-22i−2i2i−2i2i−2i2i−2i00-2200002i−2i2i−2i002-20000−22−22−22−22−i2i2−i2i2−i2i2−i2i22-20000000000002i−2i−22−22−i2i2−i2i20000000000000000
χ482-222-2-22-22i−2i2i−2i2i−2i2i−2i00-2200002i−2i2i−2i002-20000−22−22−22−22−i2i2−i2i2−i2i2−i2i2-22000000000000−2i2i2−22−2i2−i2i2−i20000000000000000
χ492-222-2-22-2−2i2i−2i2i−2i2i−2i2i00-220000−2i2i−2i2i002-200002−22−22−22−2−i2i2−i2i2−i2i2−i2i22-2000000000000−2i2i2−22−2−i2i2−i2i20000000000000000
χ502-222-2-22-2−2i2i−2i2i−2i2i−2i2i00-220000−2i2i−2i2i002-200002−22−22−22−2−i2i2−i2i2−i2i2−i2i2-220000000000002i−2i−22−22i2−i2i2−i20000000000000000
χ512-222-2-22-2−2i2i−2i2i−2i2i−2i2i00-220000−2i2i−2i2i002-20000−22−22−22−22i2−i2i2−i2i2−i2i2−i22-2000000000000−2i2i−22−22i2−i2i2−i20000000000000000
χ522-222-2-22-2−2i2i−2i2i−2i2i−2i2i00-220000−2i2i−2i2i002-20000−22−22−22−22i2−i2i2−i2i2−i2i2−i2-220000000000002i−2i2−22−2−i2i2−i2i20000000000000000
χ532-22-222-2-22i−2i−2i2i−2i2i2i−2i2-2002i−2i2i−2i0000-22000000i2−i2−i2i2−i2i2i2−i22−2−22−222−2002-22i−2i000000000000000000i2−i2i2−i22−22−200000000
χ542-22-222-2-22i−2i−2i2i−2i2i2i−2i2-2002i−2i2i−2i0000-22000000i2−i2−i2i2−i2i2i2−i22−2−22−222−200-22−2i2i000000000000000000−i2i2−i2i2−22−2200000000
χ552-22-222-2-22i−2i−2i2i−2i2i2i−2i2-2002i−2i2i−2i0000-22000000−i2i2i2−i2i2−i2−i2i2−222−22−2−22002-22i−2i000000000000000000−i2i2−i2i2−22−2200000000
χ562-22-222-2-22i−2i−2i2i−2i2i2i−2i2-2002i−2i2i−2i0000-22000000−i2i2i2−i2i2−i2−i2i2−222−22−2−2200-22−2i2i000000000000000000i2−i2i2−i22−22−200000000
χ572-22-222-2-2−2i2i2i−2i2i−2i−2i2i2-200−2i2i−2i2i0000-22000000i2−i2−i2i2−i2i2i2−i2−222−22−2−22002-2−2i2i000000000000000000i2−i2i2−i2−22−2200000000
χ582-22-222-2-2−2i2i2i−2i2i−2i−2i2i2-200−2i2i−2i2i0000-22000000i2−i2−i2i2−i2i2i2−i2−222−22−2−2200-222i−2i000000000000000000−i2i2−i2i22−22−200000000
χ592-22-222-2-2−2i2i2i−2i2i−2i−2i2i2-200−2i2i−2i2i0000-22000000−i2i2i2−i2i2−i2−i2i22−2−22−222−2002-2−2i2i000000000000000000−i2i2−i2i22−22−200000000
χ602-22-222-2-2−2i2i2i−2i2i−2i−2i2i2-200−2i2i−2i2i0000-22000000−i2i2i2−i2i2−i2−i2i22−2−22−222−200-222i−2i000000000000000000i2−i2i2−i2−22−2200000000
χ612-2-222-2-222-22-2-22-2222222-2-22-222-2-2-2-2-22-2-2200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ622-2-222-2-222-22-2-22-2222222-2-22-222-2-2-2-2-22-2-220000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ632-2-222-2-222-22-2-22-2222-2-22-2-222-2-22-2-222-222-22i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ642-2-222-2-222-22-2-22-2222-2-22-2-222-2-22-2-222-222-2−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ652-2-222-2-222-22-2-22-22-2-222-222-2-222-222-2-2-222-2000000000000000000000000000000000000000000000000002i−2i2i−2i00
χ662-2-222-2-222-22-2-22-22-2-222-222-2-222-222-2-2-222-200000000000000000000000000000000000000000000000000−2i2i−2i2i00
χ672-2-222-2-222-22-2-22-22-2-2-2-2-222-22-2-2222222-2-22000000000000000000000000000000002-2-222-2-220000000000000000
