Finite Group Databasebeta

← Group #10898401

Character table — Group #10898401

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212121212122424242448484848
order12222222344446666666444444441212121212121212121212122244444444666612121212121212121212121212121212121212128888888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-111-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ61111111111111111111111-1-111-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11
χ71111111111111111111111-1-111-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-11-11
χ81111111111111111111111-1-111-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111-11-1
χ911111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ1011111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ1111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-111
χ1211111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11-1-1111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-111-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ17222222222-2-2-2-222222222222-2-2-2-2-2-2-2-22222-2-2-2-200200-20000000022-2-2-2-2220000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-22222-2-2-2-200-200200000000-2-22222-2-20000000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2-2-2222200-2002000000002222-2-2-2-20000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-2222200200-200000000-2-2-2-222220000000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-22-2-2-2-21111-1-1-1-1-1-1-1-11111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-1-1-1-111111111-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-222-2-2-2221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-11111111122-222-2-2-2-2-2-1-1-1-1-1-111-1-1111111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-111111111-2-2-2-2-2-222221111-1-111-1-111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111222-2-22-2-222-1-1-1-111-1-111-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-2-2222222-2-2111111-1-111-1-1-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-1111100200-20000−i3−i3i3i3-1-11111-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-1111100200-20000i3i3−i3−i3-1-11111-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-1111100-20020000−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-1111100-20020000i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-100-20020000−i3−i3i3i3-1-1-1-11111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-100-20020000i3i3−i3−i3-1-1-1-11111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-100200-20000−i3−i3i3i31111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-100200-20000i3i3−i3−i31111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3722-2-22-22-222-22-222-2-22-2-2002i−2i002i−2i22-2-2000000000000002-22i−2i00002i−2i002i−2i002-22-200002i−2i2i−2i0000000000000000
χ3822-2-22-22-222-22-222-2-22-2-2002i−2i002i−2i22-2-200000000000000-22−2i2i00002i−2i002i−2i00-22-220000−2i2i−2i2i0000000000000000
χ3922-2-22-22-222-22-222-2-22-2-200−2i2i00−2i2i22-2-2000000000000002-2−2i2i0000−2i2i00−2i2i002-22-20000−2i2i−2i2i0000000000000000
χ4022-2-22-22-222-22-222-2-22-2-200−2i2i00−2i2i22-2-200000000000000-222i−2i0000−2i2i00−2i2i00-22-2200002i−2i2i−2i0000000000000000
χ4122-2-22-22-22-22-2222-2-22-2-2002i−2i00−2i2i-2-222000000002-202i−2i000002-22-22i−2i00−2i2i0000002i−2i2i−2i00000000000000000000
χ4222-2-22-22-22-22-2222-2-22-2-2002i−2i00−2i2i-2-22200000000-220−2i2i00000-22-222i−2i00−2i2i000000−2i2i−2i2i00000000000000000000
χ4322-2-22-22-22-22-2222-2-22-2-200−2i2i002i−2i-2-222000000002-20−2i2i000002-22-2−2i2i002i−2i000000−2i2i−2i2i00000000000000000000
χ4422-2-22-22-22-22-2222-2-22-2-200−2i2i002i−2i-2-22200000000-2202i−2i00000-22-22−2i2i002i−2i0000002i−2i2i−2i00000000000000000000
χ4522-2-22-22-2-12-22-2-1-111-111002i−2i002i−2i-1-111−i3−i3i3i3−i3−i3i3i30000002-22i−2i−i3i3i3−i3−ii3−3−ii3−3-11-113−3−33−ii−ii0000000000000000
χ4622-2-22-22-2-12-22-2-1-111-111002i−2i002i−2i-1-111−i3−i3i3i3−i3−i3i3i3000000-22−2i2ii3−i3−i3i3−ii3−3−ii3−31-11-1−333−3i−ii−i0000000000000000
χ4722-2-22-22-2-12-22-2-1-111-111002i−2i002i−2i-1-111i3i3−i3−i3i3i3−i3−i30000002-22i−2ii3−i3−i3i3−ii−33−ii−33-11-11−333−3−ii−ii0000000000000000
χ4822-2-22-22-2-12-22-2-1-111-111002i−2i002i−2i-1-111i3i3−i3−i3i3i3−i3−i3000000-22−2i2i−i3i3i3−i3−ii−33−ii−331-11-13−3−33i−ii−i0000000000000000
χ4922-2-22-22-2-12-22-2-1-111-11100−2i2i00−2i2i-1-111−i3−i3i3i3−i3−i3i3i30000002-2−2i2i−i3i3i3−i3i−i−33i−i−33-11-11−333−3i−ii−i0000000000000000
