Finite Group Databasebeta

← Group #318005

Character table — Group #318005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444448888888888888888448888888888888888222222224444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-11-1-11
χ172222222222-2-22-22-20000000022222222-2-20000-2-2-2-200000000000022220000-2-2-2-200000000000000000000
χ182222222222-2-22-22-20000000022222222-2-20000-2-2-2-2000000000000-2-2-2-20000222200000000000000000000
χ192222222222-2-22-22-200000000-2-2-2-2-2-2-2-2-2-20000222200000000000022-2-20000-2-22200000000000000000000
χ202222222222-2-22-22-200000000-2-2-2-2-2-2-2-2-2-200002222000000000000-2-222000022-2-200000000000000000000
χ2122222222-2-222-22-222222222200000000-2-2-2-2-2-200000000000022-2-20000-2-222000000000000000000000000
χ2222222222-2-222-22-222222222200000000-2-2-2-2-2-2000000000000-2-222000022-2-2000000000000000000000000
χ2322222222-2-222-22-22-2-2-2-2-2-2-2-200000000-2-2222200000000000022220000-2-2-2-2000000000000000000000000
χ2422222222-2-222-22-22-2-2-2-2-2-2-2-200000000-2-22222000000000000-2-2-2-200002222000000000000000000000000
χ25222-22-2-2-22-200-20202222−2−2−2−22222-2-2-2-20022−2−200002222−2−2−2−20000000000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000
χ26222-22-2-2-22-200-20202222−2−2−2−22222-2-2-2-20022−2−200002222−2−2−2−2000000000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000
χ27222-22-2-2-22-200-20202222−2−2−2−2-2-2-2-222220022−2−20000−2−2−2−222220000000000002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i20000
χ28222-22-2-2-22-200-20202222−2−2−2−2-2-2-2-222220022−2−20000−2−2−2−22222000000000000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i20000
χ29222-22-2-2-22-200-2020−2−2−2−222222222-2-2-2-200−2−2220000−2−2−2−222220000000000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i20000
χ30222-22-2-2-22-200-2020−2−2−2−222222222-2-2-2-200−2−2220000−2−2−2−22222000000000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i20000
χ31222-22-2-2-22-200-2020−2−2−2−22222-2-2-2-2222200−2−22200002222−2−2−2−20000000000002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i20000
χ32222-22-2-2-22-200-2020−2−2−2−22222-2-2-2-2222200−2−22200002222−2−2−2−2000000000000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i20000
χ3322-2-2-222-2002-2020-22i2i−2i−2i2i2i−2i−2i22−2−222−2−200000022−2−2i2i2−i2−i2i2i2−i2−i2002-200002i−2i000000i2i2−i2−i222−2−2000000000000
χ3422-2-2-222-2002-2020-22i2i−2i−2i2i2i−2i−2i22−2−222−2−200000022−2−2i2i2−i2−i2i2i2−i2−i200-220000−2i2i000000−i2−i2i2i2−2−222000000000000
χ3522-2-2-222-2002-2020-22i2i−2i−2i2i2i−2i−2i−2−222−2−222000000−2−222−i2−i2i2i2−i2−i2i2i2002-200002i−2i000000−i2−i2i2i2−2−222000000000000
χ3622-2-2-222-2002-2020-22i2i−2i−2i2i2i−2i−2i−2−222−2−222000000−2−222−i2−i2i2i2−i2−i2i2i200-220000−2i2i000000i2i2−i2−i222−2−2000000000000
χ3722-2-2-222-2002-2020-2−2i−2i2i2i−2i−2i2i2i22−2−222−2−200000022−2−2−i2−i2i2i2−i2−i2i2i2002-20000−2i2i000000−i2−i2i2i222−2−2000000000000
χ3822-2-2-222-2002-2020-2−2i−2i2i2i−2i−2i2i2i22−2−222−2−200000022−2−2−i2−i2i2i2−i2−i2i2i200-2200002i−2i000000i2i2−i2−i2−2−222000000000000
χ3922-2-2-222-2002-2020-2−2i−2i2i2i−2i−2i2i2i−2−222−2−222000000−2−222i2i2−i2−i2i2i2−i2−i2002-20000−2i2i000000i2i2−i2−i2−2−222000000000000
χ4022-2-2-222-2002-2020-2−2i−2i2i2i−2i−2i2i2i−2−222−2−222000000−2−222i2i2−i2−i2i2i2−i2−i200-2200002i−2i000000−i2−i2i2i222−2−2000000000000
χ412-22-2-22-2200-22020-22i−2i2i−2i2i−2i2i−2i2−22−22−22−20000002−22−2i2−i2i2−i2i2−i2i2−i22-2000000002i−2i00002−22−2i2−i2i2−i2000000000000
χ422-22-2-22-2200-22020-22i−2i2i−2i2i−2i2i−2i2−22−22−22−20000002−22−2i2−i2i2−i2i2−i2i2−i2-2200000000−2i2i0000−22−22−i2i2−i2i2000000000000
χ432-22-2-22-2200-22020-22i−2i2i−2i2i−2i2i−2i−22−22−22−22000000−22−22−i2i2−i2i2−i2i2−i2i22-2000000002i−2i0000−22−22−i2i2−i2i2000000000000
χ442-22-2-22-2200-22020-22i−2i2i−2i2i−2i2i−2i−22−22−22−22000000−22−22−i2i2−i2i2−i2i2−i2i2-2200000000−2i2i00002−22−2i2−i2i2−i2000000000000
χ452-22-2-22-2200-22020-2−2i2i−2i2i−2i2i−2i2i2−22−22−22−20000002−22−2−i2i2−i2i2−i2i2−i2i22-200000000−2i2i00002−22−2−i2i2−i2i2000000000000
χ462-22-2-22-2200-22020-2−2i2i−2i2i−2i2i−2i2i2−22−22−22−20000002−22−2−i2i2−i2i2−i2i2−i2i2-22000000002i−2i0000−22−22i2−i2i2−i2000000000000
χ472-22-2-22-2200-22020-2−2i2i−2i2i−2i2i−2i2i−22−22−22−22000000−22−22i2−i2i2−i2i2−i2i2−i22-200000000−2i2i0000−22−22i2−i2i2−i2000000000000
χ482-22-2-22-2200-22020-2−2i2i−2i2i−2i2i−2i2i−22−22−22−22000000−22−22i2−i2i2−i2i2−i2i2−i2-22000000002i−2i00002−22−2−i2i2−i2i2000000000000
