Finite Group Databasebeta

← Group #324421

Character table — Group #324421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444444444444488888888444444888888888888224444448888888888888888888888884444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ1011111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ1111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11
χ1211111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ17222222222222222222-2-2-2-22200000000-2-2-2-2-2-20000000000002222-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-22200000000-2-2-2-2-2-2000000000000-2-2-2-222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-222222222-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222000000000000000000000000000000000000
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
χ2322222222-2-2-2-22222-2-22222-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-2220000000022-2-22200000000000022-2-2-2-2220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-2220000000022-2-222000000000000-2-22222-2-20000000000000000000000000000
χ2922-2-22-22-200002i2i−2i−2i002-22-2002222-2-2-2-22i−2i000000002i2i−2i−2i00000000000000000000i2i2−i2−i222−2−2i2i2−i2−i222−2−20000
χ3022-2-22-22-200002i2i−2i−2i002-22-2002222-2-2-2-22i−2i000000002i2i−2i−2i00000000000000000000−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000
χ3122-2-22-22-200002i2i−2i−2i002-22-200-2-2-2-222222i−2i00000000−2i−2i2i2i00000000000000000000i2i2−i2−i222−2−2−i2−i2i2i2−2−2220000
χ3222-2-22-22-200002i2i−2i−2i002-22-200-2-2-2-222222i−2i00000000−2i−2i2i2i00000000000000000000−i2−i2i2i2−2−222i2i2−i2−i222−2−20000
χ3322-2-22-22-20000−2i−2i2i2i002-22-2002222-2-2-2-2−2i2i00000000−2i−2i2i2i00000000000000000000i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000
χ3422-2-22-22-20000−2i−2i2i2i002-22-2002222-2-2-2-2−2i2i00000000−2i−2i2i2i00000000000000000000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000
χ3522-2-22-22-20000−2i−2i2i2i002-22-200-2-2-2-22222−2i2i000000002i2i−2i−2i00000000000000000000i2i2−i2−i2−2−222−i2−i2i2i222−2−20000
χ3622-2-22-22-20000−2i−2i2i2i002-22-200-2-2-2-22222−2i2i000000002i2i−2i−2i00000000000000000000−i2−i2i2i222−2−2i2i2−i2−i2−2−2220000
χ372-22-22-2-222i2i−2i−2i2i−2i2i−2i2-200002-2i2i2−i2−i2i2i2−i2−i200000022−2−22−22−2i2i2−i2−i200002i−2i2-22−22−2i2−i2i2−i200000000000000000000
χ382-22-22-2-222i2i−2i−2i2i−2i2i−2i2-200002-2i2i2−i2−i2i2i2−i2−i200000022−2−22−22−2i2i2−i2−i20000−2i2i-22−22−22−i2i2−i2i200000000000000000000
χ392-22-22-2-222i2i−2i−2i2i−2i2i−2i2-200002-2−i2−i2i2i2−i2−i2i2i2000000−2−222−22−22−i2−i2i2i200002i−2i2-2−22−22−i2i2−i2i200000000000000000000
χ402-22-22-2-222i2i−2i−2i2i−2i2i−2i2-200002-2−i2−i2i2i2−i2−i2i2i2000000−2−222−22−22−i2−i2i2i20000−2i2i-222−22−2i2−i2i2−i200000000000000000000