χ682-2-222-2-222-22-2-22-22-2-2-2-2-222-22-2-2222222-2-2200000000000000000000000000000000-222-2-222-20000000000000000
χ692-2-222-2-22-22-222-22-22222-222-22-2-22-2-2-2-2-22-2200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ702-2-222-2-22-22-222-22-22222-222-22-2-22-2-2-2-2-22-220000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ712-2-222-2-22-22-222-22-222-2-2-222-2-222-2-2-2222-22-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ722-2-222-2-22-22-222-22-222-2-2-222-2-222-2-2-2222-22-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ732-2-222-2-22-22-222-22-2-2-2222-2-222-2-2222-2-22-22-2000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ742-2-222-2-22-22-222-22-2-2-2222-2-222-2-2222-2-22-22-200000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ752-2-222-2-22-22-222-22-2-2-2-2-22-2-22-222-22222-22-22000000000000000000000000000000002-2-22-222-20000000000000000
χ762-2-222-2-22-22-222-22-2-2-2-2-22-2-22-222-22222-22-2200000000000000000000000000000000-222-22-2-220000000000000000
χ77444-4-4-4-4444-4-4-4-444000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ78444-4-4-4-4444-4-4-4-44400000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ79444-4-4-4-44-4-44444-4-4000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ80444-4-4-4-44-4-44444-4-400000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ8144-44-44-4-44i4i4i4i−4i−4i−4i−4i00-440000−4i−4i4i4i00-44000000000000000000000000000000000000000000000000000000000000
χ8244-44-44-4-4−4i−4i−4i−4i4i4i4i4i00-4400004i4i−4i−4i00-44000000000000000000000000000000000000000000000000000000000000
χ8344-4-44-44-44i4i−4i−4i4i4i−4i−4i-4400−4i−4i4i4i0000-4400000000000000000000000000000000000000000000000000000000000000
χ8444-4-44-44-4−4i−4i4i4i−4i−4i4i4i-44004i4i−4i−4i0000-4400000000000000000000000000000000000000000000000000000000000000
χ854-444-4-44-44i−4i4i−4i4i−4i4i−4i004-40000−4i4i−4i4i00-44000000000000000000000000000000000000000000000000000000000000
χ864-444-4-44-4−4i4i−4i4i−4i4i−4i4i004-400004i−4i4i−4i00-44000000000000000000000000000000000000000000000000000000000000
χ874-44-444-4-44i−4i−4i4i−4i4i4i−4i-4400−4i4i−4i4i00004-400000000000000000000000000000000000000000000000000000000000000
χ884-44-444-4-4−4i4i4i−4i4i−4i−4i4i-44004i−4i4i−4i00004-400000000000000000000000000000000000000000000000000000000000000
χ894-4-4-4-44444-4-444-4-44000000000000000000002-2-222-2-222-2-222-2-220000000000000000000000000000000000000000
χ904-4-4-4-44444-4-444-4-4400000000000000000000-222-2-222-2-222-2-222-20000000000000000000000000000000000000000
χ914-4-4-4-4444-444-4-444-4000000000000000000002-2-222-2-22-222-2-222-20000000000000000000000000000000000000000
χ924-4-4-4-4444-444-4-444-400000000000000000000-222-2-222-22-2-222-2-220000000000000000000000000000000000000000

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