Finite Group Databasebeta

← Group #10701976

Character table — Group #10701976

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12222222222234444444466666666666121212121212121244448888888812121212121212122424242424242424242424242424242488888888224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i1-111-1-1
χ10111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11−i−iii-11-1-111
χ11111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11ii−i−i-11-1-111
χ12111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii1-111-1-1
χ13111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1−i−iii1-1-1-111
χ14111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11ii−i−i-1111-1-1
χ15111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11−i−iii-1111-1-1
χ16111-1-1-11-111-1-11111-1-1-11-111-1-1-1-1111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1ii−i−i1-1-1-111
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
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
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
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
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002i−2i2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii33−3−333−3−300000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002i−2i2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−3−333−3−33300000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000−2i2i−2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−3−333−3−33300000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000−2i2i−2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i33−3−333−3−300000000000000000000
χ2722222222-2-2-2-2222-2-22-2-222222222-2-2-2-222-2-22-22-200000000000000000000000000000000000022-2-222-2-2000000000000
χ2822222222-2-2-2-2222-2-22-2-222222222-2-2-2-222-2-22-22-2000000000000000000000000000000000000-2-222-2-222000000000000
χ2922222222-2-2-2-22-2-222-222-22222222-2-2-2-2-2-222-22-2200000000000000000000000000000000000000000000220000-2-20000
χ3022222222-2-2-2-22-2-222-222-22222222-2-2-2-2-2-222-22-2200000000000000000000000000000000000000000000-2-20000220000
χ31222-2-2-22-222-2-22-2-2-2222-2222-2-2-2-2222-2-2-2-2-2-2222200002-2-2200000000000022-2-2-2-2220000000000000000000000000000
χ32222-2-2-22-222-2-22-2-2-2222-2222-2-2-2-2222-2-2-2-2-2-222220000-222-2000000000000-2-22222-2-20000000000000000000000000000
χ33222-2-2-22-222-2-2-1222-2-2-22-2-1-11111-1-1-111-1-1-1-1111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ34222-2-2-22-222-2-2-1222-2-2-22-2-1-11111-1-1-111-1-1-1-1111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ35222-2-2-22-222-2-2-1222-2-2-22-2-1-11111-1-1-111-1-1-1-11111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ36222-2-2-22-222-2-2-1222-2-2-22-2-1-11111-1-1-111-1-1-1-11111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ37222-2-2-22-222-2-2-1-2-2-2222-22-1-11111-1-1-1111111-1-1-1-100002-2-220000−i3−i3i3i3i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i300000000000000000000
χ38222-2-2-22-222-2-2-1-2-2-2222-22-1-11111-1-1-1111111-1-1-1-100002-2-220000i3i3−i3−i3−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i300000000000000000000
χ39222-2-2-22-222-2-2-1-2-2-2222-22-1-11111-1-1-1111111-1-1-1-10000-222-20000−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000000000
χ40222-2-2-22-222-2-2-1-2-2-2222-22-1-11111-1-1-1111111-1-1-1-10000-222-20000i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000000000
χ41222-2-2-22-2-2-222222-22-22-2-222-2-2-2-22-2-22222-2-2-22-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ42222-2-2-22-2-2-222222-22-22-2-222-2-2-2-22-2-22222-2-2-22-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ43222-2-2-22-2-2-2222-2-22-22-22222-2-2-2-22-2-222-2-2222-22-2000000000000000000000000000000000000000000002-20000-220000
χ44222-2-2-22-2-2-2222-2-22-22-22222-2-2-2-22-2-222-2-2222-22-200000000000000000000000000000000000000000000-2200002-20000
χ452-2-222-22-22-22-222-2222-2-2-2-2-222-2-222-22-22-22-2-222-200000000000000000000000000000000000000000000002i−2i2i−2i000000
χ462-2-222-22-22-22-222-2222-2-2-2-2-222-2-222-22-22-22-2-222-20000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ472-2-222-22-22-22-22-22-2-2-2222-2-222-2-222-22-2-22-222-2-2200000000000000000000000000000000000000000000000000002-22-2
χ482-2-222-22-22-22-22-22-2-2-2222-2-222-2-222-22-2-22-222-2-220000000000000000000000000000000000000000000000000000-22-22
χ492-2-222-22-2-22-2222-2-2-2222-2-2-222-2-22-22-222-2-22-2-2222-22-2000000002-22-22-22-2000000000000000000000000000000000000
χ502-2-222-22-2-22-2222-2-2-2222-2-2-222-2-22-22-222-2-22-2-222-22-2200000000-22-22-22-22000000000000000000000000000000000000
