Finite Group Databasebeta

← Group #138607

Character table — Group #138607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222224444444488888888888888884488888888888888882222444488888888161616161616161616161616161616164444
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
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91-1-1-111-11-1-11111-1-111-1-1iiii−i−i−i−i11-1-11-111-1-1ii−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−i1-1
χ101-1-1-111-11-1-11111-1-111-1-1iiii−i−i−i−i11-1-11-111-1-1ii−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−ii-11
χ111-1-1-111-11-1-11111-1-111-1-1iiii−i−i−i−i11-1-11-111-1-1ii−i−iiiii−i−i−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−ii-11
χ121-1-1-111-11-1-11111-1-111-1-1iiii−i−i−i−i11-1-11-111-1-1ii−i−iiiii−i−i−i−i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111i−i1-1
χ131-1-1-111-11-1-11111-1-111-1-1−i−i−i−iiiii11-1-11-111-1-1−i−iii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111i−i-11
χ141-1-1-111-11-1-11111-1-111-1-1−i−i−i−iiiii11-1-11-111-1-1−i−iii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii1-1
χ151-1-1-111-11-1-11111-1-111-1-1−i−i−i−iiiii11-1-11-111-1-1−i−iii−i−i−i−iiiii-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−ii1-1
χ161-1-1-111-11-1-11111-1-111-1-1−i−i−i−iiiii11-1-11-111-1-1−i−iii−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1i−i-11
χ172222222222222222-2-2-2-222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222-2-222-2-22222000000002222-2-2-2-2-2-20000000000002222-2-2-2-20000000000000000000000000000
χ202222222222-2-222-2-22222000000002222-2-2-2-2-2-2000000000000-2-2-2-222220000000000000000000000000000
χ212222222222-2-222-2-2-2-2-2-200000000-2-2-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ222222222222-2-222-2-2-2-2-2-200000000-2-2-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-222-2-2220000222222220000-2-20000-2-2-2-200000000000000000000000022−2−222−2−222−2−222−2−20000
χ2422222222-2-222-2-2220000222222220000-2-20000-2-2-2-2000000000000000000000000−2−222−2−222−2−222−2−2220000
χ2522222222-2-222-2-2220000-2-2-2-2-2-2-2-20000-2-20000222200000000000000000000000022−2−222−2−2−2−222−2−2220000
χ2622222222-2-222-2-2220000-2-2-2-2-2-2-2-20000-2-200002222000000000000000000000000−2−222−2−22222−2−222−2−20000
χ27222-22-2-2-22-2002-200222222−2−222−2−2-2-2-2-20000002−22−222−2−222−2−22-22-200002−22−22−22−200000000000000000000
χ28222-22-2-2-22-2002-200222222−2−222−2−2-2-2-2-20000002−22−222−2−222−2−2-22-220000−22−22−22−2200000000000000000000
χ29222-22-2-2-22-2002-2002222−2−222−2−222-2-2-2-2000000−22−22−2−222−2−2222-22-20000−22−22−22−2200000000000000000000
χ30222-22-2-2-22-2002-2002222−2−222−2−222-2-2-2-2000000−22−22−2−222−2−222-22-2200002−22−22−22−200000000000000000000
χ31222-22-2-2-22-2002-200-2-2-2-222−2−222−2−222220000002−22−2−2−222−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i200000000000000000000
χ32222-22-2-2-22-2002-200-2-2-2-222−2−222−2−222220000002−22−2−2−222−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i200000000000000000000
χ33222-22-2-2-22-2002-200-2-2-2-2−2−222−2−2222222000000−22−2222−2−222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i200000000000000000000
χ34222-22-2-2-22-2002-200-2-2-2-2−2−222−2−2222222000000−22−2222−2−222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i200000000000000000000
χ3522-22-2-2-22002-2002-22−22−22i−2i2i−2i2i−2i2i−2i2−22−2002−22−20000i2−i2i2−i2i2−i2i2−i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ3622-22-2-2-22002-2002-22−22−22i−2i2i−2i2i−2i2i−2i2−22−2002−22−20000i2−i2i2−i2i2−i2i2−i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ3722-22-2-2-22002-2002-22−22−2−2i2i−2i2i−2i2i−2i2i2−22−2002−22−20000−i2i2−i2i2−i2i2−i2i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ3822-22-2-2-22002-2002-22−22−2−2i2i−2i2i−2i2i−2i2i2−22−2002−22−20000−i2i2−i2i2−i2i2−i2i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ3922-22-2-2-22002-2002-2−22−222i−2i2i−2i2i−2i2i−2i−22−2200−22−220000−i2i2−i2i2−i2i2−i2i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ4022-22-2-2-22002-2002-2−22−222i−2i2i−2i2i−2i2i−2i−22−2200−22−220000−i2i2−i2i2−i2i2−i2i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ4122-22-2-2-22002-2002-2−22−22−2i2i−2i2i−2i2i−2i2i−22−2200−22−220000i2−i2i2−i2i2−i2i2−i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ4222-22-2-2-22002-2002-2−22−22−2i2i−2i2i−2i2i−2i2i−22−2200−22−220000i2−i2i2−i2i2−i2i2−i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ432-22-2-2-222002-200-222−2−222-22-2-22-222−2−22002−2−2200002−22−2−22−220000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ442-22-2-2-222002-200-222−2−222-22-2-22-222−2−22002−2−2200002−22−2−22−220000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ452-22-2-2-222002-200-222−2−22-22-222-22-22−2−22002−2−220000−22−222−22−20000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ462-22-2-2-222002-200-222−2−22-22-222-22-22