Finite Group Databasebeta

← Group #10859107

Character table — Group #10859107

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order1222222234444666666622444444444412121212121212121212121212121212121212121212121244444444661212121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-11
χ1011111111111111111111-1-111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-1
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-11
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-11-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-1-1-1-1-11111111111-1-111-1-111-1-11-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-1-1-1-1-111111111-1-111-1-111-1-111-11
χ17222222222-2-2-2-222222222222-2-2-2-20000-2-2-2-2222200000000-2-2-2-2-2-2-2-2000000-2222220000-2-20000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-22200002222-2-2-2-200000000-2-2-2-2-2-2-2-20000002-222-2-20000220000000000000000000000
χ19222222222-2-2-2-22222222-2-222222200002222222200000000-2-2-2-22222000000-2-2-2-2-2-20000-2-20000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222-2-20000-2-2-2-2-2-2-2-200000000-2-2-2-2222200000022-2-2220000220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-11111-1-11111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-111111111-1-1-1-1111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-122-2-222-2-2-1-111-1-1-1-1111111-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2222-211111111-1-11111-1-1-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-2-21111-1-1-1-111111111-1-1-1-111112222-2-22-21111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2222222-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111122-2-2-2-2-2211-1-1-1-1-1-1111111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-2-1-1-1-1111111111111-1-1-1-11111-2-22222-2211-1-1111111-1-1-1-1-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-200001111-1-1-1-1−i3−i3−i3−i3i3i3i3i311111111000000-22-1-1-1-1−i3−i3i3i311−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-200001111-1-1-1-1i3i3i3i3−i3−i3−i3−i311111111000000-22-1-1-1-1i3i3−i3−i311i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2220000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3111111110000002-2-1-111i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2220000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3111111110000002-2-1-111−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222220000-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i31111-1-1-1-1000000-2-21111i3i3−i3−i311i3i3−i3−i3−i3−i3i3i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222220000-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i31111-1-1-1-1000000-2-21111−i3−i3i3i311−i3−i3i3i3i3i3−i3−i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-2000011111111−i3−i3−i3−i3i3i3i3i31111-1-1-1-10000002211-1-1−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-2000011111111i3i3i3i3−i3−i3−i3−i31111-1-1-1-10000002211-1-1i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i300000000000000
χ37222-22-2-2-2222-2-22-2-22-2-222-2002-2000000000000000000000022-2-222-2-22-2002-2002-2002-22-20000002-22-200000000000000
χ38222-22-2-2-2222-2-22-2-22-2-222-2002-2000000000000000000000022-2-222-2-2-2200-22002-200-22-22000000-22-2200000000000000
χ39222-22-2-2-2222-2-22-2-22-2-22-2200-22000000000000000000000022-2-2-2-2222-200-2200-22002-22-2000000-22-2200000000000000
χ40222-22-2-2-2222-2-22-2-22-2-22-2200-22000000000000000000000022-2-2-2-222-22002-200-2200-22-220000002-22-200000000000000
χ41222-22-2-2-22-2-2222-2-22-2-222-200-22002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i-2-222-2-222002i−2i00002-2000000002i−2i2i−2i000000000000000000
