Finite Group Databasebeta

← Group #10848838

Character table — Group #10848838

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212121212122424242448484848
order1222222234444666666644444444121212121212121212121212244444444466121212121212121212121212121212121212121212128888888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111111111-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1111111111111-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111-1-1-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-11
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ17222222222-2-2-2-2222222222-2-222-2-22222-2-2-2-2-2-2-2-220000-200002222-2-200000000-2-2000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2000020000-2-2-2-2220000000022000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-22222-2-2-2-2-2000020000-2-222-2-20000000022000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-222-2-2-2-22222-2-2-2-220000-2000022-2-22200000000-2-2000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-22-2-2-2-2-1-1-1-1-1-111111111-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-222-2-2-222-2-2111111-1-1-1-1111111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-222-2-2-2221111111111-1-1-1-1111111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-22222-2-2-2-2-211-1-1-1-1-1-1-1-1-1-1-1-111111111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-2-2-2-2-2-2222211-1-1-1-11111111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1222-2-22-2-222-1-11111-1-1-1-11111-1-11111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-12-2-222222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111111120000-20000-1-1-1-111−i3−i3i3i3−i3−i3i3i311−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111111120000-20000-1-1-1-111i3i3−i3−i3i3i3−i3−i311i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-20000200001111-1-1−i3−i3i3i3i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-20000200001111-1-1i3i3−i3−i3−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-11111-200002000011-1-111−i3−i3i3i3−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-11111-200002000011-1-111i3i3−i3−i3i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1111120000-20000-1-111-1-1−i3−i3i3i3i3i3−i3−i311i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1111120000-20000-1-111-1-1i3i3−i3−i3−i3−i3i3i311−i3−i3i3i3i3i3−i3−i30000000000000000
χ37222-2-2-22-2222-2-222-2-2-2-222i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i22-2-2000000000000000000000000000000000000002i2i−2i−2i002-20000
χ38222-2-2-22-2222-2-222-2-2-2-222i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i22-2-200000000000000000000000000000000000000−2i−2i2i2i00-220000
χ39222-2-2-22-2222-2-222-2-2-2-22−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000000000000000002i2i−2i−2i00-220000
χ40222-2-2-22-2222-2-222-2-2-2-22−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i22-2-200000000000000000000000000000000000000−2i−2i2i2i002-20000
χ41222-2-2-22-22-2-22222-2-2-2-222i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i-2-22200000000000000000000000000000000002i2i−2i−2i00002-2000000
χ42222-2-2-22-22-2-22222-2-2-2-222i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i-2-2220000000000000000000000000000000000−2i−2i2i2i0000-22000000
χ43222-2-2-22-22-2-22222-2-2-2-22−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000000000000000002i2i−2i−2i0000-22000000
χ44222-2-2-22-22-2-22222-2-2-2-22−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000000000000000000000−2i−2i2i2i00002-2000000
χ452-2-2-2222-222-22-2-2-2-2-222200002-22-2000000002-22-20000002-22-2002-22-200000000002-22-22-22-20000000000000000
χ462-2-2-2222-222-22-2-2-2-2-222200002-22-2000000002-22-2000000-22-22002-22-20000000000-22-22-22-220000000000000000
χ472-2-2-2222-222-22-2-2-2-2-22220000-22-22000000002-22-20000002-2-2200-22-2200000000002-22-2-22-220000000000000000
χ482-2-2-2222-222-22-2-2-2-2-22220000-22-22000000002-22-2000000-222-200-22-220000000000-22-222-22-20000000000000000
χ492-2-2-2222-22-22-22-2-2-2-222200002-2-2200000000-22-2202-22-200000002-2-222-22-22-22-200000000000000000000000000
χ502-2-2-2222-22-22-22-2-2-2-222200002-2-2200000000-22-220-22-2200000002-2-22-22-22-22-2200000000000000000000000000
χ512-2-2-2222-22-22-22-2-2-2-22220000-222-200000000-22-2202-2-220000000-222-22-22-2-22-2200000000000000000000000000
χ522-2-2-2222-22-22-22-2-2-2-22220000-222-200000000-22-220-222-20000000-222-2-22-222-22-200000000000000000000000000
