Finite Group Databasebeta

← Group #10827623

Character table — Group #10827623

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666224444446666121212121212121244444488881212121212121212121212121212121224242424242424242244444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ71111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-11111-1-1
χ81111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-111
χ911111111111111111111-1-11111-1-1-1-1-1-1111-1-1-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-11-1
χ1011111111111111111111-1-11111-1-1-1-1-1-1111-1-1-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-111-11
χ1111111111111111111111-1-11111-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1111-1-1-1-111-11
χ1211111111111111111111-1-11111-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-1-11111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-111111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-1111-1
χ17222222222-2-2-2-22222222220000-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000022-2-2200-200000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-222-200200000000
χ19222222222-2-2-2-22222222-2-2000022-2-2-2-2-2-2-22222-200000000000000000000000000000000002222-200-200000000
χ20222222222-2-2-2-22222222-2-2000022-2-2-2-2-2-2-22222-20000000000000000000000000000000000-2-2-2-2200200000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-21111-1-1-11111-1-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-21111-1-1-11111-1-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-12222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-122-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2922-2-22-2-2222-22-222-2-2-2-22002i2i−2i−2i00000022-20000-200002-2002i−2i2i2i−2i−2i0000000022-2-200002i2i−2i−2i0000000000000000
χ3022-2-22-2-2222-22-222-2-2-2-22002i2i−2i−2i00000022-20000-20000-2200−2i2i2i2i−2i−2i00000000-2-2220000−2i−2i2i2i0000000000000000
χ3122-2-22-2-2222-22-222-2-2-2-2200−2i−2i2i2i00000022-20000-200002-200−2i2i−2i−2i2i2i0000000022-2-20000−2i−2i2i2i0000000000000000
χ3222-2-22-2-2222-22-222-2-2-2-2200−2i−2i2i2i00000022-20000-20000-22002i−2i−2i−2i2i2i00000000-2-22200002i2i−2i−2i0000000000000000
χ3322-2-22-2-22-12-22-2-1-11111-1002i2i−2i−2i00−i3−i3i3i3-1-11−i3−i3i3i3100002-2002i−2i−i−iii33−3−3−i3−i3i3i3-1-11133−3−3−i−iii0000000000000000
χ3422-2-22-2-22-12-22-2-1-11111-1002i2i−2i−2i00−i3−i3i3i3-1-11−i3−i3i3i310000-2200−2i2i−i−iii33−3−3i3i3−i3−i311-1-1−3−333ii−i−i0000000000000000
χ3522-2-22-2-22-12-22-2-1-11111-1002i2i−2i−2i00i3i3−i3−i3-1-11i3i3−i3−i3100002-2002i−2i−i−iii−3−333i3i3−i3−i3-1-111−3−333−i−iii0000000000000000
χ3622-2-22-2-22-12-22-2-1-11111-1002i2i−2i−2i00i3i3−i3−i3-1-11i3i3−i3−i310000-2200−2i2i−i−iii−3−333−i3−i3i3i311-1-133−3−3ii−i−i0000000000000000
χ3722-2-22-2-22-12-22-2-1-11111-100−2i−2i2i2i00−i3−i3i3i3-1-11−i3−i3i3i3100002-200−2i2iii−i−i−3−333−i3−i3i3i3-1-111−3−333ii−i−i0000000000000000
χ3822-2-22-2-22-12-22-2-1-11111-100−2i−2i2i2i00−i3−i3i3i3-1-11−i3−i3i3i310000-22002i−2iii−i−i−3−333i3i3−i3−i311-1-133−3−3−i−iii0000000000000000
χ3922-2-22-2-22-12-22-2-1-11111-100−2i−2i2i2i00i3i3−i3−i3-1-11i3i3−i3−i3100002-200−2i2iii−i−i33−3−3i3i3−i3−i3-1-11133−3−3ii−i−i0000000000000000
χ4022-2-22-2-22-12-22-2-1-11111-100−2i−2i2i2i00i3i3−i3−i3-1-11i3i3−i3−i310000-22002i−2iii−i−i33−3−3−i3−i3i3i311-1-1−3−333−i−iii0000000000000000
χ412-22-2-22-2222-2-22-2-222-2-22002i−2i2i−2i0000002-220000-2002-2002i−2i002i−2i2i−2i00002-22-200002i−2i2i−2i00000000000000000000
χ422-22-2-22-2222-2-22-2-222-2-22002i−2i2i−2i0000002-220000-200-2200−2i2i002i−2i2i−2i0000-22-220000−2i2i−2i2i00000000000000000000
χ432-22-2-22-2222-2-22-2-222-2-2200−2i2i−2i2i0000002-220000-2002-200−2i2i00−2i2i−2i2i00002-22-20000−2i2i−2i2i00000000000000000000
χ442-22-2-22-2222-2-22-2-222-2-2200−2i2i−2i2i0000002-220000-200-22002i−2i00−2i2i−2i2i0000-22-2200002i−2i2i−2i00000000000000000000
χ452-22-2-22-22-12-2-2211-1-111-1002i−2i2i−2i00−i3i3−i3i3-11-1−i3i3−i3i31002-2002i−2i00−ii−ii3−33−3-11-11−i3i3−i3i3−ii−ii3−33−30000000000000000
χ462-22-2-22-22-12-2-2211-1-111-1002i−2i2i−2i00−i3i3−i3i3-11-1−i3i3−i3i3100-2200−2i2i00−ii−ii3−33−31-11-1i3−i3i3−i3i−ii−i−33−330000000000000000
χ472-22-2-22-22-12-2-2211-1-111-1002i−2i2i−2i00i3−i3i3−i3-11-1i3−i3i3−i31002-2002i−2i00−ii−ii−33−33-11-11i3−i3i3−i3−ii−ii−33−330000000000000000
χ482-22-2-22-22-12-2-2211-1-111-1002i−2i2i−2i00i3−i3i3−i3-11-1i3−i3i3−i3100-2200−2i2i00−ii−ii−33−331-11-1−i3i3−i3i3i−ii−i3−33−30000000000000000
χ492-22-2-22-22-12-2-2211-1-111-100−2i2i−2i2i00−i3i3−i3i3-11-1−i3i3−i3i31002-200−2i2i00i−ii−i−33−33-11-11−i3i3−i3i3i−ii−i−33−330000000000000000
