Finite Group Databasebeta

← Group #10822708

Character table — Group #10822708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222222222223444444446666666666612121212121212122244444444446666121212121212121212121212121212121212121288888888222244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-111-1-11-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-111-1-11-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-1-1-1111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-1-1-1111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1311111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1111-1-1-11-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1111-1-1-11-1-111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ1511111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-111-1111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ1611111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-111-1111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-22-20000-22000022-2-200000000-2-2220000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2200002-20000-2-2220000000022-2-20000000000000000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-11111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-21111-1-1-1-1-1-1-1-111111111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-20000-220000-1-111−i3−i3i3i3−i3−i3i3i311-1-1−i3−i3i3i3−i3−i3i3i300000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-20000-220000-1-111i3i3−i3−i3i3i3−i3−i311-1-1i3i3−i3−i3i3i3−i3−i300000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2200002-2000011-1-1−i3−i3i3i3−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i300000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2200002-2000011-1-1i3i3−i3−i3i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2722222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-22222220000-2-20000222200000000-2-2-2-20000000000000000000000000000
χ2822222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-22222-2-20000220000-2-2-2-20000000022220000000000000000000000000000
χ2922222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-111112-222-2-22-222-2-2-1-111-1-1-1-11111-1-111-1-1-1-1111100000000000000000000
χ3022222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-111112-2-2-2222-2-2-222-1-1111111-1-1-1-1-1-1111111-1-1-1-100000000000000000000
χ3122222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2222-2-2-22-2-22211-1-1-1-1-1-1111111-1-11111-1-1-1-100000000000000000000
χ3222222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-22-2-222-2222-2-211-1-11111-1-1-1-111-1-1-1-1-1-1111100000000000000000000
χ3322222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1220000-2-20000-1-1-1-1−i3−i3i3i3i3i3−i3−i31111−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3422222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1220000-2-20000-1-1-1-1i3i3−i3−i3−i3−i3i3i31111i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3522222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-2-200002200001111−i3−i3i3i3i3i3−i3−i3-1-1-1-1i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3622222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-2-200002200001111i3i3−i3−i3−i3−i3i3i3-1-1-1-1−i3−i3i3i3i3i3−i3−i300000000000000000000
