Finite Group Databasebeta

← Group #7533621

Character table — Group #7533621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444888888882222444444444444888888888888222224444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1111111-1-1111111111111-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1111111-1-1111111111111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1111-1-111-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-11-11-11-11
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1-1-11111111111-111-11-1-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-1111111111-1-11-111-1
χ9111111111111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-111
χ10111111111111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-1
χ11111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-1
χ12111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-111-1-1-11-1-1111-1-111-1-111-1-111-1-1111-11-1-111-1
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1111-1-1111-1-111-1-1-1-111-1-111-11-111-1-11
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111111-1-11-111-1-1-1-1-11111-1-111-1-111-1-1-111-1-11-11
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111-1-1111-1-1-111-111-1-1-1-11111-1-111-1-11-1-111-11-1
χ1711111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-111
χ1811111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ1911111111-1-1-1-11111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ2011111111-1-1-1-11111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111
χ2111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111111-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1-11-11-111-1
χ2211111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111111-1-111-1-111-1-11-1-111-1-1111111-1-1-1-11-11-11-1-11
χ2311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-111-1-11111-1-1-111-1-1-1-111-1-1-1-111111-1-11-11-11
χ2411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-11111-1-111-1-1-11111-1-1-1-1-1-11111-111-11-11-1
χ2511111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111111-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ2611111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1111111111-1-11111-1-11111-1-1-1-1
χ2711111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ2811111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-111111-11111-1-1-1-111-1-1-1-111-1-111-1-111
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111111111-1-1-1-1-111-1-11-111-1-11-1-111-1-11111-1-1-1-111-11-111-11-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1111-1-1-111111-1-111-1-111-1-1-1-1111-11-1-11-11
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-11-1-111-1-1-11111-1-1-1-11111-1-11-1-111-1-11
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-11-1-111-1111-1-1-111-1-1-1-111-1-11111-1-1-111-1-111-1
χ332222222222222222-2-2-2-20000000022222222-2-2-2-2-2-222000000000000-20000-2-20000-2000000000000000000000000
χ342222222222222222-2-2-2-20000000022-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000200002200002000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-2-2-22222-2-2000000000000200002-20000-2000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2-2-222-2-2222222000000000000-20000-2200002000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-200000000-2-222-2-2-2-222-2-22222000000000000-20000220000-2000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-200000000-2-2-2-2222222-2-222-2-200000000000020000-2-200002000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2222222-2-2-2-200000000000020000-220000-2000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-22222-2-222000000000000-200002-200002000000000000000000000000
