Finite Group Databasebeta

← Group #10845247

Character table — Group #10845247

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order12222222344446666666444444444444121212121212121212121212121212121212121212121212224444446666121212121212121212121212121222448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-11
χ51111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-11
χ1011111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-1
χ1111111111111111111111-1-11111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ1211111111111111111111-1-11111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1111111-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ17222222222-2-2-2-2222222222000022-2-22222222222-2-2-2-200000000222200-20000-20000-2-2-2-200000000-2-200000000000000
χ18222222222-2-2-2-22222222220000-2-222-2-2-2-2-2-22222-2-2-2-200000000-2-2-2-20020000-20000222200000000-2-200000000000000
χ19222222222-2-2-2-22222222-2-200002222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200-200002000022-2-2000000002200000000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2222222-2-2-2-2-2-2-2-200000000-2-2-2-2002000020000-2-222000000002200000000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2-2222111111111111-1-1-1-1-1-100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-2-22-2-2-2-221111-1-1-1-111111111-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-111111111111122-222-2-22-1-1-1-11111-1-1-1-11111-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-2-2-2-2-2-1-1-1-111-1-1111111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-22222-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-222-2-2-21111-1-111-1-1-1-111111100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-211111111-1-1-1-111111111-1-1-1-1-2-222222-2111111-1-1-1-1-1-1-1-1-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-11111-1-1-1-111111111111122-2-2-222-2-1-1-1-1-1-1111111-1-1-1-11100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122000022-2-222-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-1-1-1-100-20000-2−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i31100000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122000022-2-222-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-1-1-1-100-20000-2i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i31100000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-1220000-2-222-2-21111-1-1-1-11111−i3−i3−i3−i3i3i3i3i311110020000-2i3i3−i3−i3-1-1-1-1i3i3−i3−i3−i3−i3i3i31100000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-1220000-2-222-2-21111-1-1-1-11111i3i3i3i3−i3−i3−i3−i311110020000-2−i3−i3i3i3-1-1-1-1−i3−i3i3i3i3i3−i3−i31100000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-200002222-2-2111111111111−i3−i3−i3−i3i3i3i3i3-1-1-1-100-200002−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i3-1-100000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-200002222-2-2111111111111i3i3i3i3−i3−i3−i3−i3-1-1-1-100-200002i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i3-1-100000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-222-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3111100200002i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i3-1-100000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-222-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3111100200002−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i3-1-100000000000000
χ37222-22-2-2-222-2-222-2-22-22-2002i2i−2i−2i0000000000000022-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002-2002i−2i00000000
χ38222-22-2-2-222-2-222-2-22-22-2002i2i−2i−2i0000000000000022-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-2200−2i2i00000000
