Finite Group Databasebeta

← Group #10831706

Character table — Group #10831706

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order1222222234444666666622224444121212121212121212121212224444666666668888121212121212121224242424242424244444444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-11-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-111-11
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-111-11
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-11-1-11111-1-11-1
χ911111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-111-1-11-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1111-1-1-1-1111-1
χ17222222222-2-2-2-22222222000022-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000022-2-2-220000000000
χ18222222222-2-2-2-22222222000022-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000-2-2222-20000000000
χ19222222222-2-2-2-222222220000-2-222-2-2-2-2-2-22222-2-200000000000000000000000000000000002222-2-20000000000
χ20222222222-2-2-2-222222220000-2-222-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-2-2-2220000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111-2-2-2-2-1-1-1-11111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-122-2-2-2-2-1-1-1-1-1-1-1-122-2-211111111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-2-222-2-2-1-1-1-11111-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-21111-1-1-1-1111111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111222211111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-122-2-2221111-1-1-1-1-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-1-2-222221111111122-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-2-2-2222-2-222-2-22-2-222-2-200002-2000000002-22-2000022-2-222-2-22-2000000000022-2-200000000000000000000
χ302222-2-2-2-2222-2-222-2-22-2-222-2-200002-2000000002-2-22000022-2-2-2-222-220000000000-2-22200000000000000000000
χ312222-2-2-2-2222-2-222-2-22-2-2-2-22200002-2000000002-22-20000-2-22222-2-2-220000000000-2-22200000000000000000000
χ322222-2-2-2-2222-2-222-2-22-2-2-2-22200002-2000000002-2-220000-2-222-2-2222-2000000000022-2-200000000000000000000
χ332222-2-2-2-2-122-2-2-1-111-11122-2-20000-1133−3−333−3−3-112-20000-1-111-1-1112-20033−3−333−3−3-1-11133−3−30000000000000000
χ342222-2-2-2-2-122-2-2-1-111-11122-2-20000-1133−3−333−3−3-11-220000-1-11111-1-1-220033−3−3−3−33311-1-1−3−3330000000000000000
χ352222-2-2-2-2-122-2-2-1-111-11122-2-20000-11−3−333−3−333-112-20000-1-111-1-1112-200−3−333−3−333-1-111−3−3330000000000000000
χ362222-2-2-2-2-122-2-2-1-111-11122-2-20000-11−3−333−3−333-11-220000-1-11111-1-1-2200−3−33333−3−311-1-133−3−30000000000000000
χ372222-2-2-2-2-122-2-2-1-111-111-2-2220000-1133−3−333−3−3-112-2000011-1-1-1-111-2200−3−33333−3−311-1-1−3−3330000000000000000
χ382222-2-2-2-2-122-2-2-1-111-111-2-2220000-1133−3−333−3−3-11-22000011-1-111-1-12-200−3−333−3−333-1-11133−3−30000000000000000
χ392222-2-2-2-2-122-2-2-1-111-111-2-2220000-11−3−333−3−333-112-2000011-1-1-1-111-220033−3−3−3−33311-1-133−3−30000000000000000
χ402222-2-2-2-2-122-2-2-1-111-111-2-2220000-11−3−333−3−333-11-22000011-1-111-1-12-20033−3−333−3−3-1-111−3−3330000000000000000
χ412-2-2222-2-22-22-22-2-2222-2-22-22-20000-22000000002-2002i−2i002-22-20000002i−2i00002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ422-2-2222-2-22-22-22-2-2222-2-22-22-20000-22000000002-200−2i2i002-22-2000000−2i2i0000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ432-2-2222-2-22-22-22-2-2222-2-2-22-220000-22000000002-2002i−2i00-22-22000000−2i2i00002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ442-2-2222-2-22-22-22-2-2222-2-2-22-220000-22000000002-200−2i2i00-22-220000002i−2i0000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ452-2-2222-2-2-1-22-2211-1-1-1112-22-200001-13−33−33−33−3-11002i−2i00-11-11−i3i3−i3i3002i−2i3−33−3−ii−ii−i3i3−i3i3−ii−ii0000000000000000
χ462-2-2222-2-2-1-22-2211-1-1-1112-22-200001-13−33−33−33−3-1100−2i2i00-11-11i3−i3i3−i300−2i2i3−33−3i−ii−ii3−i3i3−i3i−ii−i0000000000000000
χ472-2-2222-2-2-1-22-2211-1-1-1112-22-200001-1−33−33−33−33-11002i−2i00-11-11i3−i3i3−i3002i−2i−33−33−ii−iii3−i3i3−i3−ii−ii0000000000000000
χ482-2-2222-2-2-1-22-2211-1-1-1112-22-200001-1−33−33−33−33-1100−2i2i00-11-11−i3i3−i3i300−2i2i−33−33i−ii−i−i3i3−i3i3i−ii−i0000000000000000
χ492-2-2222-2-2-1-22-2211-1-1-111-22-2200001-13−33−33−33−3-11002i−2i001-11-1−i3i3−i3i300−2i2i−33−33−ii−iii3−i3i3−i3i−ii−i0000000000000000