χ4122-22-2-2-222i2i−2i−2i00002-2-222222-2-2-2-2000000002i−2i0000002i2i−2i−2i0000000000000002i−2i2i−2i000002-22-20000000000000000
χ4222-22-2-2-222i2i−2i−2i00002-2-222222-2-2-2-2000000002i−2i0000002i2i−2i−2i000000000000000−2i2i−2i2i00000-22-220000000000000000
χ4322-22-2-2-222i2i−2i−2i00002-2-22-2-2-2-22222000000002i−2i000000−2i−2i2i2i0000000000000002i−2i−2i2i000002-2-220000000000000000
χ4422-22-2-2-222i2i−2i−2i00002-2-22-2-2-2-22222000000002i−2i000000−2i−2i2i2i000000000000000−2i2i2i−2i00000-222-20000000000000000
χ4522-22-2-2-22−2i−2i2i2i00002-2-222222-2-2-2-200000000−2i2i000000−2i−2i2i2i0000000000000002i−2i2i−2i00000-22-220000000000000000
χ4622-22-2-2-22−2i−2i2i2i00002-2-222222-2-2-2-200000000−2i2i000000−2i−2i2i2i000000000000000−2i2i−2i2i000002-22-20000000000000000
χ4722-22-2-2-22−2i−2i2i2i00002-2-22-2-2-2-2222200000000−2i2i0000002i2i−2i−2i0000000000000002i−2i−2i2i00000-222-20000000000000000
χ4822-22-2-2-22−2i−2i2i2i00002-2-22-2-2-2-2222200000000−2i2i0000002i2i−2i−2i000000000000000−2i2i2i−2i000002-2-220000000000000000
χ4922-2-22-22-22i−2i2i−2i2i2i−2i−2i000022−2−222−2−22-22-22i−2i2-20000002i−2ii2−i2i2−i2i2i2−i2−i222−2−200000000000000000000i2−i22−22−2i2−i200000000
χ5022-2-22-22-22i−2i2i−2i2i2i−2i−2i000022−2−222−2−22-2-22−2i2i-22000000−2i2ii2−i2i2−i2i2i2−i2−i222−2−200000000000000000000−i2i2−22−22−i2i200000000
χ5122-2-22-22-22i−2i2i−2i2i2i−2i−2i0000−2−222−2−2222-22-22i−2i2-20000002i−2i−i2i2−i2i2−i2−i2i2i2−2−22200000000000000000000−i2i2−22−22−i2i200000000
χ5222-2-22-22-22i−2i2i−2i2i2i−2i−2i0000−2−222−2−2222-2-22−2i2i-22000000−2i2i−i2i2−i2i2−i2−i2i2i2−2−22200000000000000000000i2−i22−22−2i2−i200000000
χ5322-2-22-22-22i−2i2i−2i−2i−2i2i2i000022−2−222−2−2-222-22i−2i-22000000−2i2ii2−i2i2−i2−i2−i2i2i2−2−22200000000000000000000i2−i2−222−2−i2i200000000
χ5422-2-22-22-22i−2i2i−2i−2i−2i2i2i000022−2−222−2−2-22-22−2i2i2-20000002i−2ii2−i2i2−i2−i2−i2i2i2−2−22200000000000000000000−i2i22−2−22i2−i200000000
χ5522-2-22-22-22i−2i2i−2i−2i−2i2i2i0000−2−222−2−222-222-22i−2i-22000000−2i2i−i2i2−i2i2i2i2−i2−i222−2−200000000000000000000−i2i22−2−22i2−i200000000
χ5622-2-22-22-22i−2i2i−2i−2i−2i2i2i0000−2−222−2−222-22-22−2i2i2-20000002i−2i−i2i2−i2i2i2i2−i2−i222−2−200000000000000000000i2−i2−222−2−i2i200000000
χ5722-2-22-22-2−2i2i−2i2i2i2i−2i−2i000022−2−222−2−2-222-2−2i2i-220000002i−2i−i2i2−i2i2i2i2−i2−i2−2−22200000000000000000000−i2i2−222−2i2−i200000000
χ5822-2-22-22-2−2i2i−2i2i2i2i−2i−2i000022−2−222−2−2-22-222i−2i2-2000000−2i2i−i2i2−i2i2i2i2−i2−i2−2−22200000000000000000000i2−i22−2−22−i2i200000000
χ5922-2-22-22-2−2i2i−2i2i2i2i−2i−2i0000−2−222−2−222-222-2−2i2i-220000002i−2ii2−i2i2−i2−i2−i2i2i222−2−200000000000000000000i2−i22−2−22−i2i200000000
χ6022-2-22-22-2−2i2i−2i2i2i2i−2i−2i0000−2−222−2−222-22-222i−2i2-2000000−2i2ii2−i2i2−i2−i2−i2i2i222−2−200000000000000000000−i2i2−222−2i2−i200000000
χ6122-2-22-22-2−2i2i−2i2i−2i−2i2i2i000022−2−222−2−22-22-2−2i2i2-2000000−2i2i−i2i2−i2i2−i2−i2i2i222−2−200000000000000000000−i2i22−22−2−i2i200000000
χ6222-2-22-22-2−2i2i−2i2i−2i−2i2i2i000022−2−222−2−22-2-222i−2i-220000002i−2i−i2i2−i2i2−i2−i2i2i222−2−200000000000000000000i2−i2−22−22i2−i200000000
