Finite Group Databasebeta

← Group #7523611

Character table — Group #7523611

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111111122222222222244444444444444444444444444444444448888888888888888888888888881616161616161616
order12222222222244444444444444444444444444888888888888888822222224444444444448888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111-11-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1111-1-1-1-1-1-1-1-1-11-1-11-111
χ51111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-11-1-111-11111-1-111-1-1-11-1-1-1-11-1
χ61111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-11111-1-111111-1-111-1-1-1-1-111-1-111-1-1-1-11-1-11
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-111-1-11-11111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11-1-1-1-1-111-1-111-1-1111111-111-1
χ91111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1111111-11-1111-1-111-1-1-1-1-1-1-111-1-11-1-1
χ101111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1111111-1-11-11111
χ111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11111-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-11-1-111-111
χ121111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-11-1-1-11-1-1-1-111111111-11-1-1-1-1
χ131111111111111-1-1-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1111-1-1-11111-1-11111-111-1-11
χ141111111111111-1-1-1-111111-1-1-1-111-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1111-111-1-1-1-111-1-11-1-11-1-11-1
χ151111111111111-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-11-1-1-1111111-1-111-1-11-1-111-1
χ161111111111111-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-111-111-11
χ1711111111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1111-1-1-1
χ1811111111-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-11111-1111-1-111
χ1911111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1111-1-1-1-111-1-1-1-111-1-1-1111
χ2011111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-11111111-1-111111-1-1-111-1-1
χ2111111111-1-1-1-111111111-1-1-1-111-1-111-1-1111111111111111111-1-1-1-1-111-1-111-1-111-111-1-1-111-1-1-1-1-1-1111-1-1-1-11-11
χ2211111111-1-1-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-111-1-1-1-1-1111111-1-111-1-1111-1
χ2311111111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-1-1-1-1-1-111-11111-11-1
χ2411111111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-111-11111-111111111-1-1-1-111-1-1-11
χ2511111111-1-1-1-11-1-1-1-1111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1111111-1-11-11-1-11-1-1-1-1-1-111111-11-1-1-111
χ2611111111-1-1-1-11-1-1-1-1111-1-111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1111-11-1-11111111-1-1-1-1111-11-1-1-1
χ2711111111-1-1-1-11-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1111-1111111-1-1-1-11111-11-1111-1-1
χ2811111111-1-1-1-11-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-11-11111-1-11111-1-1-1-1-1-1-11-1111
χ2911111111-1-1-1-11-1-1-1-1111-1-1-1-11111-1-111-1-1111111111111-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1
χ3011111111-1-1-1-11-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111-11-11-11-11
χ3111111111-1-1-1-11-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-111-111-1-11111-1-1111-1-1-1-11
χ3211111111-1-1-1-11-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-11111-111-1-1-111-1-1-1-1111-11-11-11-1
χ33222222222222-22222-2-2-2-2-2222222-2-2222200000000000000000000-20000000000-2-2-200-2000000000000000000
