Finite Group Databasebeta

← Group #10845253

Character table — Group #10845253

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666444444441212121212121212121212122244446666888812121212121212121212121224242424242424244444224444888844
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
χ51111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11-1-1-1-111
χ61111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-11111-1-1
χ71111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-111111-1-1
χ81111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-1-1-1-111
χ911111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-11-1
χ1011111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-111-11
χ1111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1111-1-111-11
χ1211111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111111-1-1-111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1111-1-1-1111-1
χ17222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000022-2-200200-2000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-22200-2002000000
χ19222222222-2-2-2-22222222-2-2000022-2-22222-2-2-2-2-2-20000000000000000000000000000000000222200-200-2000000
χ20222222222-2-2-2-22222222-2-2000022-2-22222-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2002002000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-122-2-222-1-1-1-1-2-2-2-211111111-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-111111111-1-122-2-2-2-2-1-1-1-122-2-2-1-1-1-111111111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-111111111-1-1-2-2-2-2221111-2-222-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-12222-2-2-1-1-1-1-2-2221111-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-1-2-22222111122-2-21111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ29222-2-22-2-222-2-222-22-22-2-2002i2i−2i−2i002-2000000002-22-2000022-2-22i−2i002i2i−2i−2i000000002i2i−2i−2i00000000000000000000
χ30222-2-22-2-222-2-222-22-22-2-2002i2i−2i−2i002-2000000002-2-220000-2-222−2i2i002i2i−2i−2i00000000−2i−2i2i2i00000000000000000000
χ31222-2-22-2-222-2-222-22-22-2-200−2i−2i2i2i002-2000000002-22-2000022-2-2−2i2i00−2i−2i2i2i00000000−2i−2i2i2i00000000000000000000
χ32222-2-22-2-222-2-222-22-22-2-200−2i−2i2i2i002-2000000002-2-220000-2-2222i−2i00−2i−2i2i2i000000002i2i−2i−2i00000000000000000000
χ33222-2-22-2-2-12-2-22-11-11-111002i2i−2i−2i00-1133−3−333−3−3-112-20000-1-1112i−2i00−i−iii−i3−i3i3i333−3−3−i−iii−i3−i3i3i30000000000000000
χ34222-2-22-2-2-12-2-22-11-11-111002i2i−2i−2i00-1133−3−333−3−3-11-22000011-1-1−2i2i00−i−iii−i3−i3i3i3−3−333ii−i−ii3i3−i3−i30000000000000000
χ35222-2-22-2-2-12-2-22-11-11-111002i2i−2i−2i00-11−3−333−3−333-112-20000-1-1112i−2i00−i−iiii3i3−i3−i3−3−333−i−iiii3i3−i3−i30000000000000000
χ36222-2-22-2-2-12-2-22-11-11-111002i2i−2i−2i00-11−3−333−3−333-11-22000011-1-1−2i2i00−i−iiii3i3−i3−i333−3−3ii−i−i−i3−i3i3i30000000000000000
χ37222-2-22-2-2-12-2-22-11-11-11100−2i−2i2i2i00-1133−3−333−3−3-112-20000-1-111−2i2i00ii−i−ii3i3−i3−i333−3−3ii−i−ii3i3−i3−i30000000000000000
χ38222-2-22-2-2-12-2-22-11-11-11100−2i−2i2i2i00-1133−3−333−3−3-11-22000011-1-12i−2i00ii−i−ii3i3−i3−i3−3−333−i−iii−i3−i3i3i30000000000000000
χ39222-2-22-2-2-12-2-22-11-11-11100−2i−2i2i2i00-11−3−333−3−333-112-20000-1-111−2i2i00ii−i−i−i3−i3i3i3−3−333ii−i−i−i3−i3i3i30000000000000000
χ40222-2-22-2-2-12-2-22-11-11-11100−2i−2i2i2i00-11−3−333−3−333-11-22000011-1-12i−2i00ii−i−i−i3−i3i3i333−3−3−i−iiii3i3−i3−i30000000000000000
χ412-2-22-22-22222-2-2-2-222-2-222-22i−2i2i−2i2-2222-22-22-22-2-2-2002i−2i00000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ422-2-22-22-22222-2-2-2-222-2-222-2−2i2i−2i2i2-2222-22-22-22-2-2-200−2i2i0000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ432-2-22-22-22222-2-2-2-222-2-22-222i−2i2i−2i-2222-22-22-22-22-2-200−2i2i00000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ442-2-22-22-22222-2-2-2-222-2-22-22−2i2i−2i2i-2222-22-22-22-22-2-2002i−2i0000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ452-2-22-22-222-2-222-2-222-2-222-20000-22-2-2-22-222-22-222000000000000000000000000000000000000002-202-20000000
χ462-2-22-22-222-2-222-2-222-2-222-20000-22-2-2-22-222-22-22200000000000000000000000000000000000000-220-220000000
χ472-2-22-22-222-2-222-2-222-2-22-2200002-2-2-22-22-2-22-2222000000000000000000000000000000000000002-20-220000000
χ482-2-22-22-222-2-222-2-222-2-22-2200002-2-2-22-22-2-22-222200000000000000000000000000000000000000-2202-20000000
χ492-2-22-22-22-122-2-211-1-111-12-22i−2i2i−2i2-2-1-1-11-11-11-1111002i−2i00−i3i3−i3i30000−ii−ii−ii−ii−i3i3−i3i33−33−33−33−30000000000000000
χ502-2-22-22-22-122-2-211-1-111-12-22i−2i2i−2i2-2-1-1-11-11-11-1111002i−2i00i3−i3i3−i30000−ii−ii−ii−iii3−i3i3−i3−33−33−33−330000000000000000
