Finite Group Databasebeta

← Group #10853234

Character table — Group #10853234

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order12222222344446666666224444444444666612121212121212121212121212121212121212124444444412121212121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ1111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111-111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-11
χ1211111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111-111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1111111-1-111-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-1111-1
χ17222222222-2-2-2-2222222222-2-200002222222222222222-2-2-2-200000000-20000-200-2-2-2-2-2-200000000000000000000000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000020000200-2-2222200000000000000000000000000
χ19222222222-2-2-2-22222222-2-222000022-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000-2000020022-2-22200000000000000000000000000
χ20222222222-2-2-2-22222222-2-2220000-2-222-2-2-2-2-2-2-2-22222-2-2-2-20000000020000-2002222-2-200000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-222-2-2-2-1-1111111111111-1-1-1-100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111112-2-2-2-22-2-2-1-1-1-1-1-111111111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-111111111-222-2-2-222-1-11111-1-1-1-1-1-1-1-1111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-22211-1-111-1-1-1-11111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-222-2-22-2-21111-1-11111-1-1-1-1111100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-21111-1-1-1-11111-1-1-1-11111111122222-2-2-211-1-1111111-1-1-1-1-1-1-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-2-2-2222221111-1-1-1-1-1-11111-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-200002222-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-20000-200111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-200002222-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-20000-200111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-2-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i32000020011-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-2-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i32000020011-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3-20000200-1-111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-21111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3-20000200-1-111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-22211111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i320000-200-1-1-1-111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-22211111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i320000-200-1-1-1-111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ37222-22-2-2-2222-2-22-2-22-2-222-22-222-2-2000022-2-20000000022-2-222-2-222-2-20002-20002-20000000000002-22-200000000000000
χ38222-22-2-2-2222-2-22-2-22-2-222-22-2-2-222000022-2-20000000022-2-2-2-222-2-222000-220002-2000000000000-22-2200000000000000
χ39222-22-2-2-2222-2-22-2-22-2-22-22-2222-2-20000-2-2220000000022-2-222-2-222-2-2000-22000-22000000000000-22-2200000000000000
χ40222-22-2-2-2222-2-22-2-22-2-22-22-22-2-2220000-2-2220000000022-2-2-2-222-2-2220002-2000-220000000000002-22-200000000000000
χ41222-22-2-2-22-2-2222-2-22-2-222-2-220000000022-2-200000000-2-2220000000002i−2i0002i−2i-2200002i−2i2i−2i2i−2i2i−2i000000000000000000
χ42222-22-2-2-22-2-2222-2-22-2-222-2-220000000022-2-200000000-2-222000000000−2i2i000−2i2i-220000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ43222-22-2-2-22-2-2222-2-22-2-22-222-200000000-2-22200000000-2-2220000000002i−2i000−2i2i2-20000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ44222-22-2-2-22-2-2222-2-22-2-22-222-200000000-2-22200000000-2-222000000000−2i2i0002i−2i2-200002i−2i2i−2i−2i2i−2i2i000000000000000000
χ45222-22-2-2-2-122-2-2-111-111-12-22-222-2-20000-1-11133−3−333−3−3-1-111-1-111-1-1110002-2000-113−33−33−3−333−3−33-11-1100000000000000
χ46222-22-2-2-2-122-2-2-111-111-12-22-222-2-20000-1-111−3−333−3−333-1-111-1-111-1-1110002-2000-11−33−33−333−3−333−3-11-1100000000000000
χ47222-22-2-2-2-122-2-2-111-111-12-22-2-2-2220000-1-11133−3−333−3−3-1-11111-1-111-1-1000-22000-113−33−3−333−3−333−31-11-100000000000000
χ48222-22-2-2-2-122-2-2-111-111-12-22-2-2-2220000-1-111−3−333−3−333-1-11111-1-111-1-1000-22000-11−33−333−3−333−3−331-11-100000000000000
χ49222-22-2-2-2-122-2-2-111-111-1-22-2222-2-2000011-1-133−3−3−3−333-1-111-1-111-1-111000-220001-13−3−333−3−33−333−31-11-100000000000000
χ50222-22-2-2-2-122-2-2-111-111-1-22-2222-2-2000011-1-1−3−33333−3−3-1-111-1-111-1-111000-220001-1−333−3−333−33−3−331-11-100000000000000
χ51222-22-2-2-2-122-2-2-111-111-1-22-22-2-222000011-1-133−3−3−3−333-1-11111-1-111-1-10002-20001-13−3−33−333−33−3−33-11-1100000000000000
χ52222-22-2-2-2-122-2-2-111-111-1-22-22-2-222000011-1-1−3−33333−3−3-1-11111-1-111-1-10002-20001-1−333−33−3−33−333−3-11-1100000000000000
χ53222-22-2-2-2-1-2-222-111-111-12-2-2200000000-1-11133−3−333−3−311-1-1−i3−i3i3i3i3i3−i3−i302i−2i0002i−2i1-1−33−33−ii−ii−ii−ii−i3i3i3−i300000000000000
χ54222-22-2-2-2-1-2-222-111-111-12-2-2200000000-1-11133−3−333−3−311-1-1i3i3−i3−i3−i3−i3i3i30−2i2i000−2i2i1-1−33−33i−ii−ii−ii−ii3−i3−i3i300000000000000