χ6322-2-22-22-2−2i2i−2i2i−2i−2i2i2i0000−2−222−2−2222-22-2−2i2i2-2000000−2i2ii2−i2i2−i2i2i2−i2−i2−2−22200000000000000000000i2−i2−22−22i2−i200000000
χ6422-2-22-22-2−2i2i−2i2i−2i−2i2i2i0000−2−222−2−2222-2-222i−2i-220000002i−2ii2−i2i2−i2i2i2−i2−i2−2−22200000000000000000000−i2i22−22−2−i2i200000000
χ652-2-2-2-222200002-22-2-22-222-22-22-22-200000000002-2000000002-22-2000002-22-200000002-22-200000000000000000000
χ662-2-2-2-222200002-22-2-22-222-22-22-22-200000000002-2000000002-22-200000-22-220000000-22-2200000000000000000000
χ672-2-2-2-222200002-22-2-22-22-22-22-22-2200000000002-200000000-22-22000002-2-2200000002-2-2200000000000000000000
χ682-2-2-2-222200002-22-2-22-22-22-22-22-2200000000002-200000000-22-2200000-222-20000000-222-200000000000000000000
χ692-2-2-2-22220000-22-22-22-222-22-22-22-20000000000-2200000000-22-22000002-22-20000000-22-2200000000000000000000
χ702-2-2-2-22220000-22-22-22-222-22-22-22-20000000000-2200000000-22-2200000-22-2200000002-22-200000000000000000000
χ712-2-2-2-22220000-22-22-22-22-22-22-22-220000000000-22000000002-22-2000002-2-220000000-222-200000000000000000000
χ722-2-2-2-22220000-22-22-22-22-22-22-22-220000000000-22000000002-22-200000-222-200000002-2-2200000000000000000000
χ73444-4-44-4-44-4-44000000002222−22−22−22−222222000000000000000022−22−222200000000000000000000000000000000000000000000
χ74444-4-44-4-44-4-4400000000−22−2222222222−22−220000000000000000−222222−2200000000000000000000000000000000000000000000
χ75444-4-44-4-4-444-4000000002222−22−22−22−2222220000000000000000−222222−2200000000000000000000000000000000000000000000
χ76444-4-44-4-4-444-400000000−22−2222222222−22−22000000000000000022−22−222200000000000000000000000000000000000000000000
χ7744-44-4-4-444i4i−4i−4i0000-444-40000000000000000−4i4i000000000000000000000000000000000000000000000000000000
χ7844-44-4-4-44−4i−4i4i4i0000-444-400000000000000004i−4i000000000000000000000000000000000000000000000000000000
χ794-444-4-44-400004i−4i−4i4i000022−22−222222−22−2222000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ804-444-4-44-400004i−4i−4i4i0000−222222−22−222222−2200000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ814-444-4-44-40000−4i4i4i−4i000022−22−222222−22−222200000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ824-444-4-44-40000−4i4i4i−4i0000−222222−22−222222−22000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ834-44-44-4-440000000044-4-4000000000000000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ844-44-44-4-440000000044-4-400000000000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ854-44-44-4-4400000000-4-4444-44-4-44-440000000000000000000000000000000000000000000000000000000000000000
χ864-44-44-4-4400000000-4-444-44-444-44-40000000000000000000000000000000000000000000000000000000000000000
χ874-4-4444-4-400000000000022−22−2222−222222−220000000000004i−4i00000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ884-4-4444-4-400000000000022−22−2222−222222−22000000000000−4i4i0000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ894-4-4444-4-4000000000000−222222−2222−22−22220000000000004i−4i0000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ904-4-4444-4-4000000000000−222222−2222−22−2222000000000000−4i4i00000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ914-4-4-4-444400004-44-44-44-4000000000000000000-440000000000000000000000000000000000000000000000000000
χ924-4-4-4-44440000-44-444-44-40000000000000000004-40000000000000000000000000000000000000000000000000000

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