Finite Group Databasebeta

← Group #10822170

Character table — Group #10822170

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446661212121266666612121212121222224444666666668888121212121212121224242424242424242244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-111-1111-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ1011111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-111-1111-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ1111111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-111-1-1-11-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111-11-111-1-1-1-111-1-111
χ1211111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-111-1-1-11-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-11-11-1-11111-1-111-1-1
χ1311111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11-1111-11-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111-1-1
χ1411111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11-1111-11-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-11111-11-1111-1-111-1-1-1-111
χ1511111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11-11-1-1-1111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-11-11-1-1-11111-1-1-1-111
χ1611111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-11-11-1-1-1111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-1111-1-1-1-11111-1-1
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000000000002-22-200000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000-22-2200000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-2-2-2-2-1-1-1-11111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1-2-2-2-21111-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222-2-2-2-222-2-22222-2-2222222222-2-2-2-2-2-2-222-200000000000000000000000000000000000000002-2-2200000000
χ2422222-2-2-2-222-2-22222-2-2222222222-2-2-2-2-2-2-222-20000000000000000000000000000000000000000-222-200000000
χ2522222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-111-12-2222-2-2-2-1-111-1-1-1-122-2-2-1-1111111-1-1-1-111110000000000000000
χ2622222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-111-12-2-2-22-222-1-1111111-2-222-1-111-1-1-1-11111-1-1-1-10000000000000000
χ2722222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-111-1-2222-22-2-211-1-1-1-1-1-1-2-22211-1-111111111-1-1-1-10000000000000000
χ2822222-2-2-2-22-122-2-2-2-222-1-1-11111-1-11111-1-1-111-1-22-2-2-222211-1-1111122-2-211-1-1-1-1-1-1-1-1-1-111110000000000000000
χ292222-222-2-2-222-222-2-22-22222222-2-222-2-22-2-2-2-222-200-220022-2-200000000-2-2220000000000000000000000000000
χ302222-222-2-2-222-222-2-22-22222222-2-222-2-22-2-2-2-22-22002-200-2-2220000000022-2-20000000000000000000000000000
χ312222-222-2-2-22-22-2-222-22222-2-2-2-2-2-222-2-2-22222-20000000000000000000000000000000000002-2-22000000000000
χ322222-222-2-2-22-22-2-222-22222-2-2-2-2-2-222-2-2-22222-2000000000000000000000000000000000000-222-2000000000000
χ332222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-11111-12-200-2200-1-111−i3−i3i3i3000011-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ342222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-11111-12-200-2200-1-111i3i3−i3−i3000011-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ352222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-11111-1-22002-20011-1-1−i3−i3i3i30000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ362222-222-2-2-2-12-222-2-22-2-1-1-1-1-1-1-111-1-111-11111-1-22002-20011-1-1i3i3−i3−i30000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ372222-2-2-222-222-2-2-2222-2222-2-2-2-2-2-2-2-2222-2-22222200-2-200222200000000-2-2-2-20000000000000000000000000000
χ382222-2-2-222-222-2-2-2222-2222-2-2-2-2-2-2-2-2222-2-2222-2-2002200-2-2-2-20000000022220000000000000000000000000000
χ392222-2-2-222-22-2222-2-2-222222222-2-2-2-222-222-2-2-200000000000000000000000000000000000022-2-2000000000000
χ402222-2-2-222-22-2222-2-2-222222222-2-2-2-222-222-2-2-2000000000000000000000000000000000000-2-222000000000000
χ412222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-111-1-1-12200-2-200-1-1-1-1−i3−i3i3i300001111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ422222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-111-1-1-12200-2-200-1-1-1-1i3i3−i3−i300001111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ432222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-111-1-1-1-2-20022001111−i3−i3i3i30000-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ442222-2-2-222-2-12-2-2-2222-2-1-1-111111111-1-1-111-1-1-1-2-20022001111i3i3−i3−i30000-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ452-22-222-22-2-22222-22-2-2-2-2-2222-2-22-22-22-222-22-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ462-22-222-22-2-22222-22-2-2-2-2-2222-2-22-22-22-222-22-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ472-22-222-22-2-22-2-2-22-2222-2-22-2-2222-22-22-2-2-22-222002-2002-200002-22-2000000002-22-2000000000000000000000000
