Finite Group Databasebeta

← Group #10827599

Character table — Group #10827599

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order1222222234444666666622444444666612121212121212122244446666888812121212121212121212121224242424242424242244444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-111-11
χ1211111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-11-1-11111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-1-11-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1111-1-1-1-1111-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-200000000000000000000000000000000002222-2-20000000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2220000000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-22222-2000000000000000000000000000000000022-2-2-220000000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-22222-20000000000000000000000000000000000-2-2222-20000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-2-222-1-1-1-1-2-2-2-211111111-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-11111-122-2-2-2-2-1-1-1-122-2-2-1-1-1-111111111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-11111-1-2-2-2-2221111-2-222-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-12222-2-2-1-1-1-1-2-2221111-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-1-2-22222111122-2-21111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ2922-2-22-22-222-22-222-2-2-22-200002i2i−2i−2i000022-20000-200002-20000002i−2i2i2i−2i−2i000022-2-200002i2i−2i−2i0000000000000000
χ3022-2-22-22-222-22-222-2-2-22-200002i2i−2i−2i000022-20000-20000-22000000−2i2i2i2i−2i−2i0000-2-2220000−2i−2i2i2i0000000000000000
χ3122-2-22-22-222-22-222-2-2-22-20000−2i−2i2i2i000022-20000-200002-2000000−2i2i−2i−2i2i2i000022-2-20000−2i−2i2i2i0000000000000000
χ3222-2-22-22-222-22-222-2-2-22-20000−2i−2i2i2i000022-20000-20000-220000002i−2i−2i−2i2i2i0000-2-22200002i2i−2i−2i0000000000000000
χ3322-2-22-22-2-12-22-2-1-1111-1100002i2i−2i−2i−i3−i3i3i3-1-11−i3−i3i3i3100002-2−i3−i3i3i3002i−2i−i−iii33−3−3-1-11133−3−3−i−iii0000000000000000
χ3422-2-22-22-2-12-22-2-1-1111-1100002i2i−2i−2i−i3−i3i3i3-1-11−i3−i3i3i310000-22i3i3−i3−i300−2i2i−i−iii33−3−311-1-1−3−333ii−i−i0000000000000000
χ3522-2-22-22-2-12-22-2-1-1111-1100002i2i−2i−2ii3i3−i3−i3-1-11i3i3−i3−i3100002-2i3i3−i3−i3002i−2i−i−iii−3−333-1-111−3−333−i−iii0000000000000000
χ3622-2-22-22-2-12-22-2-1-1111-1100002i2i−2i−2ii3i3−i3−i3-1-11i3i3−i3−i310000-22−i3−i3i3i300−2i2i−i−iii−3−33311-1-133−3−3ii−i−i0000000000000000
χ3722-2-22-22-2-12-22-2-1-1111-110000−2i−2i2i2i−i3−i3i3i3-1-11−i3−i3i3i3100002-2−i3−i3i3i300−2i2iii−i−i−3−333-1-111−3−333ii−i−i0000000000000000
χ3822-2-22-22-2-12-22-2-1-1111-110000−2i−2i2i2i−i3−i3i3i3-1-11−i3−i3i3i310000-22i3i3−i3−i3002i−2iii−i−i−3−33311-1-133−3−3−i−iii0000000000000000
χ3922-2-22-22-2-12-22-2-1-1111-110000−2i−2i2i2ii3i3−i3−i3-1-11i3i3−i3−i3100002-2i3i3−i3−i300−2i2iii−i−i33−3−3-1-11133−3−3ii−i−i0000000000000000
χ4022-2-22-22-2-12-22-2-1-1111-110000−2i−2i2i2ii3i3−i3−i3-1-11i3i3−i3−i310000-22−i3−i3i3i3002i−2iii−i−i33−3−311-1-1−3−333−i−iii0000000000000000
χ412-22-2-222-222-2-22-2-222-22-200002i−2i2i−2i00002-220000-22-200002-22-22i−2i002i−2i2i−2i000000002i−2i2i−2i00000000000000000000
χ422-22-2-222-222-2-22-2-222-22-200002i−2i2i−2i00002-220000-2-220000-22-22−2i2i002i−2i2i−2i00000000−2i2i−2i2i00000000000000000000
χ432-22-2-222-222-2-22-2-222-22-20000−2i2i−2i2i00002-220000-22-200002-22-2−2i2i00−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000
χ442-22-2-222-222-2-22-2-222-22-20000−2i2i−2i2i00002-220000-2-220000-22-222i−2i00−2i2i−2i2i000000002i−2i2i−2i00000000000000000000
χ452-22-2-222-2-12-2-2211-1-11-1100002i−2i2i−2i−i3i3−i3i3-11-1−i3i3−i3i312-20000-11-112i−2i00−ii−ii3−33−3−i3i3−i3i3−ii−ii3−33−30000000000000000
χ462-22-2-222-2-12-2-2211-1-11-1100002i−2i2i−2i−i3i3−i3i3-11-1−i3i3−i3i31-2200001-11-1−2i2i00−ii−ii3−33−3i3−i3i3−i3i−ii−i−33−330000000000000000
χ472-22-2-222-2-12-2-2211-1-11-1100002i−2i2i−2ii3−i3i3−i3-11-1i3−i3i3−i312-20000-11-112i−2i00−ii−ii−33−33i3−i3i3−i3−ii−ii−33−330000000000000000
χ482-22-2-222-2-12-2-2211-1-11-1100002i−2i2i−2ii3−i3i3−i3-11-1i3−i3i3−i31-2200001-11-1−2i2i00−ii−ii−33−33−i3i3−i3i3i−ii−i3−33−30000000000000000
χ492-22-2-222-2-12-2-2211-1-11-110000−2i2i−2i2i−i3i3−i3i3-11-1−i3i3−i3i312-20000-11-11−2i2i00i−ii−i−33−33−i3i3−i3i3i−ii−i−33−330000000000000000
χ502-22-2-222-2-12-2-2211-1-11-110000−2i2i−2i2i−i3i3−i3i3-11-1−i3i3−i3i31-2200001-11-12i−2i00i−ii−i−33−33i3−i3i3−i3−ii−ii3−33−30000000000000000
