Finite Group Databasebeta

← Group #138142

Character table — Group #138142

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222222222444444444444888888884444448888888888888888888888888888161616161616161616161616161616164444
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
χ5111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-1
χ6111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-11
χ7111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-11
χ8111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-11-1
χ911111111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-11
χ1011111111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1
χ1111111111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1
χ1211111111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1-11
χ1311111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1411111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1611111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222222222-2-2-2-2200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ192222222222222222222-2-2-2-2200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ20222222222222-2-2-2-2-2-2-22222-222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000
χ2322222222-2-2-2-22222-2-2-22222-22222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ2622222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222222222000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2222-2-2-2-220000000022-2-222000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ2822222222-2-2-2-2-2-2-2-2222-2-2-2-220000000022-2-2220000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ29222-22-2-2-222-2-222-2-222-20000-222−2−222−2−200000022−2−222−2−222−2−20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ30222-22-2-2-222-2-222-2-222-20000-222−2−222−2−200000022−2−222−2−222−2−20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ31222-22-2-2-222-2-222-2-222-20000-2−2−222−2−222000000−2−222−2−222−2−2220000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ32222-22-2-2-222-2-222-2-222-20000-2−2−222−2−222000000−2−222−2−222−2−2220000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ33222-22-2-2-222-2-2-2-222-2-220000222−2−222−2−2000000−2−222−2−22222−2−20000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ34222-22-2-2-222-2-2-2-222-2-220000222−2−222−2−2000000−2−222−2−22222−2−20000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ35222-22-2-2-222-2-2-2-222-2-2200002−2−222−2−22200000022−2−222−2−2−2−2220000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ36222-22-2-2-222-2-2-2-222-2-2200002−2−222−2−22200000022−2−222−2−2−2−2220000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ37222-22-2-2-2-2-22222-2-2-2-220000222−2−222−2−2000000−2−22222−2−2−2−2220000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ38222-22-2-2-2-2-22222-2-2-2-220000222−2−222−2−2000000−2−22222−2−2−2−2220000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ39222-22-2-2-2-2-22222-2-2-2-2200002−2−222−2−22200000022−2−2−2−22222−2−20000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ40222-22-2-2-2-2-22222-2-2-2-2200002−2−222−2−22200000022−2−2−2−22222−2−20000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ41222-22-2-2-2-2-222-2-22222-20000-222−2−222−2−200000022−2−2−2−222−2−2220000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ42222-22-2-2-2-2-222-2-22222-20000-222−2−222−2−200000022−2−2−2−222−2−2220000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ43222-22-2-2-2-2-222-2-22222-20000-2−2−222−2−222000000−2−22222−2−222−2−20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ44222-22-2-2-2-2-222-2-22222-20000-2−2−222−2−222000000−2−22222−2−222−2−20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ4522-22-2-2-2200002i−2i2i−2i0002-22-202-22-22-22-22i−2i000000002i−2i2i−2i0000i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000000000000000
χ4622-22-2-2-2200002i−2i2i−2i0002-22-202-22-22-22-22i−2i000000002i−2i2i−2i0000−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000000000000000
χ4722-22-2-2-2200002i−2i2i−2i0002-22-20-22-22-22-222i−2i00000000−2i2i−2i2i000022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000000000
χ4822-22-2-2-2200002i−2i2i−2i0002-22-20-22-22-22-222i−2i00000000−2i2i−2i2i0000−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000000000