χ42222-22-2-2-22-2-2222-2-22-2-222-200-2200−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i-2-222-2-22200−2i2i00002-200000000−2i2i−2i2i000000000000000000
χ43222-22-2-2-22-2-2222-2-22-2-22-22002-2002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i-2-22222-2-200−2i2i0000-2200000000−2i2i−2i2i000000000000000000
χ44222-22-2-2-22-2-2222-2-22-2-22-22002-200−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i-2-22222-2-2002i−2i0000-22000000002i−2i2i−2i000000000000000000
χ45222-22-2-2-2-122-2-2-111-111-12-2002-200000033−3−333−3−333−3−3−3−333-1-111-1-1112-2002-200-113−3-11-113−33−3−33-11-1100000000000000
χ46222-22-2-2-2-122-2-2-111-111-12-2002-200000033−3−333−3−3−3−33333−3−3-1-111-1-111-2200-2200-113−31-11-13−3−333−31-11-100000000000000
χ47222-22-2-2-2-122-2-2-111-111-12-2002-2000000−3−333−3−33333−3−3−3−333-1-111-1-111-2200-2200-11−331-11-1−333−3−331-11-100000000000000
χ48222-22-2-2-2-122-2-2-111-111-12-2002-2000000−3−333−3−333−3−33333−3−3-1-111-1-1112-2002-200-11−33-11-11−33−333−3-11-1100000000000000
χ49222-22-2-2-2-122-2-2-111-111-1-2200-2200000033−3−3−3−33333−3−3−3−333-1-11111-1-12-200-22001-13−3-11-11−33−333−31-11-100000000000000
χ50222-22-2-2-2-122-2-2-111-111-1-2200-2200000033−3−3−3−333−3−33333−3−3-1-11111-1-1-22002-2001-13−31-11-1−333−3−33-11-1100000000000000
χ51222-22-2-2-2-122-2-2-111-111-1-2200-22000000−3−33333−3−333−3−3−3−333-1-11111-1-1-22002-2001-1−331-11-13−3−333−3-11-1100000000000000
χ52222-22-2-2-2-122-2-2-111-111-1-2200-22000000−3−33333−3−3−3−33333−3−3-1-11111-1-12-200-22001-1−33-11-113−33−3−331-11-100000000000000
χ53222-22-2-2-2-1-2-222-111-111-12-200-22002i2i−2i−2i33−3−3−3−333−i−iii−i−iii11-1-111-1-1002i−2i0000-11−33i3−i3−i3i33−3−ii−iii3−i3−i3i300000000000000
χ54222-22-2-2-2-1-2-222-111-111-12-200-22002i2i−2i−2i−3−33333−3−3−i−iii−i−iii11-1-111-1-1002i−2i0000-113−3−i3i3i3−i3−33−ii−ii−i3i3i3−i300000000000000
χ55222-22-2-2-2-1-2-222-111-111-12-200-2200−2i−2i2i2i33−3−3−3−333ii−i−iii−i−i11-1-111-1-100−2i2i0000-11−33−i3i3i3−i33−3i−ii−i−i3i3i3−i300000000000000
χ56222-22-2-2-2-1-2-222-111-111-12-200-2200−2i−2i2i2i−3−33333−3−3ii−i−iii−i−i11-1-111-1-100−2i2i0000-113−3i3−i3−i3i3−33i−ii−ii3−i3−i3i300000000000000
χ57222-22-2-2-2-1-2-222-111-111-1-22002-2002i2i−2i−2i33−3−333−3−3−i−iii−i−iii11-1-1-1-11100−2i2i00001-1−33i3−i3−i3i3−33i−ii−i−i3i3i3−i300000000000000
χ58222-22-2-2-2-1-2-222-111-111-1-22002-2002i2i−2i−2i−3−333−3−333−i−iii−i−iii11-1-1-1-11100−2i2i00001-13−3−i3i3i3−i33−3i−ii−ii3−i3−i3i300000000000000
χ59222-22-2-2-2-1-2-222-111-111-1-22002-200−2i−2i2i2i33−3−333−3−3ii−i−iii−i−i11-1-1-1-111002i−2i00001-1−33−i3i3i3−i3−33−ii−iii3−i3−i3i300000000000000
χ60222-22-2-2-2-1-2-222-111-111-1-22002-200−2i−2i2i2i−3−333−3−333ii−i−iii−i−i11-1-1-1-111002i−2i00001-13−3i3−i3−i3i33−3−ii−ii−i3i3i3−i300000000000000
χ612-2-222-22-222-22-2-2-2-2-2222000000002-22-2000000002-22-22-22-22-22-2000000000000000000000000000000002i−2i00002i−2i0000
χ622-2-222-22-222-22-2-2-2-2-2222000000002-22-2000000002-22-22-22-22-22-200000000000000000000000000000000−2i2i0000−2i2i0000
χ632-2-222-22-222-22-2-2-2-2-222200000000-22-2200000000-22-22-22-222-22-2000000000000000000000000000000002i−2i0000−2i2i0000
χ642-2-222-22-222-22-2-2-2-2-222200000000-22-2200000000-22-22-22-222-22-200000000000000000000000000000000−2i2i00002i−2i0000
χ652-2-2-222-222-222-2-222-2-2-22000000002i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i-222-20000000000000000000000000000002-200002i−2i000000
χ662-2-2-222-222-222-2-222-2-2-22000000002i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i-222-2000000000000000000000000000000-220000−2i2i000000
