Finite Group Databasebeta

← Group #72282418

Character table — Group #72282418

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size11112222222244444444444444444448888888888888888888816161616161616161616161616161616161616161616161616161616161616163232323232323232
order1222222222442222222222224444444222222444444444444442244444444444444888888888888888824444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111-1-1-1-11111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111-1-1-1-11111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-1-11111-1-1-1111111111-1-1-1-111-1-1-1iiii−i−i−i−i-1-1-111ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ10111111111111-1-1-1-1-11111-1-1-1111111111-1-1-1-111-1-1-1iiii−i−i−i−i-1-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ11111111111111-1-1-1-1-11111-1-1-1111111111-1-1-1-111-1-1-1−i−i−i−iiiii-1-1-111−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ12111111111111-1-1-1-1-11111-1-1-1111111111-1-1-1-111-1-1-1−i−i−i−iiiii-1-1-111−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1iiii−i−i−i−i-111-1-1ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1iiii−i−i−i−i-111-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1−i−i−i−iiiii-111-1-1−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1−i−i−i−iiiii-111-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ1711111-1-1-1-11111111-111-1-1-1-1-1-1-111-1-111-111-1-11-111-1ii−i−iii−i−i-11-11-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ1811111-1-1-1-11111111-111-1-1-1-1-1-1-111-1-111-111-1-11-111-1ii−i−iii−i−i-11-11-1i−ii−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ1911111-1-1-1-11111111-111-1-1-1-1-1-1-111-1-111-111-1-11-111-1−i−iii−i−iii-11-11-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ2011111-1-1-1-11111111-111-1-1-1-1-1-1-111-1-111-111-1-11-111-1−i−iii−i−iii-11-11-1−ii−ii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ2111111-1-1-1-11111111-1-1-111-1-1-1-1-111-1-11-11-1-1111-111-1ii−i−iii−i−i-1-11-11i−ii−i−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ2211111-1-1-1-11111111-1-1-111-1-1-1-1-111-1-11-11-1-1111-111-1ii−i−iii−i−i-1-11-11i−ii−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ2311111-1-1-1-11111111-1-1-111-1-1-1-1-111-1-11-11-1-1111-111-1−i−iii−i−iii-1-11-11−ii−iiii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ2411111-1-1-1-11111111-1-1-111-1-1-1-1-111-1-11-11-1-1111-111-1−i−iii−i−iii-1-11-11−ii−iiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ2511111-1-1-1-1111-1-1-1-1111-1-1111-1-111-1-111-1-1-1111-1-1-1111-1-1-1-1111-111-11-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-11
χ2611111-1-1-1-1111-1-1-1-1111-1-1111-1-111-1-111-1-1-1111-1-1-1111-1-1-1-1111-111-11-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-111-1-111-1
χ2711111-1-1-1-1111-1-1-1-1111-1-1111-1-111-1-111-1-1-1111-1-1-11-1-11111-1-11-111-1-111-1-1-11111-1-111-1-1-1-111-1-11111-1-11-1-11-111-1
χ2811111-1-1-1-1111-1-1-1-1111-1-1111-1-111-1-111-1-1-1111-1-1-11-1-11111-1-11-111-1-111-1-1-11111-1-1-1-11111-1-111-1-1-1-111-111-11-1-11
χ2911111-1-1-1-1111-1-1-1-11-1-111111-1-111-1-11-1111-1-11-1-1-1111-1-1-1-11111-1-111-1-11-1-11111-1-111-1-1-1-11111-1-1-1-111-111-1-111-1
χ3011111-1-1-1-1111-1-1-1-11-1-111111-1-111-1-11-1111-1-11-1-1-1111-1-1-1-11111-1-111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-111-1-11
χ3111111-1-1-1-1111-1-1-1-11-1-111111-1-111-1-11-1111-1-11-1-1-11-1-11111-1-111-1-11-111-111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-1-11
χ3211111-1-1-1-1111-1-1-1-11-1-111111-1-111-1-11-1111-1-11-1-1-11-1-11111-1-111-1-11-111-111-1-1-1-111-1-11111-1-111-1-1-1-1111-1-11-111-1
χ3322222222222222-2-222222-22-222-2-2-2-2222-2-2-2-2-2-22-2-200000000222-2-2000000000000000000000000000000000000
χ3422222222222222-2-22-2-2-2-2-22-222-2-2-2-22-2-22222-2-22-2-2000000002-2-222000000000000000000000000000000000000
χ35222222222222-2-222-222222-2222-2-2-2-22222222-2-2-22200000000-2-2-2-2-2000000000000000000000000000000000000
χ36222222222222-2-222-2-2-2-2-22-2222-2-2-2-22-2-2-2-2-2-2-2-2-22200000000-22222000000000000000000000000000000000000
χ372222222222-2-2222220000222-2-22222-2000000-2-2-2-2-222222222-20000-2-2-2-200000000000000000000000000000000
χ382222222222-2-2222220000222-2-22222-2000000-2-2-2-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ392222222222-2-222-2-220000-22-2-2-2-2-2-2-2-200000022-22200000000-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ402222222222-2-222-2-220000-22-2-2-2-2-2-2-2-200000022-22200000000-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ412222222222-2-2-2-222-200002-22-2-2-2-2-2-2-2000000222-2-2000000002000000002-22-2-22-22000000000000000000000000
χ422222222222-2-2-2-222-200002-22-2-2-2-2-2-2-2000000222-2-200000000200000000-22-222-22-2000000000000000000000000
χ432222222222-2-2-2-2-2-2-20000-2-2-2-2-22222-2000000-2-22222i2i2i2i−2i−2i−2i−2i20000−2i−2i2i2i00000000000000000000000000000000