χ4922-22-2-2-220000−2i2i−2i2i0002-22-202-22-22-22-2−2i2i00000000−2i2i−2i2i0000i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000000000000000
χ5022-22-2-2-220000−2i2i−2i2i0002-22-202-22-22-22-2−2i2i00000000−2i2i−2i2i0000−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000000000000000
χ5122-22-2-2-220000−2i2i−2i2i0002-22-20-22-22-22-22−2i2i000000002i−2i2i−2i000022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000000000
χ5222-22-2-2-220000−2i2i−2i2i0002-22-20-22-22-22-22−2i2i000000002i−2i2i−2i0000−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000000000
χ532-22-2-2-2222-22-20000000-222-202222-2-2-2-200002-2000000002-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000000
χ542-22-2-2-2222-22-20000000-222-202222-2-2-2-200002-2000000002-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000000000
χ552-22-2-2-2222-22-20000000-222-20-2-2-2-2222200002-200000000-22-222−22−22−22−2−22−22−22−2200000000000000000000
χ562-22-2-2-2222-22-20000000-222-20-2-2-2-2222200002-200000000-22-22−22−22−22−222−22−22−22−200000000000000000000
χ572-22-2-2-222-22-220000000-222-202222-2-2-2-20000-2200000000-22-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000000000000000
χ582-22-2-2-222-22-220000000-222-202222-2-2-2-20000-2200000000-22-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ592-22-2-2-222-22-220000000-222-20-2-2-2-222220000-22000000002-22-22−22−2−22−222−22−2−22−2200000000000000000000
χ602-22-2-2-222-22-220000000-222-20-2-2-2-222220000-22000000002-22-2−22−222−22−2−22−222−22−200000000000000000000
χ612-2-2-222-22000000002-22-2-222-22-22-2-22-22002-2002-22-20000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ622-2-2-222-22000000002-22-2-222-22-22-2-22-22002-2002-22-2000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ632-2-2-222-22000000002-22-2-222-2-22-222-22-2002-200-22-22000000002i−2i−2i2i00000000−2i2i2i−2i00000000000000000000
χ642-2-2-222-22000000002-22-2-222-2-22-222-22-2002-200-22-2200000000−2i2i2i−2i000000002i−2i−2i2i00000000000000000000
χ652-2-2-222-2200000000-22-2-2-22222-22-2-22-2200-2200-22-22000000002-2-22000000002-2-2200000000000000000000
χ662-2-2-222-2200000000-22-2-2-22222-22-2-22-2200-2200-22-2200000000-222-200000000-222-200000000000000000000
χ672-2-2-222-2200000000-22-2-2-2222-22-222-22-200-22002-22-20000000000002-2-22-222-2000000000000000000000000
χ682-2-2-222-2200000000-22-2-2-2222-22-222-22-200-22002-22-2000000000000-222-22-2-22000000000000000000000000
χ6944-44-4-4-4400004i−4i4i−4i000-44-44000000000−4i4i0000000000000000000000000000000000000000000000000000
χ7044-44-4-4-440000−4i4i−4i4i000-44-440000000004i−4i0000000000000000000000000000000000000000000000000000
χ7144-4-4-444-400004i−4i−4i4i0000000022−22−222222−22−222200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ7244-4-4-444-400004i−4i−4i4i00000000−222222−22−222222−220000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ7344-4-4-444-40000−4i4i4i−4i0000000022−22−222222−22−22220000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ7444-4-4-444-40000−4i4i4i−4i00000000−222222−22−222222−2200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ754-444-44-4-44-4-440000000000002222−22−22−22−2222220000000000000022−22−2222000000000000000000000000000000000000
χ764-444-44-4-44-4-44000000000000−22−2222222222−22−2200000000000000−222222−22000000000000000000000000000000000000
χ774-444-44-4-4-444-40000000000002222−22−22−22−22222200000000000000−222222−22000000000000000000000000000000000000
χ784-444-44-4-4-444-4000000000000−22−2222222222−22−220000000000000022−22−2222000000000000000000000000000000000000
χ794-44-4-4-4444-44-400000004-4-440000000000000-44000000000000000000000000000000000000000000000000
χ804-44-4-4-444-44-4400000004-4-4400000000000004-4000000000000000000000000000000000000000000000000
χ814-4-444-44-4000000004-4-40000422−22−2222−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ824-4-444-44-4000000004-4-400004−222222−2222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ834-4-444-44-400000000-4440000-422−22−2222−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ844-4-444-44-400000000-4440000-4−222222−2222−22−222200000022−22−222200000000000000000000000000000000000000000000
χ854-4-4-444-44000000004-4444-4-4-40000000000-4400000000000000000000000000000000000000000000000000
χ864-4-4-444-4400000000-44-444-4-4400000000004-400000000000000000000000000000000000000000000000000

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