Finite Group Databasebeta

← Group #278021

Character table — Group #278021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222222244444444444488888888444444888888888888224444448888888888888888888888884444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1
χ911111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11
χ172222222222222-2-2-2-2-2-2-2222-222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000000000000000
χ19222222222222-22222222-2-2-2200000000-2-2-2-2-2-20000000000002222-2-2-2-20000000000000000000000000000
χ20222222222222-22222222-2-2-2200000000-2-2-2-2-2-2000000000000-2-2-2-222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-2-2-22-2-2-22222222-222222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22-2-2-22222222-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-2-2-2-2222-2-2-2-2-2-2-2200000000-2-2222200000000000022-2-222-2-20000000000000000000000000000
χ2622222222-2-2-2-2-2222-2-2-2-2-2-2-2200000000-2-22222000000000000-2-222-2-2220000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2922-2-2-222-2000020002i2i−2i−2i-2-2202222-2-2-2-2002i−2i0000002i2i−2i−2i0000000000000000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i20000
χ3022-2-2-222-2000020002i2i−2i−2i-2-2202222-2-2-2-2002i−2i0000002i2i−2i−2i00000000000000000000−2−222−i2−i2i2i2−2−222−i2−i2i2i20000
χ3122-2-2-222-2000020002i2i−2i−2i-2-220-2-2-2-22222002i−2i000000−2i−2i2i2i0000000000000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000
χ3222-2-2-222-2000020002i2i−2i−2i-2-220-2-2-2-22222002i−2i000000−2i−2i2i2i00000000000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i20000
χ3322-2-2-222-200002000−2i−2i2i2i-2-2202222-2-2-2-200−2i2i000000−2i−2i2i2i0000000000000000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i20000
χ3422-2-2-222-200002000−2i−2i2i2i-2-2202222-2-2-2-200−2i2i000000−2i−2i2i2i00000000000000000000−2−222i2i2−i2−i2−2−222i2i2−i2−i20000
χ3522-2-2-222-200002000−2i−2i2i2i-2-220-2-2-2-2222200−2i2i0000002i2i−2i−2i0000000000000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000
χ3622-2-2-222-200002000−2i−2i2i2i-2-220-2-2-2-2222200−2i2i0000002i2i−2i−2i00000000000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i20000
χ372-222-22-2-222-2-2-200000002-22022-2-222-2-200002-20000000022-2-20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000
χ382-222-22-2-222-2-2-200000002-22022-2-222-2-200002-20000000022-2-20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000
χ392-222-22-2-222-2-2-200000002-220-2-222-2-22200002-200000000-2-2220000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000
χ402-222-22-2-222-2-2-200000002-220-2-222-2-22200002-200000000-2-2220000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000
χ412-222-22-2-2-2-222-200000002-22022-2-222-2-20000-2200000000-2-2220000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000
χ422-222-22-2-2-2-222-200000002-22022-2-222-2-20000-2200000000-2-2220000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000
χ432-222-22-2-2-2-222-200000002-220-2-222-2-2220000-220000000022-2-20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000
χ442-222-22-2-2-2-222-200000002-220-2-222-2-2220000-220000000022-2-20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000
χ452-22-2-2-2222-22-2022-22-22-2000-22−22−22−22−200000022−2−22−22−22−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000000000000000
χ462-22-2-2-2222-22-2022-22-22-2000-22−22−22−22−200000022−2−22−22−22−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000000000000000
χ472-22-2-2-2222-22-2022-22-22-2000-2−22−22−22−22000000−2−222−22−22−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000000000000000
χ482-22-2-2-2222-22-2022-22-22-2000-2−22−22−22−22000000−2−222−22−22−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000000000000000
χ492-22-2-2-2222-22-20-2-22-22-2200022−22−22−22−2000000−2−222−22−222−22−22-22-200002−2−222−2−2200000000000000000000
χ502-22-2-2-2222-22-20-2-22-22-2200022−22−22−22−2000000−2−222−22−222−22−2-22-220000−222−2−222−200000000000000000000
χ512-22-2-2-2222-22-20-2-22-22-220002−22−22−22−2200000022−2−22−22−2−22−222-22-20000−222−2−222−200000000000000000000