χ34222222222222-22222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000020000000000-222002000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2-2-200000000000000000000200000000002-2200-2000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000-2000000000022-2002000000000000000000
χ3722222222-2-2-2-2-22222-2-2-22222-2-222-2-2-2-2-2-200000000000000000000-2000000000022200-2000000000000000000
χ3822222222-2-2-2-2-22222-2-2-222-2-222-2-2-2-2-2-22200000000000000000000200000000002-2-2002000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222220000000000000000000020000000000-22-200-2000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222222222-2-200000000000000000000-20000000000-2-22002000000000000000000
χ41222-22-2-2-2000022i2i−2i−2i-2-22000000002i−2i00002i2i−2i−2i2i2i−2i−2i000022-2-2000002-2002-200000000002i−2i0000000000000000
χ42222-22-2-2-2000022i2i−2i−2i-2-22000000002i−2i00002i2i−2i−2i−2i−2i2i2i0000-2-222000002-200-220000000000−2i2i0000000000000000
χ43222-22-2-2-2000022i2i−2i−2i-2-22000000002i−2i0000−2i−2i2i2i2i2i−2i−2i000022-2-200000-2200-220000000000−2i2i0000000000000000
χ44222-22-2-2-2000022i2i−2i−2i-2-22000000002i−2i0000−2i−2i2i2i−2i−2i2i2i0000-2-22200000-22002-200000000002i−2i0000000000000000
χ45222-22-2-2-200002−2i−2i2i2i-2-2200000000−2i2i00002i2i−2i−2i2i2i−2i−2i0000-2-22200000-22002-20000000000−2i2i0000000000000000
χ46222-22-2-2-200002−2i−2i2i2i-2-2200000000−2i2i00002i2i−2i−2i−2i−2i2i2i000022-2-200000-2200-2200000000002i−2i0000000000000000
χ47222-22-2-2-200002−2i−2i2i2i-2-2200000000−2i2i0000−2i−2i2i2i2i2i−2i−2i0000-2-222000002-200-2200000000002i−2i0000000000000000
χ48222-22-2-2-200002−2i−2i2i2i-2-2200000000−2i2i0000−2i−2i2i2i−2i−2i2i2i000022-2-2000002-2002-20000000000−2i2i0000000000000000
χ4922-22-22-2-222-2-202i−2i2i−2i000002-22-22i−2i002i−2i2i−2i0000i2−i2i2−i2i2i2−i2−i22−22−2i2i2−i2−i20000000000000000000i2−i22−22−22−200000000
χ5022-22-22-2-222-2-202i−2i2i−2i000002-22-22i−2i002i−2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22−i2−i2i2i20000000000000000000−i2i2−22−22−2200000000
χ5122-22-22-2-222-2-202i−2i2i−2i00000-22-22−2i2i002i−2i−2i2i0000i2−i2i2−i2−i2−i2i2i22−22−2−i2−i2i2i20000000000000000000i2−i2−222−2−2200000000
χ5222-22-22-2-222-2-202i−2i2i−2i00000-22-22−2i2i002i−2i−2i2i0000−i2i2−i2i2i2i2−i2−i2−22−22i2i2−i2−i20000000000000000000−i2i22−2−222−200000000
χ5322-22-22-2-222-2-20−2i2i−2i2i000002-22-2−2i2i00−2i2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22i2i2−i2−i20000000000000000000i2−i2−22−22−2200000000
χ5422-22-22-2-222-2-20−2i2i−2i2i000002-22-2−2i2i00−2i2i−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−2−i2−i2i2i20000000000000000000−i2i22−22−22−200000000
χ5522-22-22-2-222-2-20−2i2i−2i2i00000-22-222i−2i00−2i2i2i−2i0000i2−i2i2−i2−i2−i2i2i2−22−22−i2−i2i2i20000000000000000000i2−i22−2−222−200000000
χ5622-22-22-2-222-2-20−2i2i−2i2i00000-22-222i−2i00−2i2i2i−2i0000−i2i2−i2i2i2i2−i2−i22−22−2i2i2−i2−i20000000000000000000−i2i2−222−2−2200000000
χ5722-22-22-2-2-2-22202i−2i2i−2i000002-2-222i−2i00−2i2i−2i2i0000i2−i2i2−i2−i2−i2i2i22−22−2i2i2−i2−i20000000000000000000−i2i22−2−22−2200000000
χ5822-22-22-2-2-2-22202i−2i2i−2i000002-2-222i−2i00−2i2i−2i2i0000−i2i2−i2i2i2i2−i2−i2−22−22−i2−i2i2i20000000000000000000i2−i2−222−22−200000000
χ5922-22-22-2-2-2-22202i−2i2i−2i00000-222-2−2i2i00−2i2i2i−2i0000i2−i2i2−i2i2i2−i2−i22−22−2−i2−i2i2i20000000000000000000−i2i2−22−222−200000000
χ6022-22-22-2-2-2-22202i−2i2i−2i00000-222-2−2i2i00−2i2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22i2i2−i2−i20000000000000000000i2−i22−22−2−2200000000