χ502-2-2222-2-2-1-22-2211-1-1-111-22-2200001-13−33−33−33−3-1100−2i2i001-11-1i3−i3i3−i3002i−2i−33−33i−ii−i−i3i3−i3i3−ii−ii0000000000000000
χ512-2-2222-2-2-1-22-2211-1-1-111-22-2200001-1−33−33−33−33-11002i−2i001-11-1i3−i3i3−i300−2i2i3−33−3−ii−ii−i3i3−i3i3i−ii−i0000000000000000
χ522-2-2222-2-2-1-22-2211-1-1-111-22-2200001-1−33−33−33−33-1100−2i2i001-11-1−i3i3−i3i3002i−2i3−33−3i−ii−ii3−i3i3−i3−ii−ii0000000000000000
χ532-2-22-2-22222-2-22-2-2-2-222200002-22-2222-2-22-222-2-2-200000000000000000000000000000000000000002-22-2000000
χ542-2-22-2-22222-2-22-2-2-2-222200002-22-2222-2-22-222-2-2-20000000000000000000000000000000000000000-22-22000000
χ552-2-22-2-22222-2-22-2-2-2-22220000-22-2222-222-22-2-22-2-200000000000000000000000000000000000000002-2-22000000
χ562-2-22-2-22222-2-22-2-2-2-22220000-22-2222-222-22-2-22-2-20000000000000000000000000000000000000000-222-2000000
χ572-2-22-2-2222-222-2-2-2-2-22222-2-222-2-22-2-22-2-222-2-222200002-22-2-22000000002-2-220000000000000000000000000000
χ582-2-22-2-2222-222-2-2-2-2-22222-2-22-222-2-2-2-222-2-222-2220000-222-2-2200000000-222-20000000000000000000000000000
χ592-2-22-2-2222-222-2-2-2-2-2222-222-22-2-22-2-22-2-222-2-22220000-22-222-200000000-222-20000000000000000000000000000
χ602-2-22-2-2222-222-2-2-2-2-2222-222-2-222-2-2-2-222-2-222-22200002-2-222-2000000002-2-220000000000000000000000000000
χ612-2-22-2-222-1-222-21111-1-1-12-2-222-2-2211-111-1-111-1-1-100002-2-111-1−i3i3i3−i30000-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ622-2-22-2-222-1-222-21111-1-1-12-2-222-2-2211-111-1-111-1-1-100002-2-111-1i3−i3−i3i30000-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ632-2-22-2-222-1-222-21111-1-1-12-2-22-222-2111-1-111-1-11-1-10000-22-111-1−i3i3i3−i300001-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ642-2-22-2-222-1-222-21111-1-1-12-2-22-222-2111-1-111-1-11-1-10000-22-111-1i3−i3−i3i300001-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ652-2-22-2-222-1-222-21111-1-1-1-222-22-2-2211-111-1-111-1-1-10000-221-1-11−i3i3i3−i300001-1-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ662-2-22-2-222-1-222-21111-1-1-1-222-22-2-2211-111-1-111-1-1-10000-221-1-11i3−i3−i3i300001-1-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ672-2-22-2-222-1-222-21111-1-1-1-222-2-222-2111-1-111-1-11-1-100002-21-1-11−i3i3i3−i30000-111-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ682-2-22-2-222-1-222-21111-1-1-1-222-2-222-2111-1-111-1-11-1-100002-21-1-11i3−i3−i3i30000-111-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-422-2-2-2-222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-444222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ714444-4-4-4-44-4-44444-4-44-4-400000000-4400000000-4400000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4-444-2-222-222000000002-22323−23−23−23−2323232-200000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-2-4-444-2-222-222000000002-2−23−2323232323−23−232-200000000000000000000000000000000000000000000000000
χ7444-4-44-44-4400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7544-4-44-44-4400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7644-4-4-44-44400004-4-44-4-44000000000000000000000000000000000000000000000000000000004-4000000000000
χ7744-4-4-44-44400004-4-44-4-4400000000000000000000000000000000000000000000000000000000-44000000000000
χ784-44-44-4-4440000-444-4-4-440000000000000000000000000000000000000000000000000000004-400000000000000
χ794-44-44-4-4440000-444-4-4-44000000000000000000000000000000000000000000000000000000-4400000000000000
χ804-44-4-444-440000-44-44-44-40000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ814-44-4-444-440000-44-44-44-400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ824-4-4444-4-444-44-4-4-4444-4-4000000004-400000000-4400000000000000000000000000000000000000000000000000
χ834-4-4444-4-4-24-44-422-2-2-22200000000-2223−2323−23−2323−23232-200000000000000000000000000000000000000000000000000
χ844-4-4444-4-4-24-44-422-2-2-22200000000-22−2323−232323−2323−232-200000000000000000000000000000000000000000000000000
χ854-4-44-4-444-24-4-442222-2-2-200004-44-4-2-2-222-22-2-222200000000000000000000000000000000000000000000000000
χ864-4-44-4-444-24-4-442222-2-2-20000-44-44-2-22-2-22-222-22200000000000000000000000000000000000000000000000000
χ8788-8-88-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-88-8-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000000000

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