χ412-22-22-2-222i2i−2i−2i−2i2i−2i2i-220000-22i2i2−i2−i2i2i2−i2−i200000022−2−2−22−22−i2−i2i2i22-22i−2i0000i2−i2−i2i2−222−200000000000000000000
χ422-22-22-2-222i2i−2i−2i−2i2i−2i2i-220000-22i2i2−i2−i2i2i2−i2−i200000022−2−2−22−22−i2−i2i2i2-22−2i2i0000−i2i2i2−i22−2−2200000000000000000000
χ432-22-22-2-222i2i−2i−2i−2i2i−2i2i-220000-22−i2−i2i2i2−i2−i2i2i2000000−2−2222−22−2i2i2−i2−i22-22i−2i0000−i2i2i2−i22−2−2200000000000000000000
χ442-22-22-2-222i2i−2i−2i−2i2i−2i2i-220000-22−i2−i2i2i2−i2−i2i2i2000000−2−2222−22−2i2i2−i2−i2-22−2i2i0000i2−i2−i2i2−222−200000000000000000000
χ452-22-22-2-22−2i−2i2i2i2i−2i2i−2i-220000-22i2i2−i2−i2i2i2−i2−i2000000−2−2222−22−2−i2−i2i2i22-2−2i2i0000i2−i2−i2i22−2−2200000000000000000000
χ462-22-22-2-22−2i−2i2i2i2i−2i2i−2i-220000-22i2i2−i2−i2i2i2−i2−i2000000−2−2222−22−2−i2−i2i2i2-222i−2i0000−i2i2i2−i2−222−200000000000000000000
χ472-22-22-2-22−2i−2i2i2i2i−2i2i−2i-220000-22−i2−i2i2i2−i2−i2i2i200000022−2−2−22−22i2i2−i2−i22-2−2i2i0000−i2i2i2−i2−222−200000000000000000000
χ482-22-22-2-22−2i−2i2i2i2i−2i2i−2i-220000-22−i2−i2i2i2−i2−i2i2i200000022−2−2−22−22i2i2−i2−i2-222i−2i0000i2−i2−i2i22−2−2200000000000000000000
χ492-22-22-2-22−2i−2i2i2i−2i2i−2i2i2-200002-2i2i2−i2−i2i2i2−i2−i2000000−2−222−22−22i2i2−i2−i200002i−2i-222−22−2−i2i2−i2i200000000000000000000
χ502-22-22-2-22−2i−2i2i2i−2i2i−2i2i2-200002-2i2i2−i2−i2i2i2−i2−i2000000−2−222−22−22i2i2−i2−i20000−2i2i2-2−22−22i2−i2i2−i200000000000000000000
χ512-22-22-2-22−2i−2i2i2i−2i2i−2i2i2-200002-2−i2−i2i2i2−i2−i2i2i200000022−2−22−22−2−i2−i2i2i200002i−2i-22−22−22i2−i2i2−i200000000000000000000
χ522-22-22-2-22−2i−2i2i2i−2i2i−2i2i2-200002-2−i2−i2i2i2−i2−i2i2i200000022−2−22−22−2−i2−i2i2i20000−2i2i2-22−22−2−i2i2−i2i200000000000000000000
χ532-22-2-222-22i−2i2i−2i0000002-2-22002i−2i2i−2i2i−2i2i−2i00002i−2i2-22-20000000000000000000000002−22−2i2−i2i2−i2i2−i2i2−i22−22−20000
χ542-22-2-222-22i−2i2i−2i0000002-2-22002i−2i2i−2i2i−2i2i−2i00002i−2i2-22-2000000000000000000000000−22−22−i2i2−i2i2−i2i2−i2i2−22−220000
χ552-22-2-222-22i−2i2i−2i0000002-2-2200−2i2i−2i2i−2i2i−2i2i00002i−2i-22-220000000000000000000000002−22−2i2−i2i2−i2−i2i2−i2i2−22−220000
χ562-22-2-222-22i−2i2i−2i0000002-2-2200−2i2i−2i2i−2i2i−2i2i00002i−2i-22-22000000000000000000000000−22−22−i2i2−i2i2i2−i2i2−i22−22−20000
χ572-22-2-222-2−2i2i−2i2i0000002-2-22002i−2i2i−2i2i−2i2i−2i0000−2i2i-22-220000000000000000000000002−22−2−i2i2−i2i2i2−i2i2−i2−22−220000
χ582-22-2-222-2−2i2i−2i2i0000002-2-22002i−2i2i−2i2i−2i2i−2i0000−2i2i-22-22000000000000000000000000−22−22i2−i2i2−i2−i2i2−i2i22−22−20000
χ592-22-2-222-2−2i2i−2i2i0000002-2-2200−2i2i−2i2i−2i2i−2i2i0000−2i2i2-22-20000000000000000000000002−22−2−i2i2−i2i2−i2i2−i2i22−22−20000
χ602-22-2-222-2−2i2i−2i2i0000002-2-2200−2i2i−2i2i−2i2i−2i2i0000−2i2i2-22-2000000000000000000000000−22−22i2−i2i2−i2i2−i2i2−i2−22−220000