χ672-2-2-222-222-222-2-222-2-2-2200000000−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i-222-20000000000000000000000000000002-20000−2i2i000000
χ682-2-2-222-222-222-2-222-2-2-2200000000−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i-222-2000000000000000000000000000000-2200002i−2i000000
χ6944-44-44-4-44000044-4-44-4-400000000000000000000000000000000000000000000000000000000000000000022−2200000000
χ7044-44-44-4-44000044-4-44-4-4000000000000000000000000000000000000000000000000000000000000000000−222200000000
χ7144-4-4-4-444400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7244-4-4-4-444400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ734-444-4-4-4440000-4-4444-4-40000004i−4i00004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ744-444-4-4-4440000-4-4444-4-4000000−4i4i0000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ754-444-4-4-44-2000022-2-2-2220000004i−4i0000−2i2i−2i2i−2i32i3−2i32i300000000000023−2323−230000000000000000000000000000000000000000
χ764-444-4-4-44-2000022-2-2-2220000004i−4i0000−2i2i−2i2i2i3−2i32i3−2i3000000000000−2323−23230000000000000000000000000000000000000000
χ774-444-4-4-44-2000022-2-2-222000000−4i4i00002i−2i2i−2i−2i32i3−2i32i3000000000000−2323−23230000000000000000000000000000000000000000
χ784-444-4-4-44-2000022-2-2-222000000−4i4i00002i−2i2i−2i2i3−2i32i3−2i300000000000023−2323−230000000000000000000000000000000000000000
χ794-44-4-444-440000-44-44-44-4004i−4i0000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ804-44-4-444-440000-44-44-44-400−4i4i000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ814-44-4-444-4-200002-22-22-22004i−4i00000000−2i32i32i3−2i3−2i2i2i−2i000000000000−232323−230000000000000000000000000000000000000000
χ824-44-4-444-4-200002-22-22-22004i−4i000000002i3−2i3−2i32i3−2i2i2i−2i00000000000023−23−23230000000000000000000000000000000000000000
χ834-44-4-444-4-200002-22-22-2200−4i4i00000000−2i32i32i3−2i32i−2i−2i2i00000000000023−23−23230000000000000000000000000000000000000000
χ844-44-4-444-4-200002-22-22-2200−4i4i000000002i3−2i3−2i32i32i−2i−2i2i000000000000−232323−230000000000000000000000000000000000000000
χ854-4-444-44-44-44-44-4-4-4-44440000000000000000000000000000-44-4400000000000000000000000000000000000000000000
χ864-4-444-44-4-24-44-42222-2-2-2000000004-44-400000000-22-22-22-22-22-2200000000000000000000000000000000000000000000
χ874-4-444-44-4-24-44-42222-2-2-200000000-44-44000000002-22-22-22-2-22-2200000000000000000000000000000000000000000000
χ884-4-444-44-4-2-44-442222-2-2-200000000000000000000−2i32i3−2i32i32i3−2i32i3−2i32-22-200000000000000000000000000000000000000000000
χ894-4-444-44-4-2-44-442222-2-2-2000000000000000000002i3−2i32i3−2i3−2i32i3−2i32i32-22-200000000000000000000000000000000000000000000
χ904-4-4-444-4444-4-44-444-4-4-4400000000000000000000000000004-4-4400000000000000000000000000000000000000000000
χ914-4-4-444-44-24-4-442-2-2222-20000000000000000000023−23−2323−232323−23-222-200000000000000000000000000000000000000000000
χ924-4-4-444-44-24-4-442-2-2222-200000000000000000000−232323−2323−23−2323-222-200000000000000000000000000000000000000000000
χ934-4-4-444-44-2-444-42-2-2222-2000000004i−4i−4i4i00000000−2i2i2i−2i−2i2i2i−2i2-2-2200000000000000000000000000000000000000000000
χ944-4-4-444-44-2-444-42-2-2222-200000000−4i4i4i−4i000000002i−2i−2i2i2i−2i−2i2i2-2-2200000000000000000000000000000000000000000000
χ9588-88-88-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-8-888-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000000000

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