Finite Group Databasebeta

← Group #7572279

Character table — Group #7572279

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111111122222222222244444444444444444444444444444444448888888888888888888888888881616161616161616
order12222222444444444444222244444444444444888888888888888844444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-111-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1-11111-1-1-1-1-1-11-1-11-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-11-1-1111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-1-1-111-111-111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111-1-1
χ91111111111111-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1-1-11-1-1
χ101111111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-111
χ111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-111111
χ121111111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1111111-1-111-1-1-1-1-111-1-1-1-1-1-1111-1-1-1
χ131111111111111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1111-111
χ141111111111111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-1111111-1-1-1111-1-1
χ151111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-11111111-1-1-1-1-1
χ161111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111-1-1-1111
χ17111111111-1-1-1-11111111111111-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-111-1-11-1-11-1-11-1
χ18111111111-1-1-1-11111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-11-1-11-11111-1-1111-111-11-11
χ19111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1111111-1-111-1-1-11-1-11-1-1-1-1-1-111-11-1-11-1-11
χ20111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-1-11111111-1-1-111-1111-1
χ21111111111-1-1-1-11111111-1-1-1-111-1-1-1-111-1-111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-111-1-1-111-111-11
χ22111111111-1-1-1-11111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111-1-11-11111-1-111-11-1-11-11-1
χ23111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-11-1-11-1-1-1-1-1-1111-111-111-1
χ24111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-11-1-11111111-1-11-1-11-1-1-11
χ25111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1111-1-1-111-1-1111-11-11-1-11
χ26111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1111-111-1-111-1-11-1-1-1111-1
χ27111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-11-11-1-11111-1-1-1111-1-11-1
χ28111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1111-1-1-1-111-11-11-11-11
χ29111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1111-1-1-111-1-111-11-11-111-1
χ30111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1111-111-1-111-1-1-1111-1-1-11
χ31111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11-11-11-1-11111-1-11-1-1-111-11
χ32111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-11-11-1111-1-1-1-1111-11-11-11-1
χ3322222222-222222222-2-2-20000-2-2-2-22222222222000000000000000000000000000000-2-2-2-2-20000000000000000
χ3422222222-222222222-2-2-20000-2-2-2-222-2-2-2-2-2-2-2-200000000000000000000000000000022-2220000000000000000
χ3522222222-22222-2-2-2-2-2-2-2000022-2-2-2-22222-2-2-2-2000000000000000000000000000000222-2-20000000000000000
χ3622222222-22222-2-2-2-2-2-2-2000022-2-2-2-2-2-2-2-22222000000000000000000000000000000-2-22220000000000000000
χ3722222222-2-2-2-2-22222-2-2-20000-2-222-2-222-2-222-2-2000000000000000000000000000000-222-220000000000000000
χ3822222222-2-2-2-2-22222-2-2-20000-2-222-2-2-2-222-2-2220000000000000000000000000000002-222-20000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-2000022222222-2-2-2-2220000000000000000000000000000002-2-2-220000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-22222-2-2000000000000000000000000000000-22-22-20000000000000000
χ41222-22-2-2-22000022-2-22-2-222-2-22-200000000000022-2-222-2-200000000002-22-22-2000000000000000000000000000
χ42222-22-2-2-22000022-2-22-2-222-2-22-2000000000000-2-222-2-2220000000000-222-2-22000000000000000000000000000
χ43222-22-2-2-22000022-2-22-2-2-2-2222-200000000000022-2-222-2-20000000000-22-22-22000000000000000000000000000
χ44222-22-2-2-22000022-2-22-2-2-2-2222-2000000000000-2-222-2-22200000000002-2-222-2000000000000000000000000000
χ45222-22-2-2-220000-2-2222-2-222-2-2-2200000000000022-2-2-2-22200000000002-2-22-22000000000000000000000000000
χ46222-22-2-2-220000-2-2222-2-222-2-2-22000000000000-2-22222-2-20000000000-22-222-2000000000000000000000000000
χ47222-22-2-2-220000-2-2222-2-2-2-222-2200000000000022-2-2-2-2220000000000-222-22-2000000000000000000000000000
χ48222-22-2-2-220000-2-2222-2-2-2-222-22000000000000-2-22222-2-200000000002-22-2-22000000000000000000000000000
χ4922-22-22-2-2222-2-20000-22-22-22-2002-200000000000000000022-2-222-2-22-20000002-22-200000000000000000000000