χ37222-2-22-2-222-2-222-222-2-22-222-2-2-22-222-2-222-2-222-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ38222-2-22-2-222-2-222-222-2-22-222-2-2-22-222-2-222-2-222-2-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ39222-2-22-2-222-2-22-22-2-222-2222-2-2-22-222-2-2-2-222-2-222002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ40222-2-22-2-222-2-22-22-2-222-2222-2-2-22-222-2-2-2-222-2-22200−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ41222-2-22-2-222-2-2-12-222-2-22-2-1-1111-11-1-111-1-111-1-111000000002i−2i2i−2i−i3i3−i3i33−3−333−3−33−i3i3−i3i3−ii−ii−ii−ii00000000000000000000
χ42222-2-22-2-222-2-2-12-222-2-22-2-1-1111-11-1-111-1-111-1-111000000002i−2i2i−2ii3−i3i3−i3−333−3−333−3i3−i3i3−i3−ii−ii−ii−ii00000000000000000000
χ43222-2-22-2-222-2-2-12-222-2-22-2-1-1111-11-1-111-1-111-1-11100000000−2i2i−2i2i−i3i3−i3i3−333−3−333−3−i3i3−i3i3i−ii−ii−ii−i00000000000000000000
χ44222-2-22-2-222-2-2-12-222-2-22-2-1-1111-11-1-111-1-111-1-11100000000−2i2i−2i2ii3−i3i3−i33−3−333−3−33i3−i3i3−i3i−ii−ii−ii−i00000000000000000000
χ45222-2-22-2-222-2-2-1-22-2-222-22-1-1111-11-1-11111-1-111-1-1002i−2i2i−2i000000−i3i3i3−i3−ii−ii−ii−iii3−i3−i3i33−3−333−3−3300000000000000000000
χ46222-2-22-2-222-2-2-1-22-2-222-22-1-1111-11-1-11111-1-111-1-1002i−2i2i−2i000000i3−i3−i3i3−ii−ii−ii−ii−i3i3i3−i3−333−3−333−300000000000000000000
χ47222-2-22-2-222-2-2-1-22-2-222-22-1-1111-11-1-11111-1-111-1-100−2i2i−2i2i000000−i3i3i3−i3i−ii−ii−ii−ii3−i3−i3i3−333−3−333−300000000000000000000
χ48222-2-22-2-222-2-2-1-22-2-222-22-1-1111-11-1-11111-1-111-1-100−2i2i−2i2i000000i3−i3−i3i3i−ii−ii−ii−i−i3i3i3−i33−3−333−3−3300000000000000000000
χ49222-2-22-2-2-2-22222-2-2-2222-222-2-2-22-2-2-22222-2-2-2-222000000002i−2i−2i2i00000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ50222-2-22-2-2-2-22222-2-2-2222-222-2-2-22-2-2-22222-2-2-2-22200000000−2i2i2i−2i0000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ51222-2-22-2-2-2-2222-2222-2-2-2222-2-2-22-2-2-222-2-22222-2-2002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ52222-2-22-2-2-2-2222-2222-2-2-2222-2-2-22-2-2-222-2-22222-2-200−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ53222-2-22-2-2-2-222-12-2-2-2222-2-1-1111-1111-1-1-1-11111-1-1000000002i−2i−2i2i−i3i3i3−i33−3−33−333−3−i3i3i3−i3−ii−iii−ii−i00000000000000000000
χ54222-2-22-2-2-2-222-12-2-2-2222-2-1-1111-1111-1-1-1-11111-1-1000000002i−2i−2i2ii3−i3−i3i3−333−33−3−33i3−i3−i3i3−ii−iii−ii−i00000000000000000000
χ55222-2-22-2-2-2-222-12-2-2-2222-2-1-1111-1111-1-1-1-11111-1-100000000−2i2i2i−2i−i3i3i3−i3−333−33−3−33−i3i3i3−i3i−ii−i−ii−ii00000000000000000000
χ56222-2-22-2-2-2-222-12-2-2-2222-2-1-1111-1111-1-1-1-11111-1-100000000−2i2i2i−2ii3−i3−i3i33−3−33−333−3i3−i3−i3i3i−ii−i−ii−ii00000000000000000000
χ57222-2-22-2-2-2-222-1-2222-2-2-22-1-1111-1111-1-111-1-1-1-111002i−2i−2i2i000000−i3i3−i3i3−ii−iii−ii−ii3−i3i3−i33−3−33−333−300000000000000000000
χ58222-2-22-2-2-2-222-1-2222-2-2-22-1-1111-1111-1-111-1-1-1-111002i−2i−2i2i000000i3−i3i3−i3−ii−iii−ii−i−i3i3−i3i3−333−33−3−3300000000000000000000
χ59222-2-22-2-2-2-222-1-2222-2-2-22-1-1111-1111-1-111-1-1-1-11100−2i2i2i−2i000000−i3i3−i3i3i−ii−i−ii−iii3−i3i3−i3−333−33−3−3300000000000000000000
χ60222-2-22-2-2-2-222-1-2222-2-2-22-1-1111-1111-1-111-1-1-1-11100−2i2i2i−2i000000i3−i3i3−i3i−ii−i−ii−ii−i3i3−i3i33−3−33−333−300000000000000000000
χ612-2-2222-2-22-22-22222-22-2-2-2-2-2-2222-22-22-22-22-22-22-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ622-2-2222-2-22-22-22222-22-2-2-2-2-2-2222-22-22-22-22-22-22-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ632-2-2222-2-22-22-22-2-2-22-2222-2-2-2222-22-22-2-22-22-22-2200000000000000000000000000000000000000000000000000002-22-2
χ642-2-2222-2-22-22-22-2-2-22-2222-2-2-2222-22-22-2-22-22-22-220000000000000000000000000000000000000000000000000000-22-22