χ532-2-2-2222-2-12-22-21111-1-1-100002-22-2−i3i3−i3i3−i3i3−i3i3-11-110000002-22-2−i3i3-11-11−i3i3i3−i3−i3i3i3−i3−i3i3-11-11-11-110000000000000000
χ542-2-2-2222-2-12-22-21111-1-1-100002-22-2−i3i3−i3i3−i3i3−i3i3-11-11000000-22-22−i3i3-11-11i3−i3−i3i3i3−i3−i3i3−i3i31-11-11-11-10000000000000000
χ552-2-2-2222-2-12-22-21111-1-1-100002-22-2i3−i3i3−i3i3−i3i3−i3-11-110000002-22-2i3−i3-11-11i3−i3−i3i3i3−i3−i3i3i3−i3-11-11-11-110000000000000000
χ562-2-2-2222-2-12-22-21111-1-1-100002-22-2i3−i3i3−i3i3−i3i3−i3-11-11000000-22-22i3−i3-11-11−i3i3i3−i3−i3i3i3−i3i3−i31-11-11-11-10000000000000000
χ572-2-2-2222-2-12-22-21111-1-1-10000-22-22−i3i3−i3i3−i3i3−i3i3-11-110000002-2-22i3−i31-11-1−i3i3i3−i3i3−i3−i3i3i3−i3-11-111-11-10000000000000000
χ582-2-2-2222-2-12-22-21111-1-1-10000-22-22−i3i3−i3i3−i3i3−i3i3-11-11000000-222-2i3−i31-11-1i3−i3−i3i3−i3i3i3−i3i3−i31-11-1-11-110000000000000000
χ592-2-2-2222-2-12-22-21111-1-1-10000-22-22i3−i3i3−i3i3−i3i3−i3-11-110000002-2-22−i3i31-11-1i3−i3−i3i3−i3i3i3−i3−i3i3-11-111-11-10000000000000000
χ602-2-2-2222-2-12-22-21111-1-1-10000-22-22i3−i3i3−i3i3−i3i3−i3-11-11000000-222-2−i3i31-11-1−i3i3i3−i3i3−i3−i3i3−i3i31-11-1-11-110000000000000000
χ612-2-2-2222-2-1-22-221111-1-1-100002-2-22−i3i3−i3i3i3−i3i3−i31-11-102-22-200000−i3i3-111-1-11-11-11-11i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ622-2-2-2222-2-1-22-221111-1-1-100002-2-22−i3i3−i3i3i3−i3i3−i31-11-10-22-2200000−i3i3-111-11-11-11-11-1i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ632-2-2-2222-2-1-22-221111-1-1-100002-2-22i3−i3i3−i3−i3i3−i3i31-11-102-22-200000i3−i3-111-1-11-11-11-11−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ642-2-2-2222-2-1-22-221111-1-1-100002-2-22i3−i3i3−i3−i3i3−i3i31-11-10-22-2200000i3−i3-111-11-11-11-11-1−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ652-2-2-2222-2-1-22-221111-1-1-10000-222-2−i3i3−i3i3i3−i3i3−i31-11-102-2-2200000i3−i31-1-11-11-111-11-1−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ662-2-2-2222-2-1-22-221111-1-1-10000-222-2−i3i3−i3i3i3−i3i3−i31-11-10-222-200000i3−i31-1-111-11-1-11-11−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ672-2-2-2222-2-1-22-221111-1-1-10000-222-2i3−i3i3−i3−i3i3−i3i31-11-102-2-2200000−i3i31-1-11-11-111-11-1i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ682-2-2-2222-2-1-22-221111-1-1-10000-222-2i3−i3i3−i3−i3i3−i3i31-11-10-222-200000−i3i31-1-111-11-1-11-11i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ69444-4-4-44-4-244-4-4-2-22222-24i−4i4i−4i0000−2i−2i2i2i−2i−2i2i2i-2-22200000000000000000000000000000000000000000000000000
χ70444-4-4-44-4-244-4-4-2-22222-2−4i4i−4i4i00002i2i−2i−2i2i2i−2i−2i-2-22200000000000000000000000000000000000000000000000000
χ71444-4-4-44-4-2-4-444-2-22222-24i−4i−4i4i0000−2i−2i2i2i2i2i−2i−2i22-2-200000000000000000000000000000000000000000000000000
χ72444-4-4-44-4-2-4-444-2-22222-2−4i4i4i−4i00002i2i−2i−2i−2i−2i2i2i22-2-200000000000000000000000000000000000000000000000000
χ7344-444-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ7444-444-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ7544-4-4-44-44400004-4-44-44-4000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ7644-4-4-44-44400004-4-44-44-40000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ774-444-44-4-440000-444-4-44-4000000000000000000000000000000000000000000000000000000000022−2222−2200000000
χ784-444-44-4-440000-444-4-44-40000000000000000000000000000000000000000000000000000000000−2222−222200000000
χ794-44-44-4-4440000-44-444-4-40000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ804-44-44-4-4440000-44-444-4-400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ814-4-44-4-44444-4-44-4-444-4-4400000000000000004-4-4400000000000000000000000000000000000000000000000000
χ824-4-44-4-4444-444-4-4-444-4-440000000000000000-444-400000000000000000000000000000000000000000000000000
χ834-4-44-4-444-24-4-4422-2-222-20000000023−23−232323−23−2323-222-200000000000000000000000000000000000000000000000000
χ844-4-44-4-444-24-4-4422-2-222-200000000−232323−23−232323−23-222-200000000000000000000000000000000000000000000000000
χ854-4-44-4-444-2-444-422-2-222-20000000023−23−2323−232323−232-2-2200000000000000000000000000000000000000000000000000
χ864-4-44-4-444-2-444-422-2-222-200000000−232323−2323−23−23232-2-2200000000000000000000000000000000000000000000000000
χ8788-888-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-88-8-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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