Finite Group Databasebeta

← Group #511977

Character table — Group #511977

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222224444444444444444888888882244448888888888882222444444444444161616161616161616161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1
χ611111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11
χ711111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11
χ811111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1
χ91111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ121111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ131111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ141111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ151111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ161111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222000000000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2000000000000000000000000000000000000
χ2122222222-2-2222222222222-2-200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ2222222222-2-2222222222222-2-200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-2000000002222-2-2000000000000000000000000000022−2−2−2−22222−2−2−2−2220000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2000000002222-2-20000000000000000000000000000−2−22222−2−2−2−22222−2−20000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-20000000022-2-222000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-20000000022-2-2220000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ29222-22-2-2-22-222-2-2000000002-22222-2-2-2-22-2000022-2-20000000022-2-222-2-20000000000000000000000000000
χ30222-22-2-2-22-222-2-2000000002-22222-2-2-2-22-2000022-2-200000000-2-222-2-2220000000000000000000000000000
χ31222-22-2-2-22-222-2-2000000002-2-2-2-2-222222-20000-2-22200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ32222-22-2-2-22-222-2-2000000002-2-2-2-2-222222-20000-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ33222-22-2-2-22-2-2-222000000002-22222-2-2-2-2-220000-2-2220000000022-2-2-2-2220000000000000000000000000000
χ34222-22-2-2-22-2-2-222000000002-22222-2-2-2-2-220000-2-22200000000-2-22222-2-20000000000000000000000000000
χ35222-22-2-2-22-2-2-222000000002-2-2-2-2-22222-22000022-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ36222-22-2-2-22-2-2-222000000002-2-2-2-2-22222-22000022-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ3722-2-2-222-2002i−2i2i−2i22-2-22i2i−2i−2i0022−2−222−2−2000000i2−i2i2−i222−2−2i2i2−i2−i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ3822-2-2-222-2002i−2i2i−2i22-2-22i2i−2i−2i0022−2−222−2−2000000i2−i2i2−i222−2−2i2i2−i2−i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ3922-2-2-222-2002i−2i2i−2i22-2-22i2i−2i−2i00−2−222−2−222000000−i2i2−i2i2−2−222−i2−i2i2i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ4022-2-2-222-2002i−2i2i−2i22-2-22i2i−2i−2i00−2−222−2−222000000−i2i2−i2i2−2−222−i2−i2i2i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ4122-2-2-222-2002i−2i2i−2i-2-222−2i−2i2i2i0022−2−222−2−2000000i2−i2i2−i2−2−222−i2−i2i2i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ4222-2-2-222-2002i−2i2i−2i-2-222−2i−2i2i2i0022−2−222−2−2000000i2−i2i2−i2−2−222−i2−i2i2i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ4322-2-2-222-2002i−2i2i−2i-2-222−2i−2i2i2i00−2−222−2−222000000−i2i2−i2i222−2−2i2i2−i2−i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ4422-2-2-222-2002i−2i2i−2i-2-222−2i−2i2i2i00−2−222−2−222000000−i2i2−i2i222−2−2i2i2−i2−i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ4522-2-2-222-200−2i2i−2i2i22-2-2−2i−2i2i2i0022−2−222−2−2000000−i2i2−i2i222−2−2−i2−i2i2i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ4622-2-2-222-200−2i2i−2i2i22-2-2−2i−2i2i2i0022−2−222−2−2000000−i2i2−i2i222−2−2−i2−i2i2i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ4722-2-2-222-200−2i2i−2i2i22-2-2−2i−2i2i2i00−2−222−2−222000000i2−i2i2−i2−2−222i2i2−i2−i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ4822-2-2-222-200−2i2i−2i2i22-2-2−2i−2i2i2i00−2−222−2−222000000i2−i2i2−i2−2−222i2i2−i2−i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ4922-2-2-222-200−2i2i−2i2i-2-2222i2i−2i−2i0022−2−222−2−2000000−i2i2−i2i2−2−222i2i2−i2−i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ5022-2-2-222-200−2i2i−2i2i-2-2222i2i−2i−2i0022−2−222−2−2000000−i2i2−i2i2−2−222i2i2−i2−i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ5122-2-2-222-200−2i2i−2i2i-2-2222i2i−2i−2i00−2−222−2−222000000i2−i2i2−i222−2−2−i2−i2i2i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ5222-2-2-222-200−2i2i−2i2i-2-2222i2i−2i−2i00−2−222−2−222000000i2−i2i2−i222−2−2−i2−i2i2i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ532-2-222-22-2-22000000002i−2i2i−2i2-22-22-22-22-2002i−2i00000000002i−2i2i−2i00002-22-22i−2i2i−2i000000000000000000000000