χ492-2-2222-2-222-2-2-22-222-2-222-2-22000000002-22-22-200000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ502-2-2222-2-222-2-2-22-222-2-222-2-22000000002-22-22-20000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ512-2-2222-2-222-2-2-22-22-222-2-222-2000000002-2-22-2200000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ522-2-2222-2-222-2-2-22-22-222-2-222-2000000002-2-22-220000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ532-2-2222-2-2-2-2222-22-2000000002-2-222-2-222-20000-222-2000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000
χ542-2-2222-2-2-2-2222-22-2000000002-2-222-2-222-20000-222-200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000
χ552-2-2222-2-2-2-2222-22-200000000-222-2-222-22-200002-2-22000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000
χ562-2-2222-2-2-2-2222-22-200000000-222-2-222-22-200002-2-2200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000
χ572-2-2222-2-2-2-2-2-222222-2-222-2-222-2-222-2-22-22-22-222-2-222-2-222-2-22000000000000000000000000000000000000
χ582-2-2222-2-2-2-2-2-222222-2-222-2-22-222-2-222-2-22-22-22-222-2-222-2-222-2000000000000000000000000000000000000
χ592-2-2222-2-2-2-2-2-22222-222-2-222-22-2-222-2-22-222-22-22-2-22-222-2-222-2000000000000000000000000000000000000
χ602-2-2222-2-2-2-2-2-22222-222-2-222-2-222-2-222-2-222-22-2-222-22-2-222-2-22000000000000000000000000000000000000
χ612-2-2-22-222-2200-20202−2−22−222−22-2-22-222-200−222−200002−2−22−222−200002-22-200000000000000002−2−222−2−220000
χ622-2-2-22-222-2200-20202−2−22−222−22-2-22-222-200−222−200002−2−22−222−20000-22-220000000000000000−222−2−222−20000
χ632-2-2-22-222-2200-20202−2−22−222−2-222-22-2-2200−222−20000−222−22−2−2200002-2-2200000000000000002−2−22−222−20000
χ642-2-2-22-222-2200-20202−2−22−222−2-222-22-2-2200−222−20000−222−22−2−220000-222-20000000000000000−222−22−2−220000
χ652-2-2-22-222-2200-2020−222−22−2−222-2-22-222-2002−2−220000−222−22−2−2200002-22-20000000000000000−222−2−222−20000
χ662-2-2-22-222-2200-2020−222−22−2−222-2-22-222-2002−2−220000−222−22−2−220000-22-2200000000000000002−2−222−2−220000
χ672-2-2-22-222-2200-2020−222−22−2−22-222-22-2-22002−2−2200002−2−22−222−200002-2-220000000000000000−222−22−2−220000
χ682-2-2-22-222-2200-2020−222−22−2−22-222-22-2-22002−2−2200002−2−22−222−20000-222-200000000000000002−2−22−222−20000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-440040-4022222222−22−22−22−220000000000−22−222222000000000000000000000000000000000000000000000000
χ71444-44-4-4-4-440040-40−22−22−22−222222222200000000002222−22−22000000000000000000000000000000000000000000000000
χ7244-44-4-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i22222−22−22−22−22222200000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ7344-44-4-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i2−22−2222222222−22−220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ7444-44-4-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i22222−22−22−22−2222220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ7544-44-4-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i2−22−2222222222−22−2200000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ7644-4-4-444-400-440-404000000002222−22−222222−22−22000000−22−22222200000000000000000000000000000000000000000000
χ7744-4-4-444-400-440-40400000000−22−222222−22−2222220000002222−22−2200000000000000000000000000000000000000000000
χ784-444-4-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i222−2222−22−2222−222200000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ794-444-4-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2−2222−222222−2222−220000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ804-444-4-44-400000000−2i22i2−2i22i22i2−2i22i2−2i222−2222−22−2222−22220000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ814-444-4-44-400000000−2i22i2−2i22i22i2−2i22i2−2i2−2222−222222−2222−2200000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ824-44-4-44-44004-40-4040000000022−2222−2222−2222−22000000−2222−222200000000000000000000000000000000000000000000
χ834-44-4-44-44004-40-40400000000−2222−2222−2222−222200000022−2222−2200000000000000000000000000000000000000000000
χ844-4-4444-4-44444-4-4-4-40000000000000000-440000000000000000000000000000000000000000000000000000
χ854-4-4-44-4444-40040-4022−22−2222−222222−22000000000022−22−2222000000000000000000000000000000000000000000000000
χ864-4-4-44-4444-40040-40−222222−2222−22−22220000000000−222222−22000000000000000000000000000000000000000000000000

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