Finite Group Databasebeta

← Group #504236

Character table — Group #504236

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488881616161616161616161616161616161644444488881616161616161616222244444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ9111111111-1-1-1-111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1111111-1-11111-1-1-1-111-1-1-1-111-1-11-1
χ10111111111-1-1-1-111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111-11
χ11111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-11
χ12111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-11-1
χ13111111111-1-1-1-111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-111-1-111-1-1-11
χ14111111111-1-1-1-111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1111-1
χ15111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1111111-1-1-1-1-1-111-1-1-1-1111-1
χ16111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-11
χ172222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000220000-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-2-20000222200000000000000000000
χ19222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000002-20000-2-22200000000000000000000
χ20222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-22000022-2-200000000000000000000
χ2122222222-22222-2-2-200000000-2-2222200002222−2−2−2−22222−2−2−2−2-2-20000000022−2−222−2−2000000000000
χ2222222222-22222-2-2-200000000-2-222220000−2−2−2−22222−2−2−2−22222-2-200000000−2−222−2−222000000000000
χ2322222222-22222-2-2-200000000-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−22200000000−2−222−2−222000000000000
χ2422222222-22222-2-2-200000000-2-2-2-2-2-20000−2−2−2−22222−2−2−2−22222220000000022−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-200002222−2−2−2−2−2−2−2−22222-220000000022−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-20000−2−2−2−222222222−2−2−2−2-2200000000−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-22200002222−2−2−2−2−2−2−2−222222-200000000−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-2220000−2−2−2−222222222−2−2−2−22-20000000022−2−2−2−222000000000000
χ29222-2-2-22-2200002-2-222-2-2-2-22200000000002i2i−2i−2i2i2i−2i−2i00000000002i2i−2i−2i0000000000000000002-20000
χ30222-2-2-22-2200002-2-222-2-2-2-22200000000002i2i−2i−2i2i2i−2i−2i0000000000−2i−2i2i2i000000000000000000-220000
χ31222-2-2-22-2200002-2-222-2-2-2-2220000000000−2i−2i2i2i−2i−2i2i2i00000000002i2i−2i−2i000000000000000000-220000
χ32222-2-2-22-2200002-2-222-2-2-2-2220000000000−2i−2i2i2i−2i−2i2i2i0000000000−2i−2i2i2i0000000000000000002-20000
χ332-2222-2-2-2-222-2-222-22222-2-2-2-22-2000022-2-200000000000000000000000000000000002-22-200000000
χ342-2222-2-2-2-222-2-222-22222-2-2-2-22-2000022-2-20000000000000000000000000000000000-22-2200000000
χ352-2222-2-2-2-222-2-222-2-2-2-2-222222-20000-2-2220000000000000000002i−2i2i−2i00000000000000002i−2i000000
χ362-2222-2-2-2-222-2-222-2-2-2-2-222222-20000-2-222000000000000000000−2i2i−2i2i0000000000000000−2i2i000000
χ372-2222-2-2-2-2-2-22222-22222-2-2-2-2-220000-2-22200000000000000000000000000000000002-2-2200000000
χ382-2222-2-2-2-2-2-22222-22222-2-2-2-2-220000-2-2220000000000000000000000000000000000-222-200000000
χ392-2222-2-2-2-2-2-22222-2-2-2-2-22222-22000022-2-20000000000000000002i−2i2i−2i0000000000000000−2i2i000000
χ402-2222-2-2-2-2-2-22222-2-2-2-2-22222-22000022-2-2000000000000000000−2i2i−2i2i00000000000000002i−2i000000
χ412-22-2-22-22-200002-22-2-222-2-22200000000000000000022-2-222-2-2002-2-22000000000000000000002-200
χ422-22-2-22-22-200002-22-2-222-2-22200000000000000000022-2-222-2-200-222-200000000000000000000-2200
χ432-22-2-22-22-200002-22-2-222-2-222000000000000000000-2-222-2-222002-2-2200000000000000000000-2200
χ442-22-2-22-22-200002-22-2-222-2-222000000000000000000-2-222-2-22200-222-2000000000000000000002-200
χ452-2-22-2-22202-22-20002−22−22−22−2002-22-22−22−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ462-2-22-2-22202-22-20002−22−22−22−2002-22-22−22−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ472-2-22-2-22202-22-20002−22−22−22−200-22-222−22−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000000−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ482-2-22-2-22202-22-20002−22−22−22−200-22-222−22−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000000−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ492-2-22-2-22202-22-2000−22−22−22−22002-22-2−22−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000000−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ502-2-22-2-22202-22-2000−22−22−22−22002-22-2−22−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000000−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ512-2-22-2-22202-22-2000−22−22−22−2200-22-22−22−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ522-2-22-2-22202-22-2000−22−22−22−2200-22-22−22−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ532-2-22-2-2220-22-220002−22−22−22−2002-2-22−22−22ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ542-2-22-2-2220-22-220002−22−22−22−2002-2-22−22−22−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ552-2-22-2-2220-22-220002−22−22−22−200-222-2−22−22ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000000−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ562-2-22-2-2220-22-220002−22−22−22−200-222-2−22−22−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000000−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ572-2-22-2-2220-22-22000−22−22−22−22002-2-222−22−2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000000−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ582-2-22-2-2220-22-22000−22−22−22−22002-2-222−22−2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000000−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ592-2-22-2-2220-22-22000−22−22−22−2200-222-22−22−2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000002−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ602-2-22-2-2220-22-22000−22−22−22−2200-222-22−22−2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000002−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ61444-4-4-44-4400004-4-4-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-40000-4440000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ63444-4-4-44-4-40000-444000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6444-44-44-4-404-4-4400022−2222−22−2222−222200000022−22−22220000000000000000000000000000000000000000000000
χ6544-44-44-4-404-4-44000−2222−222222−2222−22000000−222222−220000000000000000000000000000000000000000000000
χ6644-44-44-4-40-444-400022−2222−22−2222−2222000000−222222−220000000000000000000000000000000000000000000000
χ6744-44-44-4-40-444-4000−2222−222222−2222−2200000022−22−22220000000000000000000000000000000000000000000000
χ6844-4-44-4-440000000022−22−222222−22−22220000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ6944-4-44-4-440000000022−22−222222−22−2222000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ7044-4-44-4-4400000000−222222−22−222222−220000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ7144-4-44-4-4400000000−222222−22−222222−22000000000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ724-4444-4-4-4444-4-4-4-4400000000-44000000000000000000000000000000000000000000000000000000
χ734-4444-4-4-44-4-444-4-44000000004-4000000000000000000000000000000000000000000000000000000
χ744-44-4-44-4440000-44-4000000000000000000000000002222−22−22−22−222222000000000000000000000000000000
χ754-44-4-44-4440000-44-400000000000000000000000000−22−2222222222−22−22000000000000000000000000000000
χ764-44-4-44-44-400004-4444-4-444-4-400000000000000000000000000000000000000000000000000000000
χ774-4-4-4444-40000000022−22−2222−222222−2200000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000
χ784-4-4-4444-40000000022−22−2222−222222−220000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000
χ794-4-4-4444-400000000−222222−2222−22−222200000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000
χ804-4-4-4444-400000000−222222−2222−22−22220000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000

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