χ512-2-22-22-22-122-2-211-1-111-12-2−2i2i−2i2i2-2-1-1-11-11-11-111100−2i2i00−i3i3−i3i30000i−ii−ii−ii−i−i3i3−i3i3−33−33−33−330000000000000000
χ522-2-22-22-22-122-2-211-1-111-12-2−2i2i−2i2i2-2-1-1-11-11-11-111100−2i2i00i3−i3i3−i30000i−ii−ii−ii−ii3−i3i3−i33−33−33−33−30000000000000000
χ532-2-22-22-22-122-2-211-1-111-1-222i−2i2i−2i-22-1-11-11-11-11-11100−2i2i00−i3i3−i3i30000−ii−iii−ii−ii3−i3i3−i33−33−3−33−330000000000000000
χ542-2-22-22-22-122-2-211-1-111-1-222i−2i2i−2i-22-1-11-11-11-11-11100−2i2i00i3−i3i3−i30000−ii−iii−ii−i−i3i3−i3i3−33−333−33−30000000000000000
χ552-2-22-22-22-122-2-211-1-111-1-22−2i2i−2i2i-22-1-11-11-11-11-111002i−2i00−i3i3−i3i30000i−ii−i−ii−iii3−i3i3−i3−33−333−33−30000000000000000
χ562-2-22-22-22-122-2-211-1-111-1-22−2i2i−2i2i-22-1-11-11-11-11-111002i−2i00i3−i3i3−i30000i−ii−i−ii−ii−i3i3−i3i33−33−3−33−330000000000000000
χ572-2-2-2222-222-22-2-222-2-22-2002-2-22002-200000000-2200002i−2i0000002i−2i2-2-2200002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ582-2-2-2222-222-22-2-222-2-22-2002-2-22002-200000000-220000−2i2i000000−2i2i2-2-220000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ592-2-2-2222-222-22-2-222-2-22-200-222-2002-200000000-2200002i−2i000000−2i2i-222-200002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ602-2-2-2222-222-22-2-222-2-22-200-222-2002-200000000-220000−2i2i0000002i−2i-222-20000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ612-2-2-2222-2-12-22-21-1-111-11002-2-2200-113−3−333−3−331-100002i−2i−i3i3i3−i3002i−2i-111-1−333−3−iii−i−i3i3i3−i3i−i−ii0000000000000000
χ622-2-2-2222-2-12-22-21-1-111-11002-2-2200-113−3−333−3−331-10000−2i2ii3−i3−i3i300−2i2i-111-1−333−3i−i−iii3−i3−i3i3−iii−i0000000000000000
χ632-2-2-2222-2-12-22-21-1-111-11002-2-2200-11−333−3−333−31-100002i−2ii3−i3−i3i3002i−2i-111-13−3−33−iii−ii3−i3−i3i3i−i−ii0000000000000000
χ642-2-2-2222-2-12-22-21-1-111-11002-2-2200-11−333−3−333−31-10000−2i2i−i3i3i3−i300−2i2i-111-13−3−33i−i−ii−i3i3i3−i3−iii−i0000000000000000
χ652-2-2-2222-2-12-22-21-1-111-1100-222-200-113−3−333−3−331-100002i−2i−i3i3i3−i300−2i2i1-1-113−3−33−iii−ii3−i3−i3i3−iii−i0000000000000000
χ662-2-2-2222-2-12-22-21-1-111-1100-222-200-113−3−333−3−331-10000−2i2ii3−i3−i3i3002i−2i1-1-113−3−33i−i−ii−i3i3i3−i3i−i−ii0000000000000000
χ672-2-2-2222-2-12-22-21-1-111-1100-222-200-11−333−3−333−31-100002i−2ii3−i3−i3i300−2i2i1-1-11−333−3−iii−i−i3i3i3−i3−iii−i0000000000000000
χ682-2-2-2222-2-12-22-21-1-111-1100-222-200-11−333−3−333−31-10000−2i2i−i3i3i3−i3002i−2i1-1-11−333−3i−i−iii3−i3−i3i3i−i−ii0000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2440000-4-4222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400004422-2-2-2-222222200000000000000000000000000000000000000000000000000
χ71444-4-44-4-44-444-44-44-44-4-400000000-4400000000-4400000000000000000000000000000000000000000000000000
χ72444-4-44-4-4-2-444-4-22-22-222000000002-22323−23−23−23−2323232-200000000000000000000000000000000000000000000000000
χ73444-4-44-4-4-2-444-4-22-22-222000000002-2−23−2323232323−23−232-200000000000000000000000000000000000000000000000000
χ7444-44-4-44-4400004-4-4-4-4440000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ7544-44-4-44-4400004-4-4-4-444000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ7644-4-44-4-444000044-44-4-4-40000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ7744-4-44-4-444000044-44-4-4-400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ784-4444-4-4-440000-44-4-44-44000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ794-4444-4-4-440000-44-4-44-4400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ804-44-4-4-44440000-4-4-4444-400000000000000000000000000000000000000000000000000000000000000000022−2200
χ814-44-4-4-44440000-4-4-4444-4000000000000000000000000000000000000000000000000000000000000000000−222200
χ824-4-44-44-44-2-4-44422-2-222-24-40000-44222-22-2-22-22-2-200000000000000000000000000000000000000000000000000
χ834-4-44-44-44-2-4-44422-2-222-2-4400004-422-22-222-22-2-2-200000000000000000000000000000000000000000000000000
χ844-4-4-4444-44-44-44-444-4-44-400000000-44000000004-400000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2-44-442-2-222-22000000002-223−23−2323−232323−23-2200000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-2-44-442-2-222-22000000002-2−232323−2323−23−2323-2200000000000000000000000000000000000000000000000000
χ8788-88-8-88-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-88-8-88-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000
χ898-8888-8-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-8-888-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000

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