Finite Group Databasebeta

← Group #10853225

Character table — Group #10853225

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666224444446666121212121212121244444488881212121212121212121212121212121224242424242424244444444444888844
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
χ5111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-11111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-111
χ911111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1-11
χ1011111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-1111-1
χ1111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1111-1-1-1-1111-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-1-11111-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-111111-1-11-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-111-11
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-2000000000000000000000000000000000022-2-2200-200000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-222-200200000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-22222-200000000000000000000000000000000002222-200-200000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-22222-20000000000000000000000000000000000-2-2-2-2200200000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-11111-1-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222221111-1-1-11111-1-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
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
χ292222-2-2-2-2222-2-2-2-2-2222-22-22-222-2-222-2-222-222-2-2-22-20000000022-2-222-2-200000000000000000000000000000000
χ302222-2-2-2-2222-2-2-2-2-2222-22-22-2-2-22222-2-222-222-2-2-2-2200000000-2-222-2-22200000000000000000000000000000000
χ312222-2-2-2-2222-2-2-2-2-2222-2-22-2222-2-2-2-22222-2-2-222-2-220000000022-2-2-2-22200000000000000000000000000000000
χ322222-2-2-2-2222-2-2-2-2-2222-2-22-22-2-222-2-22222-2-2-222-22-200000000-2-22222-2-200000000000000000000000000000000
χ332222-2-2-2-22-2-222-2-2-2222-22-2-22000022-2-2-2-22-2-22220000000000000000000000000000000000000002i−2i02i−2i000000
χ342222-2-2-2-22-2-222-2-2-2222-22-2-22000022-2-2-2-22-2-2222000000000000000000000000000000000000000−2i2i0−2i2i000000
χ352222-2-2-2-22-2-222-2-2-2222-2-222-20000-2-222-2-2222-2-220000000000000000000000000000000000000002i−2i0−2i2i000000
χ362222-2-2-2-22-2-222-2-2-2222-2-222-20000-2-222-2-2222-2-22000000000000000000000000000000000000000−2i2i02i−2i000000
χ372222-2-2-2-2-122-2-2111-1-1-112-22-222-2-2-1-111-1-11-1-11112-200000000-1-111-1-11133−3−333−3−333−3−333−3−30000000000000000
χ382222-2-2-2-2-122-2-2111-1-1-112-22-222-2-2-1-111-1-11-1-11112-200000000-1-111-1-111−3−333−3−333−3−333−3−3330000000000000000
χ392222-2-2-2-2-122-2-2111-1-1-112-22-2-2-222-1-111-1-11-1-1111-220000000011-1-111-1-133−3−333−3−3−3−333−3−3330000000000000000
χ402222-2-2-2-2-122-2-2111-1-1-112-22-2-2-222-1-111-1-11-1-1111-220000000011-1-111-1-1−3−333−3−33333−3−333−3−30000000000000000
χ412222-2-2-2-2-122-2-2111-1-1-11-22-2222-2-211-1-1-1-1111-1-11-2200000000-1-11111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ422222-2-2-2-2-122-2-2111-1-1-11-22-2222-2-211-1-1-1-1111-1-11-2200000000-1-11111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ432222-2-2-2-2-122-2-2111-1-1-11-22-22-2-22211-1-1-1-1111-1-112-20000000011-1-1-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ442222-2-2-2-2-122-2-2111-1-1-11-22-22-2-22211-1-1-1-1111-1-112-20000000011-1-1-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ4522-2-22-2-2222-2-2222-22-2-2-200002i−2i2i−2i00002-2-20000200002i−2i002-22i−2i2i−2i000000002i−2i2i−2i00002-22-20000000000000000
χ4622-2-22-2-2222-2-2222-22-2-2-200002i−2i2i−2i00002-2-2000020000−2i2i00-222i−2i2i−2i00000000−2i2i−2i2i0000-22-220000000000000000
χ4722-2-22-2-2222-2-2222-22-2-2-20000−2i2i−2i2i00002-2-20000200002i−2i00-22−2i2i−2i2i000000002i−2i2i−2i0000-22-220000000000000000
χ4822-2-22-2-2222-2-2222-22-2-2-20000−2i2i−2i2i00002-2-2000020000−2i2i002-2−2i2i−2i2i00000000−2i2i−2i2i00002-22-20000000000000000
χ4922-2-22-2-22-12-2-22-1-11-111100002i−2i2i−2i−i3i3−i3i3-111−i3i3−i3i3-100002i−2i002-2−ii−ii3−33−33−33−3−ii−ii−i3i3−i3i3-11-110000000000000000
χ5022-2-22-2-22-12-2-22-1-11-111100002i−2i2i−2i−i3i3−i3i3-111−i3i3−i3i3-10000−2i2i00-22−ii−ii3−33−3−33−33i−ii−ii3−i3i3−i31-11-10000000000000000
