Finite Group Databasebeta

← Group #397221

Character table — Group #397221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444222288888888888888882244444444444444444444448888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-111
χ9111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ10111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111
χ11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ12111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ13111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ14111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ15111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ16111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ172222222222222222-2-2-2-2-222222222-2-2-2-2-2-2-2000000000000000022-2-2000000000000-2-22200000000000000000000
χ182222222222222222-2-2-2-2-222222222-2-2-2-2-2-2-20000000000000000-2-22200000000000022-2-200000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222000000000000-2-2-2-200000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2000000000000222200000000000000000000
χ21222222-2-2-22-2-2-22-2-222-2-2-2000000002-220000000000002222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ22222222-2-2-22-2-2-22-2-222-2-2-2000000002-220000000000002222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ23222222-2-2-22-2-2-22-2-222-2-2-2000000002-22000000000000-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ24222222-2-2-22-2-2-22-2-222-2-2-2000000002-22000000000000-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ252222-2-22-22-22-2-2-2-22000002i2i2i2i−2i−2i−2i−2i00000002222−2−2−2−2i2i2−i2−i2i2i2−i2−i22-200000000000000002i−2i000022−2−2i2i2−i2−i200000000
χ262222-2-22-22-22-2-2-2-22000002i2i2i2i−2i−2i−2i−2i00000002222−2−2−2−2i2i2−i2−i2i2i2−i2−i2-220000000000000000−2i2i0000−2−222−i2−i2i2i200000000
χ272222-2-22-22-22-2-2-2-22000002i2i2i2i−2i−2i−2i−2i0000000−2−2−2−22222−i2−i2i2i2−i2−i2i2i22-200000000000000002i−2i0000−2−222−i2−i2i2i200000000
χ282222-2-22-22-22-2-2-2-22000002i2i2i2i−2i−2i−2i−2i0000000−2−2−2−22222−i2−i2i2i2−i2−i2i2i2-220000000000000000−2i2i000022−2−2i2i2−i2−i200000000
χ292222-2-22-22-22-2-2-2-2200000−2i−2i−2i−2i2i2i2i2i00000002222−2−2−2−2−i2−i2i2i2−i2−i2i2i22-20000000000000000−2i2i000022−2−2−i2−i2i2i200000000
χ302222-2-22-22-22-2-2-2-2200000−2i−2i−2i−2i2i2i2i2i00000002222−2−2−2−2−i2−i2i2i2−i2−i2i2i2-2200000000000000002i−2i0000−2−222i2i2−i2−i200000000
χ312222-2-22-22-22-2-2-2-2200000−2i−2i−2i−2i2i2i2i2i0000000−2−2−2−22222i2i2−i2−i2i2i2−i2−i22-20000000000000000−2i2i0000−2−222i2i2−i2−i200000000
χ322222-2-22-22-22-2-2-2-2200000−2i−2i−2i−2i2i2i2i2i0000000−2−2−2−22222i2i2−i2−i2i2i2−i2−i2-2200000000000000002i−2i000022−2−2−i2−i2i2i200000000
χ3322-2-22-2222-2-2-2-222-22-222-222-2-222-2-2-2-2222-2-2000000000000000000002i2i−2i−2i2i−2i2i−2i0000000000000000000000000000
χ3422-2-22-2222-2-2-2-222-22-222-222-2-222-2-2-2-2222-2-200000000000000000000−2i−2i2i2i−2i2i−2i2i0000000000000000000000000000
χ3522-2-22-2222-2-2-2-222-22-222-2-2-222-2-222-2-22-2-222000000000000000000002i2i−2i−2i−2i2i−2i2i0000000000000000000000000000
χ3622-2-22-2222-2-2-2-222-22-222-2-2-222-2-222-2-22-2-22200000000000000000000−2i−2i2i2i2i−2i2i−2i0000000000000000000000000000
χ3722-2-22-2222-2-2-2-222-2-22-2-2222-2-222-2-222-2-2-222000000000000000000000000000000000000000000000000002i−2i002i−2i
