Finite Group Databasebeta

← Group #419247

Character table — Group #419247

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111111111112222222244444444444444444444444444448888888888888888888888161616161616161616161616
order12222222222222224444444422224444444488888888888888882222444444444488888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ611111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ172222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000022-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000-2-22222000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000-2-222-2-2000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000022-2-222000000000000000000000000
χ2122222-2-22-22-2-2-2-2-220000000022-2-2000022-2-2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ2222222-2-22-22-2-2-2-2-220000000022-2-2000022-2-2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002-200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ2322222-2-22-22-2-2-2-2-220000000022-2-20000-2-222i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-2200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ2422222-2-22-22-2-2-2-2-220000000022-2-20000-2-222−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000-2200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ2522222-2-22-22-2-2-2-2-2200000000-2-222000022-2-2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000-2200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ2622222-2-22-22-2-2-2-2-2200000000-2-222000022-2-2−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000-2200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ2722222-2-22-22-2-2-2-2-2200000000-2-2220000-2-222i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002-200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ2822222-2-22-22-2-2-2-2-2200000000-2-2220000-2-222−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002-200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ29222-2-222-2-2-22-2-2-222222-2-22-2-20000000000002i2i−2i−2i2i2i−2i−2i0000000022-2-2000000000000000000002i−2i00000000
χ30222-2-222-2-2-22-2-2-222222-2-22-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000-2-22200000000000000000000−2i2i00000000
χ31222-2-222-2-2-22-2-2-222222-2-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i0000000022-2-200000000000000000000−2i2i00000000
χ32222-2-222-2-2-22-2-2-222222-2-22-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000-2-222000000000000000000002i−2i00000000
χ3322-22-22-222-222-2-2-2-222-2-2-2-2220000000000000000000022-2-222-2-200000000002i2i−2i−2i00000000000000002i−2i00
χ3422-22-22-222-222-2-2-2-222-2-2-2-2220000000000000000000022-2-222-2-20000000000−2i−2i2i2i0000000000000000−2i2i00
χ3522-22-22-222-222-2-2-2-222-2-2-2-22200000000000000000000-2-222-2-22200000000002i2i−2i−2i0000000000000000−2i2i00
χ3622-22-22-222-222-2-2-2-222-2-2-2-22200000000000000000000-2-222-2-2220000000000−2i−2i2i2i00000000000000002i−2i00
χ372-222-22-2-222-2-22-22-20000000000002i2i−2i−2i2i−2i2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000002-2000000i2−i2i2−i22−22−2000000000000
χ382-222-22-2-222-2-22-22-20000000000002i2i−2i−2i2i−2i2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000002-2000000−i2i2−i2i2−22−22000000000000
χ392-222-22-2-222-2-22-22-20000000000002i2i−2i−2i−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000-22000000−i2i2−i2i2−22−22000000000000
χ402-222-22-2-222-2-22-22-20000000000002i2i−2i−2i−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000-22000000i2−i2i2−i22−22−2000000000000
χ412-222-22-2-222-2-22-22-2000000000000−2i−2i2i2i2i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000-22000000i2−i2i2−i2−22−22000000000000
χ422-222-22-2-222-2-22-22-2000000000000−2i−2i2i2i2i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000-22000000−i2i2−i2i22−22−2000000000000
χ432-222-22-2-222-2-22-22-2000000000000−2i−2i2i2i−2i2i−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000002-2000000−i2i2−i2i22−22−2000000000000
χ442-222-22-2-222-2-22-22-2000000000000−2i−2i2i2i−2i2i−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000002-2000000i2−i2i2−i2−22−22000000000000
χ452-222-2-22-2-2222-22-2-22-222-2-2-22000000002i−2i−2i2i000000002-22-2-22-22000000002i−2i00000000−2i2i2i−2i000000000000