χ5122-2-22-2-22-12-2-22-1-11-111100002i−2i2i−2ii3−i3i3−i3-111i3−i3i3−i3-100002i−2i002-2−ii−ii−33−33−33−33−ii−iii3−i3i3−i3-11-110000000000000000
χ5222-2-22-2-22-12-2-22-1-11-111100002i−2i2i−2ii3−i3i3−i3-111i3−i3i3−i3-10000−2i2i00-22−ii−ii−33−333−33−3i−ii−i−i3i3−i3i31-11-10000000000000000
χ5322-2-22-2-22-12-2-22-1-11-11110000−2i2i−2i2i−i3i3−i3i3-111−i3i3−i3i3-100002i−2i00-22i−ii−i−33−333−33−3−ii−iii3−i3i3−i31-11-10000000000000000
χ5422-2-22-2-22-12-2-22-1-11-11110000−2i2i−2i2i−i3i3−i3i3-111−i3i3−i3i3-10000−2i2i002-2i−ii−i−33−33−33−33i−ii−i−i3i3−i3i3-11-110000000000000000
χ5522-2-22-2-22-12-2-22-1-11-11110000−2i2i−2i2ii3−i3i3−i3-111i3−i3i3−i3-100002i−2i00-22i−ii−i3−33−3−33−33−ii−ii−i3i3−i3i31-11-10000000000000000
χ5622-2-22-2-22-12-2-22-1-11-11110000−2i2i−2i2ii3−i3i3−i3-111i3−i3i3−i3-10000−2i2i002-2i−ii−i3−33−33−33−3i−ii−ii3−i3i3−i3-11-110000000000000000
χ5722-2-2-222-222-22-2-2-222-2-2200002i−2i−2i2i00002-220000-2002-2002i−2i002i−2i−2i2i00002-2-220000−2i2i2i−2i00000000000000000000
χ5822-2-2-222-222-22-2-2-222-2-2200002i−2i−2i2i00002-220000-200-2200−2i2i002i−2i−2i2i0000-222-200002i−2i−2i2i00000000000000000000
χ5922-2-2-222-222-22-2-2-222-2-220000−2i2i2i−2i00002-220000-2002-200−2i2i00−2i2i2i−2i00002-2-2200002i−2i−2i2i00000000000000000000
χ6022-2-2-222-222-22-2-2-222-2-220000−2i2i2i−2i00002-220000-200-22002i−2i00−2i2i2i−2i0000-222-20000−2i2i2i−2i00000000000000000000
χ6122-2-2-222-2-12-22-211-1-111-100002i−2i−2i2i−i3i3i3−i3-11-1−i3i3i3−i31002-2002i−2i00−iii−i3−3−33-111-1−i3i3i3−i3i−i−ii−333−30000000000000000
χ6222-2-2-222-2-12-22-211-1-111-100002i−2i−2i2i−i3i3i3−i3-11-1−i3i3i3−i3100-2200−2i2i00−iii−i3−3−331-1-11i3−i3−i3i3−iii−i3−3−330000000000000000
χ6322-2-2-222-2-12-22-211-1-111-100002i−2i−2i2ii3−i3−i3i3-11-1i3−i3−i3i31002-2002i−2i00−iii−i−333−3-111-1i3−i3−i3i3i−i−ii3−3−330000000000000000
χ6422-2-2-222-2-12-22-211-1-111-100002i−2i−2i2ii3−i3−i3i3-11-1i3−i3−i3i3100-2200−2i2i00−iii−i−333−31-1-11−i3i3i3−i3−iii−i−333−30000000000000000
χ6522-2-2-222-2-12-22-211-1-111-10000−2i2i2i−2i−i3i3i3−i3-11-1−i3i3i3−i31002-200−2i2i00i−i−ii−333−3-111-1−i3i3i3−i3−iii−i3−3−330000000000000000
χ6622-2-2-222-2-12-22-211-1-111-10000−2i2i2i−2i−i3i3i3−i3-11-1−i3i3i3−i3100-22002i−2i00i−i−ii−333−31-1-11i3−i3−i3i3i−i−ii−333−30000000000000000
χ6722-2-2-222-2-12-22-211-1-111-10000−2i2i2i−2ii3−i3−i3i3-11-1i3−i3−i3i31002-200−2i2i00i−i−ii3−3−33-111-1i3−i3−i3i3−iii−i−333−30000000000000000
χ6822-2-2-222-2-12-22-211-1-111-10000−2i2i2i−2ii3−i3−i3i3-11-1i3−i3−i3i3100-22002i−2i00i−i−ii3−3−331-1-11−i3i3i3−i3i−i−ii3−3−330000000000000000
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
χ714444-4-4-4-4-2-4-444222-2-2-224-4-440000-2-22222-222-2-2-200000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4-444222-2-2-22-444-4000022-2-222-2-2-222-200000000000000000000000000000000000000000000000000
χ7344-4-44-4-444-444-444-44-4-4-4000000000000-4440000-400000000000000000000000000000000000000000000000000
χ7444-4-44-4-44-2-444-4-2-22-222200000000−2i32i3−2i32i32-2-22i3−2i32i3−2i3200000000000000000000000000000000000000000000000000
χ7544-4-44-4-44-2-444-4-2-22-2222000000002i3−2i32i3−2i32-2-2−2i32i3−2i32i3200000000000000000000000000000000000000000000000000
χ7644-4-4-444-44-44-44-4-444-4-44000000000000-44-40000400000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-2-44-4422-2-222-200000000−2i32i32i3−2i32-222i3−2i3−2i32i3-200000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-2-44-4422-2-222-2000000002i3−2i3−2i32i32-22−2i32i32i3−2i3-200000000000000000000000000000000000000000000000000
χ794-44-444-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ804-44-444-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ814-44-4-4-44440000-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000022−2200
χ824-44-4-4-44440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000−222200
χ834-4-444-44-4400004-4-4-4-444000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ844-4-444-44-4400004-4-4-4-44400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ854-4-44-44-4440000-444-4-44-40000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ864-4-44-44-4440000-444-4-44-4000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ878-88-888-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8-8-888-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-888-88-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000

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