χ5022-22-22-2-2222-2-20000-22-22-22-2002-2000000000000000000-2-222-2-2222-2000000-22-2200000000000000000000000
χ5122-22-22-2-2222-2-20000-22-2-22-22002-200000000000000000022-2-222-2-2-22000000-22-2200000000000000000000000
χ5222-22-22-2-2222-2-20000-22-2-22-22002-2000000000000000000-2-222-2-222-220000002-22-200000000000000000000000
χ5322-22-22-2-22-2-2220000-22-22-22-200-2200000000000000000022-2-2-2-222-220000002-2-2200000000000000000000000
χ5422-22-22-2-22-2-2220000-22-22-22-200-22000000000000000000-2-22222-2-2-22000000-222-200000000000000000000000
χ5522-22-22-2-22-2-2220000-22-2-22-2200-2200000000000000000022-2-2-2-2222-2000000-222-200000000000000000000000
χ5622-22-22-2-22-2-2220000-22-2-22-2200-22000000000000000000-2-22222-2-22-20000002-2-2200000000000000000000000
χ572-222-2-2-2202-22-22i−2i2i−2i000000000002i−2i2i−2i2i−2i2-22-22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000002−2i2−i22−22−200000000
χ582-222-2-2-2202-22-22i−2i2i−2i000000000002i−2i2i−2i2i−2i2-22-2−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000−22−i2i2−22−2200000000
χ592-222-2-2-2202-22-22i−2i2i−2i000000000002i−2i−2i2i−2i2i-22-222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000000002−2i2−i2−22−2200000000
χ602-222-2-2-2202-22-22i−2i2i−2i000000000002i−2i−2i2i−2i2i-22-22−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000000−22−i2i22−22−200000000
χ612-222-2-2-2202-22-2−2i2i−2i2i00000000000−2i2i2i−2i2i−2i-22-222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000000002−2−i2i2−22−2200000000
χ622-222-2-2-2202-22-2−2i2i−2i2i00000000000−2i2i2i−2i2i−2i-22-22−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000000−22i2−i22−22−200000000
χ632-222-2-2-2202-22-2−2i2i−2i2i00000000000−2i2i−2i2i−2i2i2-22-22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000000002−2−i2i22−22−200000000
χ642-222-2-2-2202-22-2−2i2i−2i2i00000000000−2i2i−2i2i−2i2i2-22-2−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000−22i2−i2−22−2200000000
χ652-222-2-2-220-22-222i−2i2i−2i00000000000−2i2i2i−2i−2i2i2-2-222−22−2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000000−22−i2i22−2−2200000000
χ662-222-2-2-220-22-222i−2i2i−2i00000000000−2i2i2i−2i−2i2i2-2-22−22−22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000000000000002−2i2−i2−222−200000000
χ672-222-2-2-220-22-222i−2i2i−2i00000000000−2i2i−2i2i2i−2i-222-22−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000000−22−i2i2−222−200000000
χ682-222-2-2-220-22-222i−2i2i−2i00000000000−2i2i−2i2i2i−2i-222-2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000000002−2i2−i22−2−2200000000
χ692-222-2-2-220-22-22−2i2i−2i2i000000000002i−2i2i−2i−2i2i-222-22−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000000−22i2−i2−222−200000000
χ702-222-2-2-220-22-22−2i2i−2i2i000000000002i−2i2i−2i−2i2i-222-2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000000002−2−i2i22−2−2200000000
χ712-222-2-2-220-22-22−2i2i−2i2i000000000002i−2i−2i2i2i−2i2-2-222−22−2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000000−22i2−i22−2−2200000000
χ722-222-2-2-220-22-22−2i2i−2i2i000000000002i−2i−2i2i2i−2i2-2-22−22−22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000000000000002−2−i2i2−222−200000000
χ73444-44-4-4-4-4000044-4-4-4440000-44000000000000000000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-40000-4-444-44400004-4000000000000000000000000000000000000000000000000000000000000000
χ7544-44-44-4-4-444-4-400004-44000000-440000000000000000000000000000000000000000000000000000000000000
χ7644-44-44-4-4-4-4-44400004-440000004-40000000000000000000000000000000000000000000000000000000000000
χ7744-4-4-4-444400000000-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000
χ7844-4-4-4-444400000000-4-44-444-400000000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-4-444-40000000044-400000000000000000000000000000000000000000000004-4000000000000000000000
χ8044-4-4-4-444-40000000044-40000000000000000000000000000000000000000000000-44000000000000000000000
χ814-44-4-444-4000004i−4i−4i4i00000000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ824-44-4-444-4000004i−4i−4i4i000000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000000
χ834-44-4-444-400000−4i4i4i−4i00000000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000000
χ844-44-4-444-400000−4i4i4i−4i000000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ854-4-444-44-404-4-440000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ864-4-444-44-404-4-44000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ874-4-444-44-40-444-40000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ884-4-444-44-40-444-4000000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ898-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000000

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