χ462-222-2-22-2-2222-22-2-22-222-2-2-22000000002i−2i−2i2i00000000-22-222-22-2000000002i−2i000000002i−2i−2i2i000000000000
χ472-222-2-22-2-2222-22-2-22-222-2-2-2200000000−2i2i2i−2i000000002-22-2-22-2200000000−2i2i000000002i−2i−2i2i000000000000
χ482-222-2-22-2-2222-22-2-22-222-2-2-2200000000−2i2i2i−2i00000000-22-222-22-200000000−2i2i00000000−2i2i2i−2i000000000000
χ492-222-2-22-2-2222-22-2-2-22-2-2222-2000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000−2i2i0000-222-20000000000000000
χ502-222-2-22-2-2222-22-2-2-22-2-2222-2000000002i−2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000−2i2i00002-2-220000000000000000
χ512-222-2-22-2-2222-22-2-2-22-2-2222-200000000−2i2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000002i−2i00002-2-220000000000000000
χ522-222-2-22-2-2222-22-2-2-22-2-2222-200000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000002i−2i0000-222-20000000000000000
χ532-22-22-2222-22-22-2-2-2-22-22-22-220000000000002-2-22-222-20000000000000000002i−2i2i−2i000000000000002i−2i0000
χ542-22-22-2222-22-22-2-2-2-22-22-22-220000000000002-2-22-222-2000000000000000000−2i2i−2i2i00000000000000−2i2i0000
χ552-22-22-2222-22-22-2-2-2-22-22-22-22000000000000-222-22-2-220000000000000000002i−2i2i−2i00000000000000−2i2i0000
χ562-22-22-2222-22-22-2-2-2-22-22-22-22000000000000-222-22-2-22000000000000000000−2i2i−2i2i000000000000002i−2i0000
χ572-2-222-2-2-2-2-2222-2222-2-2-222-22000000000000000000002-2-22-222-22-22-200000000000000000000002-2000000
χ582-2-222-2-2-2-2-2222-2222-2-2-222-22000000000000000000002-2-22-222-2-22-220000000000000000000000-22000000
χ592-2-222-2-2-2-2-2222-2222-2-2-222-2200000000000000000000-222-22-2-222-22-20000000000000000000000-22000000
χ602-2-222-2-2-2-2-2222-2222-2-2-222-2200000000000000000000-222-22-2-22-22-2200000000000000000000002-2000000
χ612-2-2-2-2-2-22222-2-22222-2-22-222-22-22-22-22-2000000000000000000002-2-2200000000000000000000000000002-2
χ622-2-2-2-2-2-22222-2-22222-2-22-222-22-22-22-22-200000000000000000000-222-20000000000000000000000000000-22
χ632-2-2-2-2-2-22222-2-22222-2-22-222-2-22-22-22-22000000000000000000002-2-220000000000000000000000000000-22
χ642-2-2-2-2-2-22222-2-22222-2-22-222-2-22-22-22-2200000000000000000000-222-200000000000000000000000000002-2
χ652-2-2-2-2-2-22222-2-2222-222-22-2-222-22-2-22-220000000000000000000000000000002-2-22000000002-20000000000
χ662-2-2-2-2-2-22222-2-2222-222-22-2-222-22-2-22-22000000000000000000000000000000-222-200000000-220000000000
χ672-2-2-2-2-2-22222-2-2222-222-22-2-22-22-222-22-20000000000000000000000000000002-2-2200000000-220000000000
χ682-2-2-2-2-2-22222-2-2222-222-22-2-22-22-222-22-2000000000000000000000000000000-222-2000000002-20000000000
χ69444-4-444-4-4-44-4-4-444-4-4-444-44400000000000000000000000000000000000000000000000000000000000000
χ70444-4-4-4-4-44-4-4444-44000000000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ71444-4-4-4-4-44-4-4444-4400000000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ7244-44-44-444-444-4-4-4-4-4-44444-4-400000000000000000000000000000000000000000000000000000000000000
χ7344-44-4-444-4-4-4-4444-400000000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ7444-44-4-444-4-4-4-4444-40000000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ7544-4-444-4-4-444-444-4-444-444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7644-4-444-4-4-444-444-4-4-4-44-4-444400000000000000000000000000000000000000000000000000000000000000
χ7744-4-44-44-444-44-4-44-40000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ7844-4-44-44-444-44-4-44-4000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ794-44-444-44-4-4-44-444-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ804-44-444-44-4-4-44-444-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ814-44-44-4444-44-44-4-4-44-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ824-4-44444-44-4-4-4-44-4400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ834-4-44444-44-4-4-4-44-440000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ844-4-444-4-4-4-4-4444-444-4444-4-44-400000000000000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-44-444-4-44000000004-4-440000000000000000000000000000000000000000000000000000000000
χ864-4-4-4-4444-44-444-4-4400000000-444-40000000000000000000000000000000000000000000000000000000000

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