−2−22002−2−220000−22−222−22−20000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ472-22-2-2-222002-200-22−222−22-22-2-22-22−222−200−222−20000−22−222−22−20000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ482-22-2-2-222002-200-22−222−22-22-2-22-22−222−200−222−20000−22−222−22−20000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ492-22-2-2-222002-200-22−222−2-22-222-22-2−222−200−222−200002−22−2−22−220000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ502-22-2-2-222002-200-22−222−2-22-222-22-2−222−200−222−200002−22−2−22−220000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ512-2-222-22-2-22002-20022-2-2i2i2−i2−i2−i2−i2i2i2-2-222000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i22-2-220000i2−i2i2−i2−i2i2−i2i200000000000000000000
χ522-2-222-22-2-22002-20022-2-2i2i2−i2−i2−i2−i2i2i2-2-222000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2-222-20000−i2i2−i2i2i2−i2i2−i200000000000000000000
χ532-2-222-22-2-22002-20022-2-2−i2−i2i2i2i2i2−i2−i2-2-222000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i22-2-220000−i2i2−i2i2i2−i2i2−i200000000000000000000
χ542-2-222-22-2-22002-20022-2-2−i2−i2i2i2i2i2−i2−i2-2-222000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2-222-20000i2−i2i2−i2−i2i2−i2i200000000000000000000
χ552-2-222-22-2-22002-200-2-222i2i2−i2−i2−i2−i2i2i222-2-2000000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i200002i−2i−2i2i−222−22−2−2200000000000000000000
χ562-2-222-22-2-22002-200-2-222i2i2−i2−i2−i2−i2i2i222-2-2000000i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000−2i2i2i−2i2−2−22−222−200000000000000000000
χ572-2-222-22-2-22002-200-2-222−i2−i2i2i2i2i2−i2−i222-2-2000000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i200002i−2i−2i2i2−2−22−222−200000000000000000000
χ582-2-222-22-2-22002-200-2-222−i2−i2i2i2i2i2−i2−i222-2-2000000−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000−2i2i2i−2i−222−22−2−2200000000000000000000
χ592-2-2-222-222222-2-2-2-200002i2i2i2i−2i−2i−2i−2i0000-220000−2i−2i2i2i000000000000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000
χ602-2-2-222-222222-2-2-2-200002i2i2i2i−2i−2i−2i−2i0000-220000−2i−2i2i2i000000000000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000
χ612-2-2-222-222222-2-2-2-20000−2i−2i−2i−2i2i2i2i2i0000-2200002i2i−2i−2i000000000000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000
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χ632-2-2-222-22-2-22222-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-2222-2-2-2222i2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ642-2-2-222-22-2-22222-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-2222-2-2-222−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ652-2-2-222-22-2-2-2-2222222-2-20000000022-2-2-22-2-22200000000000022-2-2-2-2220000000000000000000000000000
χ662-2-2-222-22-2-2-2-2222222-2-20000000022-2-2-22-2-222000000000000-2-22222-2-20000000000000000000000000000
χ672-2-2-222-22-2-2-2-22222-2-22200000000-2-222-2222-2-20000000000000000000022-2-2-2-22200000000000000000000
χ682-2-2-222-22-2-2-2-22222-2-22200000000-2-222-2222-2-200000000000000000000-2-22222-2-200000000000000000000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-4400-440000002222−22−222222−22−220000000000−2222−222200000000000000000000000000000000000000000000
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χ7444-4-4-444-40000000022−2222−222i2−2i2−2i22i22i2−2i2−2i22i2−2222−222200000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ7544-4-4-444-40000000022−2222−22−2i22i22i2−2i2−2i22i22i2−2i2−2222−22220000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ7644-4-4-444-400000000−2222−22222i2−2i2−2i22i22i2−2i2−2i22i222−2222−220000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ7744-4-4-444-400000000−2222−2222−2i22i22i2−2i2−2i22i22i2−2i222−2222−2200000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ784-444-44-4-40000000022−22−222222−22−2222−222222−22−222222−2200000000002-2-22-222-2000000000000000000000000000000000000
χ794-444-44-4-40000000022−22−2222−222222−2222−22−2222−222222−220000000000-222-22-2-22000000000000000000000000000000000000
χ804-444-44-4-400000000−222222−2222−22−2222−222222−2222−22−22220000000000-222-22-2-22000000000000000000000000000000000000
χ814-444-44-4-400000000−222222−22−222222−2222−22−222222−22−222200000000002-2-22-222-2000000000000000000000000000000000000
χ824-44-4-4-44400-44004-422−22−22220000000022−22−222200−222222−22000000000000000000000000000000000000000000000000
χ834-44-4-4-44400-44004-4−222222−2200000000−222222−220022−22−2222000000000000000000000000000000000000000000000000
χ844-4-444-44-44-400-440000002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ854-4-444-44-44-400-44000000−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ864-4-4-444-4444-4-4-4-44400000000000000004-40000000000000000000000000000000000000000000000000000

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