χ502-22-2-22-22-12-2-2211-1-111-100−2i2i−2i2i00−i3i3−i3i3-11-1−i3i3−i3i3100-22002i−2i00i−ii−i−33−331-11-1i3−i3i3−i3−ii−ii3−33−30000000000000000
χ512-22-2-22-22-12-2-2211-1-111-100−2i2i−2i2i00i3−i3i3−i3-11-1i3−i3i3−i31002-200−2i2i00i−ii−i3−33−3-11-11i3−i3i3−i3i−ii−i3−33−30000000000000000
χ522-22-2-22-22-12-2-2211-1-111-100−2i2i−2i2i00i3−i3i3−i3-11-1i3−i3i3−i3100-22002i−2i00i−ii−i3−33−31-11-1−i3i3−i3i3−ii−ii−33−330000000000000000
χ532-2-22-2-222222-2-2-2-2-2-22222-22-2-222-22-2-222-2-22-2-2222-2000000002-2-222-2-2200000000000000000000000000000000
χ542-2-22-2-222222-2-2-2-2-2-22222-2-222-22-22-2-222-2-22-2-222-2200000000-222-2-222-200000000000000000000000000000000
χ552-2-22-2-222222-2-2-2-2-2-2222-222-2-22-22-222-22-2-2-222-22-22000000002-2-22-222-200000000000000000000000000000000
χ562-2-22-2-222222-2-2-2-2-2-2222-22-222-2-22-222-22-2-2-222-222-200000000-222-22-2-2200000000000000000000000000000000
χ572-2-22-2-2222-2-222-2-2-2-22222-20000-222-2-22-222-222-2-20000000000000000000000000000000000000002-202-2000000
χ582-2-22-2-2222-2-222-2-2-2-22222-20000-222-2-22-222-222-2-2000000000000000000000000000000000000000-220-22000000
χ592-2-22-2-2222-2-222-2-2-2-2222-2200002-2-222-2-2222-2-22-20000000000000000000000000000000000000002-20-22000000
χ602-2-22-2-2222-2-222-2-2-2-2222-2200002-2-222-2-2222-2-22-2000000000000000000000000000000000000000-2202-2000000
χ612-2-22-2-222-122-2-21111-1-1-12-22-2-222-2-111-1-111-111-1-12-200000000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ622-2-22-2-222-122-2-21111-1-1-12-22-2-222-2-111-1-111-111-1-12-200000000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ632-2-22-2-222-122-2-21111-1-1-12-2-222-22-2-111-1-111-111-1-1-22000000001-1-111-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ642-2-22-2-222-122-2-21111-1-1-12-2-222-22-2-111-1-111-111-1-1-22000000001-1-111-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ652-2-22-2-222-122-2-21111-1-1-1-222-2-22-221-1-11-1111-1-11-1-2200000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ662-2-22-2-222-122-2-21111-1-1-1-222-2-22-221-1-11-1111-1-11-1-2200000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ672-2-22-2-222-122-2-21111-1-1-1-22-222-2-221-1-11-1111-1-11-12-2000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ682-2-22-2-222-122-2-21111-1-1-1-22-222-2-221-1-11-1111-1-11-12-2000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2440000-4-4-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000442222222-2-2-2-2200000000000000000000000000000000000000000000000000
χ71444-4-4-44-4400004-44-44-4-40000000000000000000000000000000000000000000000000000004-400000000000000
χ72444-4-4-44-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ7344-44-44-4-4400004-4-44-44-400000000000000000000000000000000000000000000000000000000000000000022−2200
χ7444-44-44-4-4400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000−222200
χ7544-4-44-4-444-44-4444-4-4-4-44000000000000-4-440000400000000000000000000000000000000000000000000000000
χ7644-4-44-4-44-2-44-44-2-22222-200000000−2i3−2i32i32i322-22i32i3−2i3−2i3-200000000000000000000000000000000000000000000000000
χ7744-4-44-4-44-2-44-44-2-22222-2000000002i32i3−2i3−2i322-2−2i3−2i32i32i3-200000000000000000000000000000000000000000000000000
χ784-4444-4-4-440000-444-4-44-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ794-4444-4-4-440000-444-4-44-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ804-44-4-44-444-444-4-4-444-4-44000000000000-44-40000400000000000000000000000000000000000000000000000000
χ814-44-4-44-44-2-444-422-2-222-200000000−2i32i3−2i32i32-222i3−2i32i3−2i3-200000000000000000000000000000000000000000000000000
χ824-44-4-44-44-2-444-422-2-222-2000000002i3−2i32i3−2i32-22−2i32i3−2i32i3-200000000000000000000000000000000000000000000000000
χ834-4-44-4-444-2-4-4442222-2-2-24-40000-44-222-22-2-22-2-22200000000000000000000000000000000000000000000000000
χ844-4-44-4-444-2-4-4442222-2-2-2-4400004-42-2-222-2-2-222-2200000000000000000000000000000000000000000000000000
χ854-4-4-4444-440000-44-444-4-4000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ864-4-4-4444-440000-44-444-4-400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ87888-8-8-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-88-88-8-8-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-8888-8-8-8-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8888-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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