χ3822-2-22-2222-2-2-2-222-2-22-2-2222-2-222-2-222-2-2-22200000000000000000000000000000000000000000000000000−2i2i00−2i2i
χ3922-2-22-2222-2-2-2-222-2-22-2-22-2-222-2-22222-222-2-2000000000000000000000000000000000000000000000000002i−2i00−2i2i
χ4022-2-22-2222-2-2-2-222-2-22-2-22-2-222-2-22222-222-2-200000000000000000000000000000000000000000000000000−2i2i002i−2i
χ4122-2-22-2-2-2-2-22222-222-2-2-2200000000-222000022-2-222-2-200000000000000002-2-220000000022-2-20000000000000000
χ4222-2-22-2-2-2-2-22222-222-2-2-2200000000-222000022-2-222-2-20000000000000000-222-200000000-2-2220000000000000000
χ4322-2-22-2-2-2-2-22222-222-2-2-2200000000-2220000-2-222-2-22200000000000000002-2-2200000000-2-2220000000000000000
χ4422-2-22-2-2-2-2-22222-222-2-2-2200000000-2220000-2-222-2-2220000000000000000-222-20000000022-2-20000000000000000
χ452-22-22-2-222222-2-2-2-2000002i−2i2i−2i2i−2i2i−2i0000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2002-20000000000002i−2i0000002−22−2i2−i2i2−i200000000
χ462-22-22-2-222222-2-2-2-2000002i−2i2i−2i2i−2i2i−2i0000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200-22000000000000−2i2i000000−22−22−i2i2−i2i200000000
χ472-22-22-2-222222-2-2-2-2000002i−2i2i−2i2i−2i2i−2i0000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22002-20000000000002i−2i000000−22−22−i2i2−i2i200000000
χ482-22-22-2-222222-2-2-2-2000002i−2i2i−2i2i−2i2i−2i0000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200-22000000000000−2i2i0000002−22−2i2−i2i2−i200000000
χ492-22-22-2-222222-2-2-2-200000−2i2i−2i2i−2i2i−2i2i0000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22002-2000000000000−2i2i000000−22−22i2−i2i2−i200000000
χ502-22-22-2-222222-2-2-2-200000−2i2i−2i2i−2i2i−2i2i0000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200-220000000000002i−2i0000002−22−2−i2i2−i2i200000000
χ512-22-22-2-222222-2-2-2-200000−2i2i−2i2i−2i2i−2i2i0000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2002-2000000000000−2i2i0000002−22−2−i2i2−i2i200000000
χ522-22-22-2-222222-2-2-2-200000−2i2i−2i2i−2i2i−2i2i0000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200-220000000000002i−2i000000−22−22i2−i2i2−i200000000
χ532-22-2-2222-2-2-22-22-22222-2-200000000-22-20000000000002i−2i−2i2i−2i2i2i−2i00002i−2i2i−2i0000000000002-22-20000000000000000
χ542-22-2-2222-2-2-22-22-22222-2-200000000-22-20000000000002i−2i−2i2i−2i2i2i−2i0000−2i2i−2i2i000000000000-22-220000000000000000
χ552-22-2-2222-2-2-22-22-22222-2-200000000-22-2000000000000−2i2i2i−2i2i−2i−2i2i00002i−2i2i−2i000000000000-22-220000000000000000
χ562-22-2-2222-2-2-22-22-22222-2-200000000-22-2000000000000−2i2i2i−2i2i−2i−2i2i0000−2i2i−2i2i0000000000002-22-20000000000000000
χ572-22-2-22-2-22-22-2222-222-2222-22-2-22-22-2-2-22-22-22i−2i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ582-22-2-22-2-22-22-2222-222-2222-22-2-22-22-2-2-22-22-2−2i2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ592-22-2-22-2-22-22-2222-222-222-22-222-22-2-2-2-2-22-222i−2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ602-22-2-22-2-22-22-2222-222-222-22-222-22-2-2-2-2-22-22−2i2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ612-22-2-22-2-22-22-2222-2-2-22-2-22-22-2-22-22222-22-2200000000000000000000000000000000000000002-2-222-2-2200000000
χ622-22-2-22-2-22-22-2222-2-2-22-2-22-22-2-22-22222-22-220000000000000000000000000000000000000000-222-2-222-200000000