χ55222-22-2-2-2-1-2-222-111-111-12-2-2200000000-1-111−3−333−3−33311-1-1−i3−i3i3i3i3i3−i3−i30−2i2i000−2i2i1-13−33−3i−ii−ii−ii−i−i3i3i3−i300000000000000
χ56222-22-2-2-2-1-2-222-111-111-12-2-2200000000-1-111−3−333−3−33311-1-1i3i3−i3−i3−i3−i3i3i302i−2i0002i−2i1-13−33−3−ii−ii−ii−iii3−i3−i3i300000000000000
χ57222-22-2-2-2-1-2-222-111-111-1-222-20000000011-1-133−3−3−3−33311-1-1−i3−i3i3i3i3i3−i3−i30−2i2i0002i−2i-11−333−3−ii−iii−ii−ii3−i3−i3i300000000000000
χ58222-22-2-2-2-1-2-222-111-111-1-222-20000000011-1-133−3−3−3−33311-1-1i3i3−i3−i3−i3−i3i3i302i−2i000−2i2i-11−333−3i−ii−i−ii−ii−i3i3i3−i300000000000000
χ59222-22-2-2-2-1-2-222-111-111-1-222-20000000011-1-1−3−33333−3−311-1-1−i3−i3i3i3i3i3−i3−i302i−2i000−2i2i-113−3−33i−ii−i−ii−iii3−i3−i3i300000000000000
χ60222-22-2-2-2-1-2-222-111-111-1-222-20000000011-1-1−3−33333−3−311-1-1i3i3−i3−i3−i3−i3i3i30−2i2i0002i−2i-113−3−33−ii−iii−ii−i−i3i3i3−i300000000000000
χ612-222-22-2-222-2-22-22-222-2-200002i−2i2i−2i00000000000000002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000002i−2i00002-20000
χ622-222-22-2-222-2-22-22-222-2-200002i−2i2i−2i00000000000000002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000−2i2i0000-220000
χ632-222-22-2-222-2-22-22-222-2-20000−2i2i−2i2i00000000000000002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002i−2i0000-220000
χ642-222-22-2-222-2-22-22-222-2-20000−2i2i−2i2i00000000000000002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000−2i2i00002-20000
χ652-22-2-2-22222-22-2-2-222-22-200002i−2i−2i2i00000000000000002-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000002-200002i−2i000000
χ662-22-2-2-22222-22-2-2-222-22-200002i−2i−2i2i00000000000000002-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000-220000−2i2i000000
χ672-22-2-2-22222-22-2-2-222-22-20000−2i2i2i−2i00000000000000002-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000002-20000−2i2i000000
χ682-22-2-2-22222-22-2-2-222-22-20000−2i2i2i−2i00000000000000002-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000-2200002i−2i000000
χ6944-44-4-4-44400004-4-4-444-400000000004i−4i000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ7044-44-4-4-44400004-4-4-444-40000000000−4i4i00000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ7144-44-4-4-44-20000-2222-2-2200000000004i−4i−2i32i3−2i32i323−2323−23−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ7244-44-4-4-44-20000-2222-2-2200000000004i−4i2i3−2i32i3−2i3−2323−2323−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ7344-44-4-4-44-20000-2222-2-220000000000−4i4i−2i32i3−2i32i3−2323−23232i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ7444-44-4-4-44-20000-2222-2-220000000000−4i4i2i3−2i32i3−2i323−2323−232i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ7544-4-4-444-440000444-4-4-4-4000000004-40000004-4-4400000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-440000444-4-4-4-400000000-44000000-444-400000000000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-20000-2-2-22222000000004-400−2i32i32i3−2i3-222-2−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-20000-2-2-22222000000004-4002i3−2i3−2i32i3-222-22i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ7944-4-4-444-4-20000-2-2-2222200000000-4400−2i32i32i3−2i32-2-222i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ8044-4-4-444-4-20000-2-2-2222200000000-44002i3−2i3−2i32i32-2-22−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ814-444-44-4-44-444-4-44-444-4-4000000000000000000000000-44-44000000000000000000000000000000000000000000000000
χ824-444-44-4-4-24-4-442-22-2-22200004i−4i4i−4i0000000000000000-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ834-444-44-4-4-24-4-442-22-2-2220000−4i4i−4i4i0000000000000000-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ844-444-44-4-4-2-444-42-22-2-2220000000000000000000000002-22-223−2323−23−2323−23230000000000000000000000000000000000000000
χ854-444-44-4-4-2-444-42-22-2-2220000000000000000000000002-22-2−2323−232323−2323−230000000000000000000000000000000000000000
χ864-44-4-4-4444-44-44-4-444-44-4000000000000000000000000-444-4000000000000000000000000000000000000000000000000
χ874-44-4-4-444-24-44-422-2-22-2200004i−4i−4i4i0000000000000000-222-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ884-44-4-4-444-24-44-422-2-22-220000−4i4i4i−4i0000000000000000-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ894-44-4-4-444-2-44-4422-2-22-220000000000000000000000002-2-2223−23−2323−232323−230000000000000000000000000000000000000000
χ904-44-4-4-444-2-44-4422-2-22-220000000000000000000000002-2-22−232323−2323−23−23230000000000000000000000000000000000000000
χ914-4-444-44-440000-4-44-44-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200000000
χ924-4-444-44-440000-4-44-44-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200000000
χ934-4-4-444-4440000-44-4-4-44400000000000000000000000000000000000000000000000000000000000000000000000022−2200
χ944-4-4-444-4440000-44-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000−222200
χ958-8-888-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000

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