χ652-2-2222-2-2-22-22222-22-22-2-2-2-2-2222-2-22-222-22-2-22-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ662-2-2222-2-2-22-22222-22-22-2-2-2-2-2222-2-22-222-22-2-22-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ672-2-2222-2-2-22-222-2-22-22-222-2-2-2222-2-22-22-22-222-22-200000000000000000000000000000000000000000000000000002-2-22
χ682-2-2222-2-2-22-222-2-22-22-222-2-2-2222-2-22-22-22-222-22-20000000000000000000000000000000000000000000000000000-222-2
χ692-2-2-2-22222-2-2222-22-2-22-22-2-22-2-2222-2-222-2-222-2-22000000000000000000000000000000000000000000002-22-200000000
χ702-2-2-2-22222-2-2222-22-2-22-22-2-22-2-2222-2-222-2-222-2-2200000000000000000000000000000000000000000000-22-2200000000
χ712-2-2-2-22222-2-222-22-222-22-2-2-22-2-2222-2-22-222-2-222-20000000000000000000000000000000000000000000000002-22-20000
χ722-2-2-2-22222-2-222-22-222-22-2-2-22-2-2222-2-22-222-2-222-2000000000000000000000000000000000000000000000000-22-220000
χ732-2-2-2-2222-222-222-2-222-2-22-2-22-2-222-222-22-2-22-222-2000000000000000000000000000000000000000000002-2-2200000000
χ742-2-2-2-2222-222-222-2-222-2-22-2-22-2-222-222-22-2-22-222-200000000000000000000000000000000000000000000-222-200000000
χ752-2-2-2-2222-222-22-222-2-222-2-2-22-2-222-222-2-222-22-2-220000000000000000000000000000000000000000000000002-2-220000
χ762-2-2-2-2222-222-22-222-2-222-2-2-22-2-222-222-2-222-22-2-22000000000000000000000000000000000000000000000000-222-20000
χ7744-44-4-44-400004000000004-444-4-4-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ7844-44-4-44-400004000000004-444-4-4-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ7944-4-44-4-4400004000000004-4-4-44-4400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ8044-4-44-4-4400004000000004-4-4-44-44000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ814-444-4-4-440000400000000-44-44-4-44000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ824-444-4-4-440000400000000-44-44-4-440000000000000000000000000000000000000000000000000000−222222−22000000000000
χ834-44-44-44-40000400000000-444-44-4-4000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ844-44-44-44-40000400000000-444-44-4-40000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ854-4-4444-4-44-44-4-2444-44-4-4-4222-2-2-22-22-22-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ864-4-4444-4-44-44-4-2-4-4-44-4444222-2-2-22-22-222-22-22-22-200000000000000000000000000000000000000000000000000000000
χ874-4-4444-4-4-44-44-244-44-44-4-4222-2-2-222-22-2-22-222-22-200000000000000000000000000000000000000000000000000000000
χ884-4-4444-4-4-44-44-2-4-44-44-444222-2-2-222-22-22-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ894-4-4-4-44444-4-44-24-44-4-44-4422-222-2-2-222-2-222-2-222-200000000000000000000000000000000000000000000000000000000
χ904-4-4-4-44444-4-44-2-44-444-44-422-222-2-2-222-22-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ914-4-4-4-4444-444-4-24-4-444-4-4422-222-2-22-2-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-444-4-2-444-4-444-422-222-2-22-2-222-2-22-222-200000000000000000000000000000000000000000000000000000000
χ9388-88-8-88-80000-400000000-44-4-444400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-8-880000-400000000-4444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-8-8-880000-4000000004-44-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-88-88-88-80000-4000000004-4-44-44400000000000000000000000000000000000000000000000000000000000000000000

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