χ632-22-2-22-2-22-22-2222-2-2-22-2-2-22-222-22-22222-22-200000000000000000000000000000000000000002-2-22-222-200000000
χ642-22-2-22-2-22-22-2222-2-2-22-2-2-22-222-22-22222-22-20000000000000000000000000000000000000000-222-22-2-2200000000
χ652-2-22-2-222-222-222-2-22-22-22000000002-2-200002i−2i−2i2i−2i2i2i−2i0000000000002-2-2200002i−2i2i−2i000000000000000000000000
χ662-2-22-2-222-222-222-2-22-22-22000000002-2-200002i−2i−2i2i−2i2i2i−2i000000000000-222-20000−2i2i−2i2i000000000000000000000000
χ672-2-22-2-222-222-222-2-22-22-22000000002-2-20000−2i2i2i−2i2i−2i−2i2i0000000000002-2-220000−2i2i−2i2i000000000000000000000000
χ682-2-22-2-222-222-222-2-22-22-22000000002-2-20000−2i2i2i−2i2i−2i−2i2i000000000000-222-200002i−2i2i−2i000000000000000000000000
χ692-2-22-2-2-2-222-22-22222-2-22-22-2-22-222-222-22-2-2200000000000000000000000000002-2-2200002-2-220000000000000000
χ702-2-22-2-2-2-222-22-22222-2-22-22-2-22-222-222-22-2-220000000000000000000000000000-222-20000-222-20000000000000000
χ712-2-22-2-2-2-222-22-22222-2-22-2-222-22-2-2222-2-222-200000000000000000000000000002-2-220000-222-20000000000000000
χ722-2-22-2-2-2-222-22-22222-2-22-2-222-22-2-2222-2-222-20000000000000000000000000000-222-200002-2-220000000000000000
χ732-2-22-2-2-2-222-22-2222-222-222-2-22-222-2-2-22-222-20000000000000000000000000000000000000000000000002-2002-200
χ742-2-22-2-2-2-222-22-2222-222-222-2-22-222-2-2-22-222-2000000000000000000000000000000000000000000000000-2200-2200
χ752-2-22-2-2-2-222-22-2222-222-22-222-22-2-22-2-222-2-220000000000000000000000000000000000000000000000002-200-2200
χ762-2-22-2-2-2-222-22-2222-222-22-222-22-2-22-2-222-2-22000000000000000000000000000000000000000000000000-22002-200
χ77444444-4-4-44-4-4-44-4-4-4-444400000000-44-4000000000000000000000000000000000000000000000000000000000000
χ784444-4-4-44-4-4-444-44-400000000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000
χ794444-4-4-44-4-4-444-44-40000000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000
χ8044-4-44-4-4-4-4-44444-44-4444-4000000004-4-4000000000000000000000000000000000000000000000000000000000000
χ8144-4-4-444-444-444-4-4-4000004i4i−4i−4i−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-444-444-444-4-4-400000−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000000
χ8344-4-4-44-44-444-4-4-444000000000000000000002222−22−22−22−222222000000000000000000000000000000000000000000000000
χ8444-4-4-44-44-444-4-4-44400000000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000000000
χ854-44-44-44-4-44-4-44-444000000000000000000000000000022−2222−22−2222−22220000000000000000000000000000000000000000
χ864-44-44-44-4-44-4-44-4440000000000000000000000000000−2222−222222−2222−220000000000000000000000000000000000000000
χ874-44-4-4444-4-4-44-44-44-4-4-444000000004-44000000000000000000000000000000000000000000000000000000000000
χ884-4-44444-4-4-444-4-44-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ894-4-44444-4-4-444-4-44-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ904-4-4444-444-4-4-44-4-44000004i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-444-4-4-44-4-4400000−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-444-444-4-4-44-44-400000000-444000000000000000000000000000000000000000000000000000000000000

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