Finite Group Databasebeta

← Group #10896433

Character table — Group #10896433

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order122222223444466666664444444412121212121212121212121244444444441212121212121212121212121212121212121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-222-2-2-2-2-2-22222-2-2-2-22-200000000-2-222-2-20000000022000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-22222-2-2-2-2-220000000022-2-22200000000-2-2000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2-2-22222-2200000000-2-2-2-2220000000022000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-222-2-2-2-2-2-2-2-222222-2000000002222-2-200000000-2-2000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2111111-1-1-1-1111111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2221111111111-1-1-1-1111111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-111111111-2-222-2-2-2-222-1-11111-1-1-1-11111-1-11111-1-1-1-10000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-111111111-2-2-2-22222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111110000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111222222-2-2-2-211-1-1-1-1-1-1-1-1-1-1-1-111111111110000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-2-2-2-2222211-1-1-1-11111111111-1-1-1-1-1-1-1-10000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-111112-20000000011-1-111−i3−i3i3i3−i3−i3i3i3-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-111112-20000000011-1-111i3i3−i3−i3i3i3−i3−i3-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-11111-2200000000-1-111-1-1−i3−i3i3i3i3i3−i3−i311−i3−i3i3i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-11111-2200000000-1-111-1-1i3i3−i3−i3−i3−i3i3i311i3i3−i3−i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-1-22000000001111-1-1−i3−i3i3i3i3i3−i3−i3-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-1-22000000001111-1-1i3i3−i3−i3−i3−i3i3i3-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-12-200000000-1-1-1-111−i3−i3i3i3−i3−i3i3i311i3i3−i3−i3i3i3−i3−i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-12-200000000-1-1-1-111i3i3−i3−i3i3i3−i3−i311−i3−i3i3i3−i3−i3i3i30000000000000000
χ37222-2-2-22-2222-2-2222-2-2-2-22-22-2000022-2-222-2-222-2-200000000000000000000000000000000002-22-2000000000000
χ38222-2-2-22-2222-2-2222-2-2-2-22-22-2000022-2-222-2-222-2-20000000000000000000000000000000000-22-22000000000000
χ39222-2-2-22-2222-2-2222-2-2-2-2-22-22000022-2-2-2-222-2-22200000000000000000000000000000000002-2-22000000000000
χ40222-2-2-22-2222-2-2222-2-2-2-2-22-22000022-2-2-2-222-2-2220000000000000000000000000000000000-222-2000000000000
χ41222-2-2-22-22-2-222222-2-2-2-22-2-220000-2-22222-2-2-2-222000000000000000000000000000000000000002i−2i2i−2i00000000
χ42222-2-2-22-22-2-222222-2-2-2-22-2-220000-2-22222-2-2-2-22200000000000000000000000000000000000000−2i2i−2i2i00000000
χ43222-2-2-22-22-2-222222-2-2-2-2-222-20000-2-222-2-22222-2-2000000000000000000000000000000000000002i−2i−2i2i00000000
χ44222-2-2-22-22-2-222222-2-2-2-2-222-20000-2-222-2-22222-2-200000000000000000000000000000000000000−2i2i2i−2i00000000
χ452-2-222-22-222-22-22-2-2-222-200002i−2i2i−2i2-22-20000000000002-22i−2i002i−2i000000002-22-22i−2i2i−2i2i−2i00000000000000000000
χ462-2-222-22-222-22-22-2-2-222-200002i−2i2i−2i2-22-2000000000000-22−2i2i002i−2i00000000-22-222i−2i−2i2i−2i2i00000000000000000000
χ472-2-222-22-222-22-22-2-2-222-20000−2i2i−2i2i2-22-20000000000002-2−2i2i00−2i2i000000002-22-2−2i2i−2i2i−2i2i00000000000000000000
χ482-2-222-22-222-22-22-2-2-222-20000−2i2i−2i2i2-22-2000000000000-222i−2i00−2i2i00000000-22-22−2i2i2i−2i2i−2i00000000000000000000
χ492-2-222-22-22-22-222-2-2-222-200002i−2i−2i2i-22-2200000000002-200002i−2i−2i2i00002-22-200002i−2i00002i−2i2i−2i0000000000000000
χ502-2-222-22-22-22-222-2-2-222-200002i−2i−2i2i-22-220000000000-220000−2i2i−2i2i0000-22-2200002i−2i0000−2i2i−2i2i0000000000000000
χ512-2-222-22-22-22-222-2-2-222-20000−2i2i2i−2i-22-2200000000002-20000−2i2i2i−2i00002-22-20000−2i2i0000−2i2i−2i2i0000000000000000
χ522-2-222-22-22-22-222-2-2-222-20000−2i2i2i−2i-22-220000000000-2200002i−2i2i−2i0000-22-220000−2i2i00002i−2i2i−2i0000000000000000
χ532-2-222-22-2-12-22-2-1111-1-1100002i−2i2i−2i-11-113−33−33−33−300002-22i−2i00−ii−i3i3−i3i3−i3i3i3−i3-11-11−ii−ii−ii3−3−330000000000000000
