Finite Group Databasebeta

← Group #7516019

Character table — Group #7516019

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111111122222222222244444444444444444444444444444444448888888888888888888888888881616161616161616
order12222222444444444444222222444444444444888888888888888822244444444444444448888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-1-11111-1-11-11111-1-111-1-111-1-1-1-1-11-1-11-1
χ611111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1111111-1-111-1-111-11-1-1-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-111-1-1111-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1111-111111-1
χ91111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-111111111-1-1-1-11111-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-1
χ101111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-111-11-111
χ111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1111
χ121111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111111-1-11-11-1-1
χ131111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1111-1-1-1-11111-1-11111-11-11-11
χ141111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1111-1-111-1-1-1-111-1-11-1-1-1-111-1
χ151111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-11-1-111111111-1-111-1-11-11-11-1
χ161111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111111-1-1-1-11111-1-1-11-1-111-1-1-1-1-1-111-1-1-11111-1-11
χ17111111111-1-1-1-11111111-1-111-1-111-1-1111111-1-1111111111111-1-1-1-1-1111-111-1-111-11-1-111-1-1-1-111-1-1-1-11-1-1-11-1-11
χ18111111111-1-1-1-11111111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-11-1-1111111-1-1111111-111-11-1
χ19111111111-1-1-1-11111111-1-111-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-1-1-111-1-1-1111-1-111-1-111-1-1-1-1-1111-111-1
χ20111111111-1-1-1-11111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1111111-1111-1-1-1-111-1-11111-1-11-1-11-11
χ21111111111-1-1-1-11111111-1-111-1-1-1-111-1-11111111111-1-1-1-111111111111-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-11-1-1
χ22111111111-1-1-1-11111111-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1111
χ23111111111-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111111-1-1-11-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111-1-111-111
χ24111111111-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-111111-1-1-1-111-1-111111111-1-111-1-11-1-1-1
χ25111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-11-11111111-1-1-1-1-1-1-1-1-1-1-11111-11-1-1111-1
χ26111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-11-1-1-1-1-1111111-1-1-1-1-1-1-1111-11
χ27111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1111111-1-1-1-111111-111-1-1-11
χ28111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-111-1-1111-11111-1-11111-1-1-1-1111-1-1-11-1
χ29111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-11-11-1-1-111
χ30111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ31111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11-1-1-1-111111111-1-1-1-11111-1-1-11-1111-1-1
χ32111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ3322222222-222222222-2-2-2-2-2-2-2222222220000220000000000000000-200-2-2000000-2-20000000000000000000000
χ3422222222-222222222-2-2-2-2-2-2-222-2-2-2-2-2-20000-2-2000000000000000020022000000-220000000000000000000000