χ512-22-2-222-2-12-2-2211-1-11-110000−2i2i−2i2ii3−i3i3−i3-11-1i3−i3i3−i312-20000-11-11−2i2i00i−ii−i3−33−3i3−i3i3−i3i−ii−i3−33−30000000000000000
χ522-22-2-222-2-12-2-2211-1-11-110000−2i2i−2i2ii3−i3i3−i3-11-1i3−i3i3−i31-2200001-11-12i−2i00i−ii−i3−33−3−i3i3−i3i3−ii−ii−33−330000000000000000
χ532-2-22-2-222222-2-2-2-2-2-22222-22-22-2-222-2-222-2-22-2-222002-200000000002-2-222-2-220000000000000000000000000000
χ542-2-22-2-222222-2-2-2-2-2-22222-22-2-222-22-2-222-2-22-2-22200-220000000000-222-2-222-20000000000000000000000000000
χ552-2-22-2-222222-2-2-2-2-2-2222-22-222-2-22-222-22-2-2-222-2200-2200000000002-2-22-222-20000000000000000000000000000
χ562-2-22-2-222222-2-2-2-2-2-2222-22-22-222-2-222-22-2-2-222-22002-20000000000-222-22-2-220000000000000000000000000000
χ572-2-22-2-2222-2-222-2-2-2-22222-2-2200002-2-22-222-222-2-200000000000000000000000000000000000000002-22-2000000
χ582-2-22-2-2222-2-222-2-2-2-22222-2-2200002-2-22-222-222-2-20000000000000000000000000000000000000000-22-22000000
χ592-2-22-2-2222-2-222-2-2-2-2222-222-20000-222-2-2222-2-22-200000000000000000000000000000000000000002-2-22000000
χ602-2-22-2-2222-2-222-2-2-2-2222-222-20000-222-2-2222-2-22-20000000000000000000000000000000000000000-222-2000000
χ612-2-22-2-222-122-2-21111-1-1-12-22-22-2-22-111-1-111-111-1-1002-200−i3i3i3−i30000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ622-2-22-2-222-122-2-21111-1-1-12-22-22-2-22-111-1-111-111-1-1002-200i3−i3−i3i30000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ632-2-22-2-222-122-2-21111-1-1-12-22-2-222-2-111-1-111-111-1-100-2200−i3i3i3−i300001-1-111-1-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ642-2-22-2-222-122-2-21111-1-1-12-22-2-222-2-111-1-111-111-1-100-2200i3−i3−i3i300001-1-111-1-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ652-2-22-2-222-122-2-21111-1-1-1-22-222-2-221-1-11-1111-1-11-100-2200−i3i3i3−i30000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ662-2-22-2-222-122-2-21111-1-1-1-22-222-2-221-1-11-1111-1-11-100-2200i3−i3−i3i30000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ672-2-22-2-222-122-2-21111-1-1-1-22-22-222-21-1-11-1111-1-11-1002-200−i3i3i3−i300001-1-11-111-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ682-2-22-2-222-122-2-21111-1-1-1-22-22-222-21-1-11-1111-1-11-1002-200i3−i3−i3i300001-1-11-111-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44400002222222-2-2-2-2200000000000000000000000000000000000000000000000000
χ71444-4-4-4-44400004-44-4-4-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ72444-4-4-4-44400004-44-4-4-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7344-44-44-4-4400004-4-444-4-40000000000000000000000000000000000000000000000000000004-400000000000000
χ7444-44-44-4-4400004-4-444-4-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ7544-4-44-44-44-44-4444-4-4-44-4000000000000-4-440000400000000000000000000000000000000000000000000000000
χ7644-4-44-44-4-2-44-44-2-2222-2200000000−2i3−2i32i32i322-22i32i3−2i3−2i3-200000000000000000000000000000000000000000000000000
χ7744-4-44-44-4-2-44-44-2-2222-22000000002i32i3−2i3−2i322-2−2i3−2i32i32i3-200000000000000000000000000000000000000000000000000
χ784-4444-4-4-440000-444-44-4-4000000000000000000000000000000000000000000000000000000004-4000000000000
χ794-4444-4-4-440000-444-44-4-400000000000000000000000000000000000000000000000000000000-44000000000000
χ804-44-4-444-44-444-4-4-444-44-4000000000000-44-40000400000000000000000000000000000000000000000000000000
χ814-44-4-444-4-2-444-422-2-22-2200000000−2i32i3−2i32i32-222i3−2i32i3−2i3-200000000000000000000000000000000000000000000000000
χ824-44-4-444-4-2-444-422-2-22-22000000002i3−2i32i3−2i32-22−2i32i3−2i32i3-200000000000000000000000000000000000000000000000000
χ834-4-44-4-444-2-4-4442222-2-2-24-4-440000-222-22-2-22-2-22200000000000000000000000000000000000000000000000000
χ844-4-44-4-444-2-4-4442222-2-2-2-444-400002-2-222-2-2-222-2200000000000000000000000000000000000000000000000000
χ854-4-4-444-4440000-44-44-4-44000000000000000000000000000000000000000000000000000000000000000022−220000
χ864-4-4-444-4440000-44-44-4-440000000000000000000000000000000000000000000000000000000000000000−22220000
χ87888-8-8-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-88-88-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ898-8888-8-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000000000

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