Finite Group Databasebeta

← Group #10831728

Character table — Group #10831728

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666444444441212121212121212121212122244446666888812121212121212121212121224242424242424244444444444888844
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1-1-111-1-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1111-1-111-11
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1111-1-1-1-1-111-11
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-1-1-111111-1-11-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ1111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-11111-1-1
χ1211111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-1-11-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1111-1-1-1-1111-1
χ17222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000022-2-2-200200000000
χ18222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-222200-200000000
χ19222222222-2-2-2-222222220000-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000002222-200-200000000
χ20222222222-2-2-2-222222220000-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2200200000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-11111-1-122-2-2-2-2-1-1-1-122-2-2-1-1-1-111111111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-11111-1-1-2-2-2-2221111-2-222-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-2-222-1-1-1-1-2-2-2-211111111-1-1-1-1111111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-12222-2-2-1-1-1-1-2-2221111-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-1-2-22222111122-2-21111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-2-2-2222-2-222-2-2-22-222-2-2000000002-200002-22-2000022-2-22-20022-2-20000000022-2-200000000000000000000
χ302222-2-2-2-2222-2-222-2-2-22-222-2-2000000002-200002-2-220000-2-222-220022-2-200000000-2-22200000000000000000000
χ312222-2-2-2-2222-2-222-2-2-22-2-2-222000000002-200002-22-2000022-2-2-2200-2-22200000000-2-22200000000000000000000
χ322222-2-2-2-2222-2-222-2-2-22-2-2-222000000002-200002-2-220000-2-2222-200-2-2220000000022-2-200000000000000000000
χ332222-2-2-2-2-122-2-2-1-1111-1122-2-2000033−3−3-1133−3−3-112-20000-1-1112-200-1-11133−3−333−3−3-1-11133−3−30000000000000000
χ342222-2-2-2-2-122-2-2-1-1111-1122-2-2000033−3−3-1133−3−3-11-22000011-1-1-2200-1-11133−3−3−3−33311-1-1−3−3330000000000000000
χ352222-2-2-2-2-122-2-2-1-1111-1122-2-20000−3−333-11−3−333-112-20000-1-1112-200-1-111−3−333−3−333-1-111−3−3330000000000000000
χ362222-2-2-2-2-122-2-2-1-1111-1122-2-20000−3−333-11−3−333-11-22000011-1-1-2200-1-111−3−33333−3−311-1-133−3−30000000000000000
χ372222-2-2-2-2-122-2-2-1-1111-11-2-222000033−3−3-1133−3−3-112-20000-1-111-220011-1-1−3−33333−3−311-1-1−3−3330000000000000000
χ382222-2-2-2-2-122-2-2-1-1111-11-2-222000033−3−3-1133−3−3-11-22000011-1-12-20011-1-1−3−333−3−333-1-11133−3−30000000000000000
χ392222-2-2-2-2-122-2-2-1-1111-11-2-2220000−3−333-11−3−333-112-20000-1-111-220011-1-133−3−3−3−33311-1-133−3−30000000000000000
χ402222-2-2-2-2-122-2-2-1-1111-11-2-2220000−3−333-11−3−333-11-22000011-1-12-20011-1-133−3−333−3−3-1-111−3−3330000000000000000
χ412-2-2222-2-22-22-22-2-222-22-22-22-200000000-2200002-200002i−2i0000002i−2i2-22-200002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ422-2-2222-2-22-22-22-2-222-22-22-22-200000000-2200002-20000−2i2i000000−2i2i2-22-20000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ432-2-2222-2-22-22-22-2-222-22-2-22-2200000000-2200002-200002i−2i000000−2i2i-22-2200002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ442-2-2222-2-22-22-22-2-222-22-2-22-2200000000-2200002-20000−2i2i0000002i−2i-22-220000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ452-2-2222-2-2-1-22-2211-1-11-112-22-200003−33−31-13−33−3-1100002i−2i−i3i3−i3i3002i−2i-11-113−33−3−ii−ii−i3i3−i3i3−ii−ii0000000000000000
χ462-2-2222-2-2-1-22-2211-1-11-112-22-200003−33−31-13−33−3-110000−2i2ii3−i3i3−i300−2i2i-11-113−33−3i−ii−ii3−i3i3−i3i−ii−i0000000000000000
χ472-2-2222-2-2-1-22-2211-1-11-112-22-20000−33−331-1−33−33-1100002i−2ii3−i3i3−i3002i−2i-11-11−33−33−ii−iii3−i3i3−i3−ii−ii0000000000000000
χ482-2-2222-2-2-1-22-2211-1-11-112-22-20000−33−331-1−33−33-110000−2i2i−i3i3−i3i300−2i2i-11-11−33−33i−ii−i−i3i3−i3i3i−ii−i0000000000000000
χ492-2-2222-2-2-1-22-2211-1-11-11-22-2200003−33−31-13−33−3-1100002i−2i−i3i3−i3i300−2i2i1-11-1−33−33−ii−iii3−i3i3−i3i−ii−i0000000000000000