χ482-22-222-22-2-22-2-2-22-2222-2-22-2-2222-22-22-2-2-22-22200-2200-220000-22-2200000000-22-22000000000000000000000000
χ492-22-222-22-2-2-1-2-2-22-222211-111-1-1-11-11-1111-11-1-1002-2002-2−i3i3−i3i3-11-110000−i3i3−i3i3-11-11−i3i3−i3i3−i3i3−i3i30000000000000000
χ502-22-222-22-2-2-1-2-2-22-222211-111-1-1-11-11-1111-11-1-1002-2002-2i3−i3i3−i3-11-110000i3−i3i3−i3-11-11i3−i3i3−i3i3−i3i3−i30000000000000000
χ512-22-222-22-2-2-1-2-2-22-222211-111-1-1-11-11-1111-11-1-100-2200-22−i3i3−i3i31-11-10000−i3i3−i3i31-11-1i3−i3i3−i3i3−i3i3−i30000000000000000
χ522-22-222-22-2-2-1-2-2-22-222211-111-1-1-11-11-1111-11-1-100-2200-22i3−i3i3−i31-11-10000i3−i3i3−i31-11-1−i3i3−i3i3−i3i3−i3i30000000000000000
χ532-22-22-22-22-2222-22-22-2-2-2-22-2-2222-2-22-2222-2-22-2000000000000000000000000000000000000000000002i−2i−2i2i0000
χ542-22-22-22-22-2222-22-22-2-2-2-22-2-2222-2-22-2222-2-22-200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ552-22-22-22-22-22-2-22-22-222-2-2222-2-22-2-22-22-2-222-22002-200-2200002-22-200000000-22-22000000000000000000000000
χ562-22-22-22-22-22-2-22-22-222-2-2222-2-22-2-22-22-2-222-2200-22002-20000-22-22000000002-22-2000000000000000000000000
χ572-22-22-22-22-2-1-2-22-22-22211-1-1-111-111-11-111-1-11-1002-200-22−i3i3i3−i3-11-110000−i3i3i3−i31-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ582-22-22-22-22-2-1-2-22-22-22211-1-1-111-111-11-111-1-11-1002-200-22i3−i3−i3i3-11-110000i3−i3−i3i31-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ592-22-22-22-22-2-1-2-22-22-22211-1-1-111-111-11-111-1-11-100-22002-2−i3i3i3−i31-11-10000−i3i3i3−i3-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ602-22-22-22-22-2-1-2-22-22-22211-1-1-111-111-11-111-1-11-100-22002-2i3−i3−i3i31-11-10000i3−i3−i3i3-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ612-22-2-22-2-22222-22-2-22-22-2-2222-2-2-222-2-222-22-22-20000000000000000000000000000000000000000000000002-22-2
χ622-22-2-22-2-22222-22-2-22-22-2-2222-2-2-222-2-222-22-22-2000000000000000000000000000000000000000000000000-22-22
χ632-22-2-22-2-2222-22-222-22-2-2-22-2-222-222-2-22-22-22-2200000000000000002-22-2000000002-2-222-2-220000000000000000
χ642-22-2-22-2-2222-22-222-22-2-2-22-2-222-222-2-22-22-22-220000000000000000-22-2200000000-222-2-222-20000000000000000
χ652-22-2-22-2-222-1-22-222-22-211-111-1-11-1-111-11-11-11-100000000−i3i3i3−i3−i3i3i3−i32-22-2i3−i3−i3i3−i3i3i3−i3-111-1-111-10000000000000000
χ662-22-2-22-2-222-1-22-222-22-211-111-1-11-1-111-11-11-11-100000000−i3i3i3−i3i3−i3−i3i3-22-22i3−i3−i3i3i3−i3−i3i31-1-111-1-110000000000000000
χ672-22-2-22-2-222-1-22-222-22-211-111-1-11-1-111-11-11-11-100000000i3−i3−i3i3−i3i3i3−i3-22-22−i3i3i3−i3−i3i3i3−i31-1-111-1-110000000000000000
χ682-22-2-22-2-222-1-22-222-22-211-111-1-11-1-111-11-11-11-100000000i3−i3−i3i3i3−i3−i3i32-22-2−i3i3i3−i3i3−i3−i3i3-111-1-111-10000000000000000
χ692-22-2-2-222-2222-2-222-2-22-2-22-2-222-22-222-22-222-2-20000000000000000000000000000000000000000000000002-2-22
χ702-22-2-2-222-2222-2-222-2-22-2-22-2-222-22-222-22-222-2-2000000000000000000000000000000000000000000000000-222-2
χ712-22-2-2-222-222-222-2-222-2-2-2222-2-2-22-222-2-22-2-22200000000000000002-2-22000000002-2-22-222-20000000000000000
χ722-22-2-2-222-222-222-2-222-2-2-2222-2-2-22-222-2-22-2-2220000000000000000-222-200000000-222-22-2-220000000000000000
χ732-22-2-2-222-22-1-222-2-222-211-1-1-1111-11-1-111-111-1-100000000−i3i3−i3i3−i3i3i3−i32-2-22i3−i3i3−i3i3−i3−i3i3-111-11-1-110000000000000000
χ742-22-2-2-222-22-1-222-2-222-211-1-1-1111-11-1-111-111-1-100000000−i3i3−i3i3i3−i3−i3i3-222-2i3−i3i3−i3−i3i3i3−i31-1-11-111-10000000000000000
χ752-22-2-2-222-22-1-222-2-222-211-1-1-1111-11-1-111-111-1-100000000i3−i3i3−i3−i3i3i3−i3-222-2−i3i3−i3i3i3−i3−i3i31-1-11-111-10000000000000000
χ762-22-2-2-222-22-1-222-2-222-211-1-1-1111-11-1-111-111-1-100000000i3−i3i3−i3i3−i3−i3i32-2-22−i3i3−i3i3−i3i3i3−i3-111-11-1-110000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ7844444-4-4-4-44-2-4-44444-4-4-2-2-2-2-2-2-2-2-22222222-2-220000000000000000000000000000000000000000000000000000
χ794444-444-4-4-4-2-44-4-444-44-2-2-2222222-2-2222-2-2-2-220000000000000000000000000000000000000000000000000000
χ804444-4-4-444-4-2-4444-4-4-44-2-2-2-2-2-2-22222-2-22-2-22220000000000000000000000000000000000000000000000000000
χ814-44-444-44-4-4-2444-44-4-4-422-2-2-222-22-22-22-2-22-2220000000000000000000000000000000000000000000000000000
χ824-44-44-44-44-4-244-44-44-4-422-222-2-2-222-22-2-2-222-220000000000000000000000000000000000000000000000000000
χ834-44-4-44-4-444-24-44-4-44-4422-2-2-2222-2-222-2-22-22-220000000000000000000000000000000000000000000000000000
χ844-44-4-4-444-44-24-4-444-4-4422-222-2-22-22-2-22-22-2-2220000000000000000000000000000000000000000000000000000
χ8588-8-80000008000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400000000-44443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-400000000-444−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000

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