χ542-2-222-22-2-22000000002i−2i2i−2i2-22-22-22-22-2002i−2i00000000002i−2i2i−2i0000-22-22−2i2i−2i2i000000000000000000000000
χ552-2-222-22-2-22000000002i−2i2i−2i2-2-22-22-22-22002i−2i0000000000−2i2i−2i2i2-22-2000000002i−2i2i−2i00000000000000000000
χ562-2-222-22-2-22000000002i−2i2i−2i2-2-22-22-22-22002i−2i0000000000−2i2i−2i2i-22-2200000000−2i2i−2i2i00000000000000000000
χ572-2-222-22-2-2200000000−2i2i−2i2i2-22-22-22-22-200−2i2i0000000000−2i2i−2i2i00002-22-2−2i2i−2i2i000000000000000000000000
χ582-2-222-22-2-2200000000−2i2i−2i2i2-22-22-22-22-200−2i2i0000000000−2i2i−2i2i0000-22-222i−2i2i−2i000000000000000000000000
χ592-2-222-22-2-2200000000−2i2i−2i2i2-2-22-22-22-2200−2i2i00000000002i−2i2i−2i2-22-200000000−2i2i−2i2i00000000000000000000
χ602-2-222-22-2-2200000000−2i2i−2i2i2-2-22-22-22-2200−2i2i00000000002i−2i2i−2i-22-22000000002i−2i2i−2i00000000000000000000
χ612-2-2-222-22-2-200002-22-20000222-22-2-22-2200002-200002-22-2000000002-2-2200002-2-2200000000000000000000
χ622-2-2-222-22-2-200002-22-20000222-22-2-22-2200002-200002-22-200000000-222-20000-222-200000000000000000000
χ632-2-2-222-22-2-200002-22-2000022-22-222-22-200002-20000-22-2200002-2-2200002-2-22000000000000000000000000
χ642-2-2-222-22-2-200002-22-2000022-22-222-22-200002-20000-22-220000-222-20000-222-2000000000000000000000000
χ652-2-2-222-22-2-20000-22-220000222-22-2-22-220000-220000-22-22000000002-2-220000-222-200000000000000000000
χ662-2-2-222-22-2-20000-22-220000222-22-2-22-220000-220000-22-2200000000-222-200002-2-2200000000000000000000
χ672-2-2-222-22-2-20000-22-22000022-22-222-22-20000-2200002-22-200002-2-220000-222-2000000000000000000000000
χ682-2-2-222-22-2-20000-22-22000022-22-222-22-20000-2200002-22-20000-222-200002-2-22000000000000000000000000
χ69444-44-4-4-4-4444-4-400000000-4400000000-440000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-44-4-44400000000-44000000004-40000000000000000000000000000000000000000000000000000
χ7144-44-4-4-44004i−4i−4i4i00000000002222−22−22−22−2222220000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ7244-44-4-4-44004i−4i−4i4i0000000000−22−2222222222−22−22000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7344-44-4-4-4400−4i4i4i−4i00000000002222−22−22−22−222222000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7444-44-4-4-4400−4i4i4i−4i0000000000−22−2222222222−22−220000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ754-444-44-4-40000004-4-4400000022−22−2222−222222−22000000000022−22−22220000000000000000000000000000000000000000
χ764-444-44-4-40000004-4-44000000−222222−2222−22−22220000000000−222222−220000000000000000000000000000000000000000
χ774-444-44-4-4000000-444-400000022−22−2222−222222−220000000000−222222−220000000000000000000000000000000000000000
χ784-444-44-4-4000000-444-4000000−222222−2222−22−2222000000000022−22−22220000000000000000000000000000000000000000
χ794-44-4-4-44400000000004-4-440022−22−222222−22−22220000000000000022−22−2222000000000000000000000000000000000000
χ804-44-4-4-44400000000004-4-4400−222222−22−222222−2200000000000000−222222−22000000000000000000000000000000000000
χ814-44-4-4-4440000000000-444-40022−22−222222−22−222200000000000000−222222−22000000000000000000000000000000000000
χ824-44-4-4-4440000000000-444-400−222222−22−222222−220000000000000022−22−2222000000000000000000000000000000000000
χ834-4-444-44-44-4000000004i−4i4i−4i-440000000000−4i4i00000000000000000000000000000000000000000000000000
χ844-4-444-44-44-400000000−4i4i−4i4i-4400000000004i−4i00000000000000000000000000000000000000000000000000
χ854-4-4-444-444400004-44-40000-4-4000000000000-44000000000000000000000000000000000000000000000000
χ864-4-4-444-44440000-44-440000-4-40000000000004-4000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.