χ612-2-22-2-222000000002-222-2-2-222i−2i2i−2i−2i2i−2i2i002-200000000002i−2i2i−2i00000000000000002i−2i−2i2i0000-222-200000000
χ622-2-22-2-222000000002-222-2-2-222i−2i2i−2i−2i2i−2i2i002-200000000002i−2i2i−2i0000000000000000−2i2i2i−2i00002-2-2200000000
χ632-2-22-2-222000000002-222-2-2-22−2i2i−2i2i2i−2i2i−2i002-20000000000−2i2i−2i2i00000000000000002i−2i−2i2i00002-2-2200000000
χ642-2-22-2-222000000002-222-2-2-22−2i2i−2i2i2i−2i2i−2i002-20000000000−2i2i−2i2i0000000000000000−2i2i2i−2i0000-222-200000000
χ652-2-22-2-22200000000-2222-2-22-22i−2i2i−2i−2i2i−2i2i00-220000000000−2i2i−2i2i000000000000000000002i−2i−2i2i00002-2-220000
χ662-2-22-2-22200000000-2222-2-22-22i−2i2i−2i−2i2i−2i2i00-220000000000−2i2i−2i2i00000000000000000000−2i2i2i−2i0000-222-20000
χ672-2-22-2-22200000000-2222-2-22-2−2i2i−2i2i2i−2i2i−2i00-2200000000002i−2i2i−2i000000000000000000002i−2i−2i2i0000-222-20000
χ682-2-22-2-22200000000-2222-2-22-2−2i2i−2i2i2i−2i2i−2i00-2200000000002i−2i2i−2i00000000000000000000−2i2i2i−2i00002-2-220000
χ694444-4-4-4-44-4-4400000000000022−22−222222−22−222200000022−22−222200000000000000000000000000000000000000000000
χ704444-4-4-4-44-4-44000000000000−222222−22−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ714444-4-4-4-4-444-400000000000022−22−222222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ724444-4-4-4-4-444-4000000000000−222222−22−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ7344-4-44-44-400004i4i−4i−4i00-44-440000000000−4i4i0000000000000000000000000000000000000000000000000000
χ7444-4-44-44-40000−4i−4i4i4i00-44-4400000000004i−4i0000000000000000000000000000000000000000000000000000
χ7544-4-4-44-4400000000440000-4-422−22−2222−222222−220000000000000022−22−2222000000000000000000000000000000000000
χ7644-4-4-44-4400000000440000-4-4−222222−2222−22−222200000000000000−222222−22000000000000000000000000000000000000
χ7744-4-4-44-4400000000-4-400004422−22−2222−222222−2200000000000000−222222−22000000000000000000000000000000000000
χ7844-4-4-44-4400000000-4-4000044−222222−2222−22−22220000000000000022−22−2222000000000000000000000000000000000000
χ794-44-4-444-44i−4i4i−4i000000-444-400000000000000−4i4i000000000000000000000000000000000000000000000000
χ804-44-4-444-4−4i4i−4i4i000000-444-4000000000000004i−4i000000000000000000000000000000000000000000000000
χ814-4-4444-4-400004-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ824-4-4444-4-400004-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ834-4-4444-4-40000-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ844-4-4444-4-40000-444-400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ854-4-44-4-444000000004-4-4-444-440000000000-4400000000000000000000000000000000000000000000000000
χ864-4-44-4-44400000000-44-4-4444-400000000004-400000000000000000000000000000000000000000000000000

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