χ542-2-222-22-2-12-22-2-1111-1-1100002i−2i2i−2i-11-113−33−33−33−30000-22−2i2i00−ii−i3i3−i3i3i3−i3−i3i31-11-1−iii−ii−i−333−30000000000000000
χ552-2-222-22-2-12-22-2-1111-1-1100002i−2i2i−2i-11-11−33−33−33−3300002-22i−2i00−iii3−i3i3−i3i3−i3−i3i3-11-11−ii−ii−ii−333−30000000000000000
χ562-2-222-22-2-12-22-2-1111-1-1100002i−2i2i−2i-11-11−33−33−33−330000-22−2i2i00−iii3−i3i3−i3−i3i3i3−i31-11-1−iii−ii−i3−3−330000000000000000
χ572-2-222-22-2-12-22-2-1111-1-110000−2i2i−2i2i-11-113−33−33−33−300002-2−2i2i00i−ii3−i3i3−i3i3−i3−i3i3-11-11i−ii−ii−i3−3−330000000000000000
χ582-2-222-22-2-12-22-2-1111-1-110000−2i2i−2i2i-11-113−33−33−33−30000-222i−2i00i−ii3−i3i3−i3−i3i3i3−i31-11-1i−i−ii−ii−333−30000000000000000
χ592-2-222-22-2-12-22-2-1111-1-110000−2i2i−2i2i-11-11−33−33−33−3300002-2−2i2i00i−i−i3i3−i3i3−i3i3i3−i3-11-11i−ii−ii−i−333−30000000000000000
χ602-2-222-22-2-12-22-2-1111-1-110000−2i2i−2i2i-11-11−33−33−33−330000-222i−2i00i−i−i3i3−i3i3i3−i3−i3i31-11-1i−i−ii−ii3−3−330000000000000000
χ612-2-222-22-2-1-22-22-1111-1-1100002i−2i−2i2i1-11-13−33−3−33−33002-200002i−2ii−i−i3i3i3−i3-11-11−i3i3i3−i3−ii3−3−33−ii−ii0000000000000000
χ622-2-222-22-2-1-22-22-1111-1-1100002i−2i−2i2i1-11-13−33−3−33−3300-220000−2i2ii−i−i3i3i3−i31-11-1i3−i3−i3i3−ii−333−3i−ii−i0000000000000000
χ632-2-222-22-2-1-22-22-1111-1-1100002i−2i−2i2i1-11-1−33−333−33−3002-200002i−2ii−ii3−i3−i3i3-11-11i3−i3−i3i3−ii−333−3−ii−ii0000000000000000
χ642-2-222-22-2-1-22-22-1111-1-1100002i−2i−2i2i1-11-1−33−333−33−300-220000−2i2ii−ii3−i3−i3i31-11-1−i3i3i3−i3−ii3−3−33i−ii−i0000000000000000
χ652-2-222-22-2-1-22-22-1111-1-110000−2i2i2i−2i1-11-13−33−3−33−33002-20000−2i2i−iii3−i3−i3i3-11-11i3−i3−i3i3i−i3−3−33i−ii−i0000000000000000
χ662-2-222-22-2-1-22-22-1111-1-110000−2i2i2i−2i1-11-13−33−3−33−3300-2200002i−2i−iii3−i3−i3i31-11-1−i3i3i3−i3i−i−333−3−ii−ii0000000000000000
χ672-2-222-22-2-1-22-22-1111-1-110000−2i2i2i−2i1-11-1−33−333−33−3002-20000−2i2i−ii−i3i3i3−i3-11-11−i3i3i3−i3i−i−333−3i−ii−i0000000000000000
χ682-2-222-22-2-1-22-22-1111-1-110000−2i2i2i−2i1-11-1−33−333−33−300-2200002i−2i−ii−i3i3i3−i31-11-1i3−i3−i3i3i−i3−3−33−ii−ii0000000000000000
χ69444-4-4-44-4-244-4-4-2-2-222224-44-40000-2-222-2-222-2-22200000000000000000000000000000000000000000000000000
χ70444-4-4-44-4-244-4-4-2-2-22222-44-440000-2-22222-2-222-2-200000000000000000000000000000000000000000000000000
χ71444-4-4-44-4-2-4-444-2-2-222224-4-44000022-2-2-2-22222-2-200000000000000000000000000000000000000000000000000
χ72444-4-4-44-4-2-4-444-2-2-22222-444-4000022-2-222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7344-44-44-4-440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000−2i22i2
χ7444-44-44-4-440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ7544-4-44-4-4440000-44-44-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7644-4-44-4-4440000-44-44-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ774-444-4-4-4440000-4-4444-4-40000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ784-444-4-4-4440000-4-4444-4-400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ794-44-444-4-440000-4-44-4-44400000000000000000000000000000000000000000000000000000000000000−2i22i2000000
χ804-44-444-4-440000-4-44-4-444000000000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ814-4-4-4-444444-4-444-4-44-4-44000000004-4-440000000000000000000000000000000000000000000000000000000000
χ824-4-4-4-44444-444-44-4-44-4-4400000000-444-40000000000000000000000000000000000000000000000000000000000
χ834-4-4-4-4444-24-4-44-222-222-200000000-222-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ844-4-4-4-4444-24-4-44-222-222-200000000-222-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-2-444-4-222-222-2000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ864-4-4-4-4444-2-444-4-222-222-2000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ8788-88-88-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-88-8-88-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-8-8-88-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-8-4000044-444-4-40000000000000000000000000000000000000000000000000000000000000000000000

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