χ3522222222-22222-2-2-2-2-2-2-2-2-222-2-22222-2-20000-2-20000000000000000200-2-2000000220000000000000000000000
χ3622222222-22222-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2220000220000000000000000-200220000002-20000000000000000000000
χ3722222222-2-2-2-2-22222-2-2-222-2-2-2-222-2-2220000-2-20000000000000000200-220000002-20000000000000000000000
χ3822222222-2-2-2-2-22222-2-2-222-2-2-2-2-2-222-2-20000220000000000000000-2002-2000000220000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000220000000000000000-200-22000000-220000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222220000-2-200000000000000002002-2000000-2-20000000000000000000000
χ412-222-22-2-202i2i−2i−2i2i2i−2i−2i00000002-22i−2i2-22-200002i−2ii2i2−i2−i222−2−222−2−2i2i2−i2−i200000000000000000002−2i2−i2i2−i22−200000000
χ422-222-22-2-202i2i−2i−2i2i2i−2i−2i00000002-22i−2i2-22-200002i−2i−i2−i2i2i2−2−222−2−222−i2−i2i2i20000000000000000000−22−i2i2−i2i2−2200000000
χ432-222-22-2-202i2i−2i−2i2i2i−2i−2i00000002-2−2i2i-22-220000−2i2ii2i2−i2−i2−2−22222−2−2−i2−i2i2i200000000000000000002−2−i2i2i2−i2−2200000000
χ442-222-22-2-202i2i−2i−2i2i2i−2i−2i00000002-2−2i2i-22-220000−2i2i−i2−i2i2i222−2−2−2−222i2i2−i2−i20000000000000000000−22i2−i2−i2i22−200000000
χ452-222-22-2-202i2i−2i−2i−2i−2i2i2i0000000-222i−2i2-2-220000−2i2ii2i2−i2−i222−2−2−2−222i2i2−i2−i200000000000000000002−2−i2i2−i2i2−2200000000
χ462-222-22-2-202i2i−2i−2i−2i−2i2i2i0000000-222i−2i2-2-220000−2i2i−i2−i2i2i2−2−22222−2−2−i2−i2i2i20000000000000000000−22i2−i2i2−i22−200000000
χ472-222-22-2-202i2i−2i−2i−2i−2i2i2i0000000-22−2i2i-222-200002i−2ii2i2−i2−i2−2−222−2−222−i2−i2i2i200000000000000000002−2i2−i2−i2i22−200000000
χ482-222-22-2-202i2i−2i−2i−2i−2i2i2i0000000-22−2i2i-222-200002i−2i−i2−i2i2i222−2−222−2−2i2i2−i2−i20000000000000000000−22−i2i2i2−i2−2200000000
χ492-222-22-2-20−2i−2i2i2i2i2i−2i−2i0000000-222i−2i-222-20000−2i2ii2i2−i2−i222−2−222−2−2−i2−i2i2i20000000000000000000−22i2−i2−i2i2−2200000000
χ502-222-22-2-20−2i−2i2i2i2i2i−2i−2i0000000-222i−2i-222-20000−2i2i−i2−i2i2i2−2−222−2−222i2i2−i2−i200000000000000000002−2−i2i2i2−i22−200000000
χ512-222-22-2-20−2i−2i2i2i2i2i−2i−2i0000000-22−2i2i2-2-2200002i−2ii2i2−i2−i2−2−22222−2−2i2i2−i2−i20000000000000000000−22−i2i2−i2i22−200000000
χ522-222-22-2-20−2i−2i2i2i2i2i−2i−2i0000000-22−2i2i2-2-2200002i−2i−i2−i2i2i222−2−2−2−222−i2−i2i2i200000000000000000002−2i2−i2i2−i2−2200000000
χ532-222-22-2-20−2i−2i2i2i−2i−2i2i2i00000002-22i−2i-22-2200002i−2ii2i2−i2−i222−2−2−2−222−i2−i2i2i20000000000000000000−22−i2i2i2−i22−200000000
χ542-222-22-2-20−2i−2i2i2i−2i−2i2i2i00000002-22i−2i-22-2200002i−2i−i2−i2i2i2−2−22222−2−2i2i2−i2−i200000000000000000002−2i2−i2−i2i2−2200000000
χ552-222-22-2-20−2i−2i2i2i−2i−2i2i2i00000002-2−2i2i2-22-20000−2i2ii2i2−i2−i2−2−222−2−222i2i2−i2−i20000000000000000000−22i2−i2i2−i2−2200000000
χ562-222-22-2-20−2i−2i2i2i−2i−2i2i2i00000002-2−2i2i2-22-20000−2i2i−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000000000000002−2−i2i2−i2i22−200000000
χ572-22-22-22-2200002-22-22-2-2002-2000000002i2i−2i−2i002i−2i2i−2i00002i−2i2i−2i000002-2002-2000000002i−2i000000000000000000
χ582-22-22-22-2200002-22-22-2-2002-2000000002i2i−2i−2i00−2i2i−2i2i0000−2i2i−2i2i00000-2200-22000000002i−2i000000000000000000
χ592-22-22-22-2200002-22-22-2-2002-200000000−2i−2i2i2i002i−2i2i−2i00002i−2i2i−2i00000-2200-2200000000−2i2i000000000000000000