χ522-22-2-2-2222-22-20-2-22-22-220002−22−22−22−2200000022−2−22−22−2−22−22-22-2200002−2−222−2−2200000000000000000000
χ532-22-2-2-222-22-22022-2-22-22000-22−22−22−22−200000022−2−2−22−22−22−2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200000000000000000000
χ542-22-2-2-222-22-22022-2-22-22000-22−22−22−22−200000022−2−2−22−22−22−220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200000000000000000000
χ552-22-2-2-222-22-22022-2-22-22000-2−22−22−22−22000000−2−2222−22−22−22−200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i200000000000000000000
χ562-22-2-2-222-22-22022-2-22-22000-2−22−22−22−22000000−2−2222−22−22−22−20000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i200000000000000000000
χ572-22-2-2-222-22-220-2-222-22-200022−22−22−22−2000000−2−2222−22−2−22−222-2-220000−222−22−2−2200000000000000000000
χ582-22-2-2-222-22-220-2-222-22-200022−22−22−22−2000000−2−2222−22−2−22−22-222-200002−2−22−222−200000000000000000000
χ592-22-2-2-222-22-220-2-222-22-20002−22−22−22−2200000022−2−2−22−222−22−22-2-2200002−2−22−222−200000000000000000000
χ602-22-2-2-222-22-220-2-222-22-20002−22−22−22−2200000022−2−2−22−222−22−2-222-20000−222−22−2−2200000000000000000000
χ612-2-2-222-220000-22-220000-222-222-2-2-2-2222-200002-22-20000000000000000000000002i−2i−2i2i00002i−2i−2i2i00000000
χ622-2-2-222-220000-22-220000-222-222-2-2-2-2222-200002-22-2000000000000000000000000−2i2i2i−2i0000−2i2i2i−2i00000000
χ632-2-2-222-220000-22-220000-222-2-2-22222-2-22-20000-22-220000000000000000000000002i−2i−2i2i0000−2i2i2i−2i00000000
χ642-2-2-222-220000-22-220000-222-2-2-22222-2-22-20000-22-22000000000000000000000000−2i2i2i−2i00002i−2i−2i2i00000000
χ652-2-2-222-220000-2-22-20000-222222-2-2-2-222-220000-22-2200000000000000000000000000002-2-2200002-2-220000
χ662-2-2-222-220000-2-22-20000-222222-2-2-2-222-220000-22-220000000000000000000000000000-222-20000-222-20000
χ672-2-2-222-220000-2-22-20000-2222-2-22222-2-2-2200002-22-200000000000000000000000000002-2-220000-222-20000
χ682-2-2-222-220000-2-22-20000-2222-2-22222-2-2-2200002-22-20000000000000000000000000000-222-200002-2-220000
χ69444-44-4-4-44-4-4400000000000022−22−222222−22−22220000000000000022−22−2222000000000000000000000000000000000000
χ70444-44-4-4-44-4-44000000000000−222222−22−222222−2200000000000000−222222−22000000000000000000000000000000000000
χ71444-44-4-4-4-444-400000000000022−22−222222−22−222200000000000000−222222−22000000000000000000000000000000000000
χ72444-44-4-4-4-444-4000000000000−222222−22−222222−220000000000000022−22−2222000000000000000000000000000000000000
χ7344-44-4-4-44000004-4-40000000422−22−2222−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ7444-44-4-4-44000004-4-400000004−222222−2222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ7544-44-4-4-4400000-4440000000-422−22−2222−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ7644-44-4-4-4400000-4440000000-4−222222−2222−22−222200000022−22−222200000000000000000000000000000000000000000000
χ7744-4-4-444-40000-40004i4i−4i−4i44-400000000000−4i4i00000000000000000000000000000000000000000000000000
χ7844-4-4-444-40000-4000−4i−4i4i4i44-4000000000004i−4i00000000000000000000000000000000000000000000000000
χ794-444-44-4-444-4-440000000-44-40000000000000-44000000000000000000000000000000000000000000000000
χ804-444-44-4-4-4-44440000000-44-400000000000004-4000000000000000000000000000000000000000000000000
χ814-4-444-44-4000000004i−4i−4i4i000022−2222−22−2222−222200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ824-4-444-44-4000000004i−4i−4i4i0000−2222−222222−2222−220000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ834-4-444-44-400000000−4i4i4i−4i000022−2222−22−2222−22220000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ844-4-444-44-400000000−4i4i4i−4i0000−2222−222222−2222−2200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ854-4-4-444-44000044-4400004-4-4-400000000-440000000000000000000000000000000000000000000000000000
χ864-4-4-444-4400004-44-400004-4-44000000004-40000000000000000000000000000000000000000000000000000

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