χ6122-22-22-2-2-2-2220−2i2i−2i2i000002-2-22−2i2i002i−2i2i−2i0000i2−i2i2−i2−i2−i2i2i2−22−22i2i2−i2−i20000000000000000000−i2i2−222−22−200000000
χ6222-22-22-2-2-2-2220−2i2i−2i2i000002-2-22−2i2i002i−2i2i−2i0000−i2i2−i2i2i2i2−i2−i22−22−2−i2−i2i2i20000000000000000000i2−i22−2−22−2200000000
χ6322-22-22-2-2-2-2220−2i2i−2i2i00000-222-22i−2i002i−2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22−i2−i2i2i20000000000000000000−i2i22−22−2−2200000000
χ6422-22-22-2-2-2-2220−2i2i−2i2i00000-222-22i−2i002i−2i−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−2i2i2−i2−i20000000000000000000i2−i2−22−222−200000000
χ652-22-2-222-22-22-2200002-2-22-20000000000002-22-200002i−2i2i−2i00002i−2i2i−2i00000002i−2i2i−2i0002-20000000000000000000
χ662-22-2-222-22-22-2200002-2-22-20000000000002-22-20000−2i2i−2i2i0000−2i2i−2i2i0000000−2i2i−2i2i0002-20000000000000000000
χ672-22-2-222-22-22-2200002-2-22-2000000000000-22-2200002i−2i2i−2i00002i−2i2i−2i0000000−2i2i−2i2i000-220000000000000000000
χ682-22-2-222-22-22-2200002-2-22-2000000000000-22-220000−2i2i−2i2i0000−2i2i−2i2i00000002i−2i2i−2i000-220000000000000000000
χ692-22-2-222-2-22-22200002-2-2-220000000000002-22-200002i−2i2i−2i0000−2i2i−2i2i0000000−2i2i2i−2i000-220000000000000000000
χ702-22-2-222-2-22-22200002-2-2-220000000000002-22-20000−2i2i−2i2i00002i−2i2i−2i00000002i−2i−2i2i000-220000000000000000000
χ712-22-2-222-2-22-22200002-2-2-22000000000000-22-2200002i−2i2i−2i0000−2i2i−2i2i00000002i−2i−2i2i0002-20000000000000000000
χ722-22-2-222-2-22-22200002-2-2-22000000000000-22-220000−2i2i−2i2i00002i−2i2i−2i0000000−2i2i2i−2i0002-20000000000000000000
χ73444-44-4-4-40000-44i4i−4i−4i44-400000000−4i4i00000000000000000000000000000000000000000000000000000000000
χ74444-44-4-4-40000-4−4i−4i4i4i44-4000000004i−4i00000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444000004-4-4400000000000000000000022−22−2222000022−22−2222000000000000000000000000000000000000000
χ7644-4-4-4-444000004-4-44000000000000000000000−222222−220000−222222−22000000000000000000000000000000000000000
χ7744-4-4-4-44400000-444-400000000000000000000022−22−22220000−222222−22000000000000000000000000000000000000000
χ7844-4-4-4-44400000-444-4000000000000000000000−222222−22000022−22−2222000000000000000000000000000000000000000
χ794-444-4-4-44000040000-44-4000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ804-444-4-4-44000040000-44-400000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ814-444-4-4-440000-400004-4400000000000000000000000000000000000004-4000000000000000000000000000000
χ824-444-4-4-440000-400004-440000000000000000000000000000000000000-44000000000000000000000000000000
χ834-44-4-444-44-44-4-40000-444-440000000000000000000000000000000000000000000000000000000000000000000
χ844-44-4-444-4-44-44-40000-4444-40000000000000000000000000000000000000000000000000000000000000000000
χ854-4-4-444-444-4-4400000000000000000000000000000022−22−2222000022−22−222200000000000000000000000000000000000
χ864-4-4-444-444-4-44000000000000000000000000000000−222222−220000−222222−2200000000000000000000000000000000000
χ874-4-4-444-44-444-400000000000000000000000000000022−22−22220000−222222−2200000000000000000000000000000000000
χ884-4-4-444-44-444-4000000000000000000000000000000−222222−22000022−22−222200000000000000000000000000000000000
χ898-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000

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