χ602-22-22-22-2200002-22-22-2-2002-200000000−2i−2i2i2i00−2i2i−2i2i0000−2i2i−2i2i000002-2002-200000000−2i2i000000000000000000
χ612-22-22-22-220000-22-222-2-200-22000000002i2i−2i−2i002i−2i2i−2i0000−2i2i−2i2i00000-22002-200000000−2i2i000000000000000000
χ622-22-22-22-220000-22-222-2-200-22000000002i2i−2i−2i00−2i2i−2i2i00002i−2i2i−2i000002-200-2200000000−2i2i000000000000000000
χ632-22-22-22-220000-22-222-2-200-2200000000−2i−2i2i2i002i−2i2i−2i0000−2i2i−2i2i000002-200-22000000002i−2i000000000000000000
χ642-22-22-22-220000-22-222-2-200-2200000000−2i−2i2i2i00−2i2i−2i2i00002i−2i2i−2i00000-22002-2000000002i−2i000000000000000000
χ652-2-2-2-2222-22-22-200002-222-200000000002-22-20000002-22-200002-22-20000000002-2002-2002-20000000000000000
χ662-2-2-2-2222-22-22-200002-222-200000000002-22-2000000-22-220000-22-22000000000-22002-200-220000000000000000
χ672-2-2-2-2222-22-22-200002-222-20000000000-22-220000002-22-200002-22-2000000000-2200-2200-220000000000000000
χ682-2-2-2-2222-22-22-200002-222-20000000000-22-22000000-22-220000-22-220000000002-200-22002-20000000000000000
χ692-2-2-2-2222-2-22-2200002-22-2200000000002-22-20000002-22-20000-22-220000000002-200-2200-220000000000000000
χ702-2-2-2-2222-2-22-2200002-22-2200000000002-22-2000000-22-2200002-22-2000000000-2200-22002-20000000000000000
χ712-2-2-2-2222-2-22-2200002-22-220000000000-22-220000002-22-20000-22-22000000000-22002-2002-20000000000000000
χ722-2-2-2-2222-2-22-2200002-22-220000000000-22-22000000-22-2200002-22-20000000002-2002-200-220000000000000000
χ73444-4-4-4-44000004i−4i−4i4i00000000000000000000022−22−22220000−2i22i22i2−2i2000000000000000000000000000000000000000
χ74444-4-4-4-44000004i−4i−4i4i000000000000000000000−222222−2200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ75444-4-4-4-4400000−4i4i4i−4i00000000000000000000022−22−222200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ76444-4-4-4-4400000−4i4i4i−4i000000000000000000000−222222−220000−2i22i22i2−2i2000000000000000000000000000000000000000
χ7744-44-4-44-4400000000-4-44000000000000000000000000000000000000000004i−4i00000000000000000000000000
χ7844-44-4-44-4400000000-4-4400000000000000000000000000000000000000000−4i4i00000000000000000000000000
χ7944-44-4-44-4-40000000044-40000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ8044-44-4-44-4-40000000044-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ8144-4-444-4-404i−4i−4i4i0000000000000000000000000000022−22−222200002i2−2i2−2i22i200000000000000000000000000000000000
χ8244-4-444-4-404i−4i−4i4i00000000000000000000000000000−222222−220000−2i22i22i2−2i200000000000000000000000000000000000
χ8344-4-444-4-40−4i4i4i−4i0000000000000000000000000000022−22−22220000−2i22i22i2−2i200000000000000000000000000000000000
χ8444-4-444-4-40−4i4i4i−4i00000000000000000000000000000−222222−2200002i2−2i2−2i22i200000000000000000000000000000000000
χ854-44-44-44-4-400004-44-4-44400-4400000000000000000000000000000000000000000000000000000000000000000
χ864-44-44-44-4-40000-44-44-444004-400000000000000000000000000000000000000000000000000000000000000000
χ874-4-4-4-444444-44-40000-44-4-440000000000000000000000000000000000000000000000000000000000000000000
χ884-4-4-4-44444-44-440000-44-44-40000000000000000000000000000000000000000000000000000000000000000000
χ898-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000

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