χ5022-2-22-22-2-12-22-2-1-111-11100−2i2i00−2i2i-1-111−i3−i3i3i3−i3−i3i3i3000000-222i−2ii3−i3−i3i3i−i−33i−i−331-11-13−3−33−ii−ii0000000000000000
χ5122-2-22-22-2-12-22-2-1-111-11100−2i2i00−2i2i-1-111i3i3−i3−i3i3i3−i3−i30000002-2−2i2ii3−i3−i3i3i−i3−3i−i3−3-11-113−3−33i−ii−i0000000000000000
χ5222-2-22-22-2-12-22-2-1-111-11100−2i2i00−2i2i-1-111i3i3−i3−i3i3i3−i3−i3000000-222i−2i−i3i3i3−i3i−i3−3i−i3−31-11-1−333−3−ii−ii0000000000000000
χ5322-2-22-22-2-1-22-22-1-111-111002i−2i00−2i2i11-1-1−i3−i3i3i3i3i3−i3−i32-202i−2i00000-11-11−ii−33i−i3−3−i3i3i3−i3−ii−ii3−3−330000000000000000
χ5422-2-22-22-2-1-22-22-1-111-111002i−2i00−2i2i11-1-1−i3−i3i3i3i3i3−i3−i3-220−2i2i000001-11-1−ii−33i−i3−3i3−i3−i3i3i−ii−i−333−30000000000000000
χ5522-2-22-22-2-1-22-22-1-111-111002i−2i00−2i2i11-1-1i3i3−i3−i3−i3−i3i3i32-202i−2i00000-11-11−ii3−3i−i−33i3−i3−i3i3−ii−ii−333−30000000000000000
χ5622-2-22-22-2-1-22-22-1-111-111002i−2i00−2i2i11-1-1i3i3−i3−i3−i3−i3i3i3-220−2i2i000001-11-1−ii3−3i−i−33−i3i3i3−i3i−ii−i3−3−330000000000000000
χ5722-2-22-22-2-1-22-22-1-111-11100−2i2i002i−2i11-1-1−i3−i3i3i3i3i3−i3−i32-20−2i2i00000-11-11i−i3−3−ii−33−i3i3i3−i3i−ii−i−333−30000000000000000
χ5822-2-22-22-2-1-22-22-1-111-11100−2i2i002i−2i11-1-1−i3−i3i3i3i3i3−i3−i3-2202i−2i000001-11-1i−i3−3−ii−33i3−i3−i3i3−ii−ii3−3−330000000000000000
χ5922-2-22-22-2-1-22-22-1-111-11100−2i2i002i−2i11-1-1i3i3−i3−i3−i3−i3i3i32-20−2i2i00000-11-11i−i−33−ii3−3i3−i3−i3i3i−ii−i3−3−330000000000000000
χ6022-2-22-22-2-1-22-22-1-111-11100−2i2i002i−2i11-1-1i3i3−i3−i3−i3−i3i3i3-2202i−2i000001-11-1i−i−33−ii3−3−i3i3i3−i3−ii−ii−333−30000000000000000
χ612-2-2222-2-222-2-222-22-2-22-22i−2i002i−2i002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000022-2-2002i−2i0000
χ622-2-2222-2-222-2-222-22-2-22-22i−2i002i−2i002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000-2-22200−2i2i0000
χ632-2-2222-2-222-2-222-22-2-22-2−2i2i00−2i2i002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000022-2-200−2i2i0000
χ642-2-2222-2-222-2-222-22-2-22-2−2i2i00−2i2i002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000-2-222002i−2i0000
χ652-2-2222-2-22-222-22-22-2-22-22i−2i00−2i2i00-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000022-2-200002i−2i000000
χ662-2-2222-2-22-222-22-22-2-22-22i−2i00−2i2i00-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000-2-2220000−2i2i000000
χ672-2-2222-2-22-222-22-22-2-22-2−2i2i002i−2i00-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000022-2-20000−2i2i000000
χ682-2-2222-2-22-222-22-22-2-22-2−2i2i002i−2i00-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000-2-22200002i−2i000000
χ69444-4-44-4-440000-4444-4-4-400000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ70444-4-44-4-440000-4444-4-4-4000000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ7144-44-4-4-4440000-44-4-4-4440000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ7244-44-4-4-4440000-44-4-4-44400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ734-444-4-44-440000-4-4-4444-40000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ744-444-4-44-440000-4-4-4444-400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ754-44-44-4-44444-4-44-4-44-4-44000000004-4-440000000000000000000000000000000000000000000000000000000000
χ764-44-44-4-444-4-4444-4-44-4-4400000000-444-40000000000000000000000000000000000000000000000000000000000
χ774-44-44-4-44-244-4-4-222-222-200000000-222-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ784-44-44-4-44-244-4-4-222-222-200000000-222-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ794-44-44-4-44-2-4-444-222-222-2000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ804-44-44-4-44-2-4-444-222-222-2000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-24-4-44-22-222-224i−4i004i−4i00-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-24-4-44-22-222-22−4i4i00−4i4i00-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ834-4-4444-4-4-2-444-4-22-222-224i−4i00−4i4i002-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ844-4-4444-4-4-2-444-4-22-222-22−4i4i004i−4i002-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ854-4-4-4-444440000-4-44-44-4400000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ864-4-4-4-444440000-4-44-44-44000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ87888-8-88-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-8-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-8-88-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8-8888-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

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