χ39222-22-2-2-222-2-222-2-22-22-200−2i−2i2i2i0000000000000022-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002-200−2i2i00000000
χ40222-22-2-2-222-2-222-2-22-22-200−2i−2i2i2i0000000000000022-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-22002i−2i00000000
χ412-2-2222-2-222-22-2-2-2-2-2222002-22-2000000000000002-22-22-22-22-22-2000000000000000000000000000000002i−2i0000002i−2i00
χ422-2-2222-2-222-22-2-2-2-2-2222002-22-2000000000000002-22-22-22-22-22-200000000000000000000000000000000−2i2i000000−2i2i00
χ432-2-2222-2-222-22-2-2-2-2-222200-22-22000000000000002-22-2-22-22-22-22000000000000000000000000000000002i−2i000000−2i2i00
χ442-2-2222-2-222-22-2-2-2-2-222200-22-22000000000000002-22-2-22-22-22-2200000000000000000000000000000000−2i2i0000002i−2i00
χ452-2-2-22-222222-2-2-222-2-22-2002i−2i−2i2i002-22-222-2-200002-2-222i−2i−2i2i2i−2i−2i2i00000002i−2i00000002-2002i−2i2i−2i00000000000000000000
χ462-2-2-22-222222-2-2-222-2-22-2002i−2i−2i2i00-22-22-2-22200002-2-222i−2i−2i2i2i−2i−2i2i0000000−2i2i0000000-2200−2i2i−2i2i00000000000000000000
χ472-2-2-22-222222-2-2-222-2-22-200−2i2i2i−2i002-22-222-2-200002-2-22−2i2i2i−2i−2i2i2i−2i0000000−2i2i00000002-200−2i2i−2i2i00000000000000000000
χ482-2-2-22-222222-2-2-222-2-22-200−2i2i2i−2i00-22-22-2-22200002-2-22−2i2i2i−2i−2i2i2i−2i00000002i−2i0000000-22002i−2i2i−2i00000000000000000000
χ492-2-2-22-2222-2-222-222-2-22-2000000002-2-22-2-2220000-222-20000000000002-20002-202-22-22-20000002-22-20000000000000000
χ502-2-2-22-2222-2-222-222-2-22-2000000002-2-22-2-2220000-222-2000000000000-22000-220-22-222-2000000-22-220000000000000000
χ512-2-2-22-2222-2-222-222-2-22-200000000-222-222-2-20000-222-20000000000002-2000-2202-22-2-22000000-22-220000000000000000
χ522-2-2-22-2222-2-222-222-2-22-200000000-222-222-2-20000-222-2000000000000-220002-20-22-22-220000002-22-20000000000000000
χ532-2-2-22-222-122-2-21-1-111-11002i−2i−2i2i002-22-2-1-11133−3−3-111-1−iii−i−iii−i33−3−30002i−2i000−i3i3i3−i3-113−3−ii−iii3−i3−i3i33−300000000000000
χ542-2-2-22-222-122-2-21-1-111-11002i−2i−2i2i002-22-2-1-111−3−333-111-1−iii−i−iii−i−3−3330002i−2i000i3−i3−i3i3-11−33−ii−ii−i3i3i3−i3−3300000000000000
χ552-2-2-22-222-122-2-21-1-111-11002i−2i−2i2i00-22-2211-1-133−3−3-111-1−iii−i−iii−i−3−333000−2i2i000i3−i3−i3i31-1−33i−ii−ii3−i3−i3i33−300000000000000
χ562-2-2-22-222-122-2-21-1-111-11002i−2i−2i2i00-22-2211-1-1−3−333-111-1−iii−i−iii−i33−3−3000−2i2i000−i3i3i3−i31-13−3i−ii−i−i3i3i3−i3−3300000000000000
χ572-2-2-22-222-122-2-21-1-111-1100−2i2i2i−2i002-22-2-1-11133−3−3-111-1i−i−iii−i−ii33−3−3000−2i2i000i3−i3−i3i3-113−3i−ii−i−i3i3i3−i33−300000000000000
χ582-2-2-22-222-122-2-21-1-111-1100−2i2i2i−2i002-22-2-1-111−3−333-111-1i−i−iii−i−ii−3−333000−2i2i000−i3i3i3−i3-11−33i−ii−ii3−i3−i3i3−3300000000000000
χ592-2-2-22-222-122-2-21-1-111-1100−2i2i2i−2i00-22-2211-1-133−3−3-111-1i−i−iii−i−ii−3−3330002i−2i000−i3i3i3−i31-1−33−ii−ii−i3i3i3−i33−300000000000000
χ602-2-2-22-222-122-2-21-1-111-1100−2i2i2i−2i00-22-2211-1-1−3−333-111-1i−i−iii−i−ii33−3−30002i−2i000i3−i3−i3i31-13−3−ii−iii3−i3−i3i3−3300000000000000
χ612-2-2-22-222-1-2-2221-1-111-11000000002-2-2211-1-133−3−31-1-113−3−33−333−3−3−333-22000-2201-11-1-113−3−333−31-11-1−3300000000000000
χ622-2-2-22-222-1-2-2221-1-111-11000000002-2-2211-1-133−3−31-1-11−333−33−3−33−3−3332-20002-20-11-11-113−33−3−33-11-11−3300000000000000
χ632-2-2-22-222-1-2-2221-1-111-11000000002-2-2211-1-1−3−3331-1-113−3−33−333−333−3−32-20002-20-11-11-11−33−333−3-11-113−300000000000000
χ642-2-2-22-222-1-2-2221-1-111-11000000002-2-2211-1-1−3−3331-1-11−333−33−3−3333−3−3-22000-2201-11-1-11−333−3−331-11-13−300000000000000