χ502-2-2222-2-2-1-22-2211-1-11-11-22-2200003−33−31-13−33−3-110000−2i2ii3−i3i3−i3002i−2i1-11-1−33−33i−ii−i−i3i3−i3i3−ii−ii0000000000000000
χ512-2-2222-2-2-1-22-2211-1-11-11-22-220000−33−331-1−33−33-1100002i−2ii3−i3i3−i300−2i2i1-11-13−33−3−ii−ii−i3i3−i3i3i−ii−i0000000000000000
χ522-2-2222-2-2-1-22-2211-1-11-11-22-220000−33−331-1−33−33-110000−2i2i−i3i3−i3i3002i−2i1-11-13−33−3i−ii−ii3−i3i3−i3−ii−ii0000000000000000
χ532-2-22-2-22222-2-22-2-2-2-222200002-22-22-2-2222-222-2-2-20000000000000000000000000000000000000002-202-2000000
χ542-2-22-2-22222-2-22-2-2-2-222200002-22-22-2-2222-222-2-2-2000000000000000000000000000000000000000-220-22000000
χ552-2-22-2-22222-2-22-2-2-2-22220000-22-22-222-2222-2-22-2-20000000000000000000000000000000000000002-20-22000000
χ562-2-22-2-22222-2-22-2-2-2-22220000-22-22-222-2222-2-22-2-2000000000000000000000000000000000000000-2202-2000000
χ572-2-22-2-2222-222-2-2-2-2-22222-2-222-2-22-222-2-2-2-222-222002-200000000002-2-22-222-20000000000000000000000000000
χ582-2-22-2-2222-222-2-2-2-2-22222-2-22-222-22-2-22-2-22-2-222200-2200000000002-2-222-2-220000000000000000000000000000
χ592-2-22-2-2222-222-2-2-2-2-2222-222-22-2-22-222-2-2-2-222-22200-220000000000-222-22-2-220000000000000000000000000000
χ602-2-22-2-2222-222-2-2-2-2-2222-222-2-222-22-2-22-2-22-2-2222002-20000000000-222-2-222-20000000000000000000000000000
χ612-2-22-2-222-1-222-21111-1-1-12-2-222-2-221-1-11111-1-11-1-1002-200−i3i3i3−i30000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ622-2-22-2-222-1-222-21111-1-1-12-2-222-2-221-1-11111-1-11-1-1002-200i3−i3−i3i30000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ632-2-22-2-222-1-222-21111-1-1-12-2-22-222-2-111-111-111-1-1-100-2200−i3i3i3−i30000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ642-2-22-2-222-1-222-21111-1-1-12-2-22-222-2-111-111-111-1-1-100-2200i3−i3−i3i30000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ652-2-22-2-222-1-222-21111-1-1-1-222-22-2-221-1-11111-1-11-1-100-2200−i3i3i3−i300001-1-11-111-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ662-2-22-2-222-1-222-21111-1-1-1-222-22-2-221-1-11111-1-11-1-100-2200i3−i3−i3i300001-1-11-111-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ672-2-22-2-222-1-222-21111-1-1-1-222-2-222-2-111-111-111-1-1-1002-200−i3i3i3−i300001-1-111-1-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ682-2-22-2-222-1-222-21111-1-1-1-222-2-222-2-111-111-111-1-1-1002-200i3−i3−i3i300001-1-111-1-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-444-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ714444-4-4-4-44-4-44444-4-4-44-4000000000000-440000-4400000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4-444-2-2222-22000000002323−23−232-2−23−2323232-200000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-2-4-444-2-2222-2200000000−23−2323232-22323−23−232-200000000000000000000000000000000000000000000000000
χ7444-4-44-44-4400004-44-4-4-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7544-4-44-44-4400004-44-4-4-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7644-4-4-44-44400004-4-444-4-4000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ7744-4-4-44-44400004-4-444-4-400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ784-44-44-4-4440000-444-44-4-40000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ794-44-44-4-4440000-444-44-4-4000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ804-44-4-444-440000-44-44-4-440000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ814-44-4-444-440000-44-44-4-4400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ824-4-4444-4-444-44-4-4-444-44-40000000000004-40000-4400000000000000000000000000000000000000000000000000
χ834-4-4444-4-4-24-44-422-2-22-220000000023−2323−23-22−2323−23232-200000000000000000000000000000000000000000000000000
χ844-4-4444-4-4-24-44-422-2-22-2200000000−2323−2323-2223−2323−232-200000000000000000000000000000000000000000000000000
χ854-4-44-4-444-24-4-442222-2-2-200004-44-4-222-2-2-22-2-222200000000000000000000000000000000000000000000000000
χ864-4-44-4-444-24-4-442222-2-2-20000-44-442-2-22-2-2-222-22200000000000000000000000000000000000000000000000000
χ8788-8-88-88-8-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-88-8-88-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000000000

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