χ442222222222-2-2-2-2-2-2-20000-2-2-2-2-22222-2000000-2-2222−2i−2i−2i−2i2i2i2i2i200002i2i−2i−2i00000000000000000000000000000000
χ4522222-2-2-2-222222-2-2-222-2-22-22-2-2-2-22222-2-2-222-222-2200000000-22-2-22000000000000000000000000000000000000
χ4622222-2-2-2-222222-2-2-2-2-2222-22-2-2-2-2222-2222-2-2-222-2200000000-2-222-2000000000000000000000000000000000000
χ4722222-2-2-2-2222-2-222222-2-2-22-2-2-2-2-22222-222-2-2-22-22-2000000002-22-22000000000000000000000000000000000000
χ4822222-2-2-2-2222-2-2222-2-222-22-2-2-2-2-2222-22-2-222-22-22-20000000022-22-2000000000000000000000000000000000000
χ4922222-2-2-2-22-2-22222-20000-2-2-22222-2-2-2000000-22-2-222i2i−2i−2i2i2i−2i−2i20000−2i2i−2i2i00000000000000000000000000000000
χ5022222-2-2-2-22-2-22222-20000-2-2-22222-2-2-2000000-22-2-22−2i−2i2i2i−2i−2i2i2i200002i−2i2i−2i00000000000000000000000000000000
χ5122222-2-2-2-22-2-222-2-2-200002-2222-2-222-20000002-2-22-2000000002000000002-2-222-2-22000000000000000000000000
χ5222222-2-2-2-22-2-222-2-2-200002-2222-2-222-20000002-2-22-200000000200000000-222-2-222-2000000000000000000000000
χ5322222-2-2-2-22-2-2-2-22220000-22-222-2-222-20000002-22-2200000000-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5422222-2-2-2-22-2-2-2-22220000-22-222-2-222-20000002-22-2200000000-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ5522222-2-2-2-22-2-2-2-2-2-2200002222222-2-2-2000000-2222-222-2-2-2-222-20000-222-200000000000000000000000000000000
χ5622222-2-2-2-22-2-2-2-2-2-2200002222222-2-2-2000000-2222-2-2-22222-2-2-200002-2-2200000000000000000000000000000000
χ572-2-22-222-2-22002-22-2200002-2-2002-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ582-2-22-222-2-22002-22-2200002-2-2002-22-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ592-2-22-222-2-22002-22-2200002-2-2002-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ602-2-22-222-2-22002-22-2200002-2-2002-22-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ612-2-22-222-2-2200-22-22-20000-222002-22-20000000000002-22-2-22-22000000000000000002−22−2−22−222−22−2−22−2200000000
χ622-2-22-222-2-2200-22-22-20000-222002-22-20000000000002-22-2-22-2200000000000000000−22−222−22−2−22−222−22−200000000
χ632-2-22-222-2-2200-22-22-20000-222002-22-2000000000000-22-222-22-2000000000000000002−22−2−22−22−22−222−22−200000000
χ642-2-22-222-2-2200-22-22-20000-222002-22-2000000000000-22-222-22-200000000000000000−22−222−22−22−22−2−22−2200000000
χ652-2-22-2-2-2222002-22-2-20000-222002-2-220000000000002-2-222-2-22000000000000000002−2−222−2−222−2−222−2−2200000000
χ662-2-22-2-2-2222002-22-2-20000-222002-2-220000000000002-2-222-2-2200000000000000000−222−2−222−2−222−2−222−200000000
χ672-2-22-2-2-2222002-22-2-20000-222002-2-22000000000000-222-2-222-2000000000000000002−2−222−2−22−222−2−222−200000000
χ682-2-22-2-2-2222002-22-2-20000-222002-2-22000000000000-222-2-222-200000000000000000−222−2−222−22−2−222−2−2200000000
χ692-2-22-2-2-222200-22-22200002-2-2002-2-220000000000002i−2i−2i2i−2i2i2i−2i000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ702-2-22-2-2-222200-22-22200002-2-2002-2-220000000000002i−2i−2i2i−2i2i2i−2i00000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ712-2-22-2-2-222200-22-22200002-2-2002-2-22000000000000−2i2i2i−2i2i−2i−2i2i000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ722-2-22-2-2-222200-22-22200002-2-2002-2-22000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ734444-44-44-4-4440000044440004-40000-4-4-40000000000000000000000000000000000000000000000000000000000
χ744444-44-44-4-44400000-4-4-4-40004-40000-4440000000000000000000000000000000000000000000000000000000000
χ754444-44-44-4-4-4-4000000000000-4400004004-44-4000000000000000000000000000000000000000000000000000000
χ764444-44-44-4-4-4-4000000000000-440000400-44-44000000000000000000000000000000000000000000000000000000
χ774444-4-44-44-4440000044-4-4000-440000-4-440000000000000000000000000000000000000000000000000000000000
χ784444-4-44-44-44400000-4-444000-440000-44-40000000000000000000000000000000000000000000000000000000000
χ794444-4-44-44-4-4-40000000000004-400004004-4-44000000000000000000000000000000000000000000000000000000
χ804444-4-44-44-4-4-40000000000004-40000400-444-4000000000000000000000000000000000000000000000000000000
χ814-4-44-444-4-44004-4-4440000-4-4400-44-440000000000000000000000000000000000000000000000000000000000000
χ824-4-44-444-4-4400-444-4-4000044-400-44-440000000000000000000000000000000000000000000000000000000000000
χ834-4-44-4-4-4444004-4-44-4000044-400-444-40000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-4-444400-444-440000-4-4400-444-40000000000000000000000000000000000000000000000000000000000000
χ858-88-80000008-800000008-80000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-80000008-80000000-880000000000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-88000008-8000000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8000000-8800000-88000000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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