χ652-2-2-22-222-1-2-2221-1-111-1100000000-222-2-1-11133−3−31-1-113−3−33−333−333−3−32-2000-220-11-111-1−333−3−331-11-1−3300000000000000
χ662-2-2-22-222-1-2-2221-1-111-1100000000-222-2-1-11133−3−31-1-11−333−33−3−3333−3−3-220002-201-11-11-1−33−333−3-11-11−3300000000000000
χ672-2-2-22-222-1-2-2221-1-111-1100000000-222-2-1-111−3−3331-1-113−3−33−333−3−3−333-220002-201-11-11-13−33−3−33-11-113−300000000000000
χ682-2-2-22-222-1-2-2221-1-111-1100000000-222-2-1-111−3−3331-1-11−333−33−3−33−3−3332-2000-220-11-111-13−3−333−31-11-13−300000000000000
χ69444-44-4-4-44-444-44-4-44-44-400000000000000000000-4-4440000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-24-4-44-222-22-22004i4i−4i−4i00000000000000-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000
χ71444-44-4-4-4-24-4-44-222-22-2200−4i−4i4i4i00000000000000-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000
χ72444-44-4-4-4-2-444-4-222-22-220000000000000000000022-2-22323−23−23−23−23232300000000000000000000000000000000000000000000
χ73444-44-4-4-4-2-444-4-222-22-220000000000000000000022-2-2−23−2323232323−23−2300000000000000000000000000000000000000000000
χ7444-44-4-4-444000044-4-44-4-400000000000000000000000000000000000000000000000000000000000000000000−2i22i2000000
χ7544-44-4-4-444000044-4-44-4-4000000000000000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ7644-4-4-444-4400004-44-4-4-444i−4i000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7744-4-4-444-4400004-44-4-4-44−4i4i00000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-20000-22-2222-24i−4i000000000023−2323−23−2i2i−2i2i000000000000−2i32i3−2i32i30000000000000000000000000000000000000000
χ7944-4-4-444-4-20000-22-2222-24i−4i0000000000−2323−2323−2i2i−2i2i0000000000002i3−2i32i3−2i30000000000000000000000000000000000000000
χ8044-4-4-444-4-20000-22-2222-2−4i4i000000000023−2323−232i−2i2i−2i0000000000002i3−2i32i3−2i30000000000000000000000000000000000000000
χ8144-4-4-444-4-20000-22-2222-2−4i4i0000000000−2323−23232i−2i2i−2i000000000000−2i32i3−2i32i30000000000000000000000000000000000000000
χ824-444-4-44-440000-4-4444-4-40000004i−4i0000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ834-444-4-44-440000-4-4444-4-4000000−4i4i000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ844-444-4-44-4-2000022-2-2-2220000004i−4i000023−23−23232i3−2i3−2i32i3000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ854-444-4-44-4-2000022-2-2-2220000004i−4i0000−232323−23−2i32i32i3−2i3000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ864-444-4-44-4-2000022-2-2-222000000−4i4i000023−23−2323−2i32i32i3−2i30000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ874-444-4-44-4-2000022-2-2-222000000−4i4i0000−232323−232i3−2i3−2i32i30000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ884-44-4-44-4440000-44-44-4-44000000000000000000000000000000000000000000000000000000000000000000000022−220000
χ894-44-4-44-4440000-44-44-4-440000000000000000000000000000000000000000000000000000000000000000000000−22220000
χ904-4-4444-4-44-44-44-4-4-4-444400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ914-4-4444-4-4-24-44-42222-2-2-2004-44-400000000000000-22-22-22-22-22-2200000000000000000000000000000000000000000000
χ924-4-4444-4-4-24-44-42222-2-2-200-44-4400000000000000-22-222-22-22-22-200000000000000000000000000000000000000000000
χ934-4-4444-4-4-2-44-442222-2-2-2000000000000000000002-22-2−2i32i3−2i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ944-4-4444-4-4-2-44-442222-2-2-2000000000000000000002-22-22i3−2i32i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ9588-88-8-8-88-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-88-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000000000000000

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