χ512-2-222-22-2-22-222-2222-2-2-22-2-222-2-22-22-22-222-222-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ522-2-222-22-2-22-222-2222-2-2-22-2-222-2-22-22-22-222-222-2-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ532-2-222-22-2-22-22-12-2-2-2222-211-1-111-11-11-1-111-111-1-12-22-200000000-11-11-11-11−i3i3−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ542-2-222-22-2-22-22-12-2-2-2222-211-1-111-11-11-1-111-111-1-12-22-200000000-11-11-11-11i3−i3i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ552-2-222-22-2-22-22-12-2-2-2222-211-1-111-11-11-1-111-111-1-1-22-22000000001-11-11-11-1−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ562-2-222-22-2-22-22-12-2-2-2222-211-1-111-11-11-1-111-111-1-1-22-22000000001-11-11-11-1i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ572-2-222-22-2-22-22-1-2222-2-2-2211-1-111-11-11-11-1-11-1-111000000002i−2i2i−2i−i3i3i3−i3−i3i3i3−i33−3−333−3−33−ii−ii−ii−ii00000000000000000000
χ582-2-222-22-2-22-22-1-2222-2-2-2211-1-111-11-11-11-1-11-1-111000000002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−333−3−333−3−ii−ii−ii−ii00000000000000000000
χ592-2-222-22-2-22-22-1-2222-2-2-2211-1-111-11-11-11-1-11-1-11100000000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3−333−3−333−3i−ii−ii−ii−i00000000000000000000
χ602-2-222-22-2-22-22-1-2222-2-2-2211-1-111-11-11-11-1-11-1-11100000000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i33−3−333−3−33i−ii−ii−ii−i00000000000000000000
χ612-2-2-2-22222-2-2222-22-2-22-22-2-2-2-22222-2-222-22-22-2-2200000000000000000000000000000000000000000000002-2-22000000
χ622-2-2-2-22222-2-2222-22-2-22-22-2-2-2-22222-2-222-22-22-2-220000000000000000000000000000000000000000000000-222-2000000
χ632-2-2-2-22222-2-222-22-222-22-2-2-2-2-22222-2-22-22-22-222-200000000000000000000000000000000000000000000000000002-2-22
χ642-2-2-2-22222-2-222-22-222-22-2-2-2-2-22222-2-22-22-22-222-20000000000000000000000000000000000000000000000000000-222-2
χ652-2-2-2-2222-222-222-2-22-2-222-2-2-2-2222-222-22-2-2222-2-22-2-22000000002-22-2-22-22000000000000000000000000000000000000
χ662-2-2-2-2222-222-222-2-22-2-222-2-2-2-2222-222-22-2-2222-2-2-222-200000000-22-222-22-2000000000000000000000000000000000000
χ672-2-2-2-2222-222-22-222-222-2-2-2-2-2-2222-222-2-222-2-2-222000000002-2-2200000000000000002-22-2-22-2200000000000000000000
χ682-2-2-2-2222-222-22-222-222-2-2-2-2-2-2222-222-2-222-2-2-22200000000-222-20000000000000000-22-222-22-200000000000000000000
χ692-2-2-2-2222-222-2-12-2-22-2-2221111-1-1-11-1-11-111-1-1-1112-2-2200000000-11-111-11-13−33−3−33−333−3−33−333−300000000000000000000
χ702-2-2-2-2222-222-2-12-2-22-2-2221111-1-1-11-1-11-111-1-1-1112-2-2200000000-11-111-11-1−33−333−33−3−333−33−3−3300000000000000000000
χ712-2-2-2-2222-222-2-12-2-22-2-2221111-1-1-11-1-11-111-1-1-111-222-2000000001-11-1-11-113−33−3−33−33−333−33−3−3300000000000000000000
χ722-2-2-2-2222-222-2-12-2-22-2-2221111-1-1-11-1-11-111-1-1-111-222-2000000001-11-1-11-11−33−333−33−33−3−33−333−300000000000000000000
χ732-2-2-2-2222-222-2-1-222-222-2-21111-1-1-11-1-111-1-1111-1-1000000002-2-22−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-11-111-11-100000000000000000000
χ742-2-2-2-2222-222-2-1-222-222-2-21111-1-1-11-1-111-1-1111-1-1000000002-2-22i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-11-111-11-100000000000000000000
χ752-2-2-2-2222-222-2-1-222-222-2-21111-1-1-11-1-111-1-1111-1-100000000-222-2−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i31-11-1-11-1100000000000000000000
χ762-2-2-2-2222-222-2-1-222-222-2-21111-1-1-11-1-111-1-1111-1-100000000-222-2i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i31-11-1-11-1100000000000000000000
χ7744444444-4-4-4-4-244-4-44-4-44-2-2-2-2-2-2-22222-2-222-22-2200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-444-444-4-2-2-2-2-2-2-2222222-2-22-22-200000000000000000000000000000000000000000000000000000000
χ79444-4-4-44-4-4-444-244-44-44-4-4-2-22222-222-2-2-2-2222-22-200000000000000000000000000000000000000000000000000000000
χ80444-4-4-44-4-4-444-2-4-44-44-444-2-22222-222-2-222-2-2-22-2200000000000000000000000000000000000000000000000000000000
χ8144-44-44-4-400004000000004-44-44-4-40000000000000000000000000000000000000000000000000022−220022−22000000000000
χ8244-44-44-4-400004000000004-44-44-4-400000000000000000000000000000000000000000000000000−222200−2222000000000000
χ8344-4-44-4-4400004000000004-4-44-44-400000000000000000000000000000000000000000000000000−2i22i2002i2−2i2000000000000
χ8444-4-44-4-4400004000000004-4-44-44-4000000000000000000000000000000000000000000000000002i2−2i200−2i22i2000000000000
χ854-444-4-4-440000400000000-444-4-44-4000000000000000000000000000000000000000000000000−2i22i200−2i22i200000000000000
χ864-444-4-4-440000400000000-444-4-44-40000000000000000000000000000000000000000000000002i2−2i2002i2−2i200000000000000
χ874-44-444-4-40000400000000-44-444-4-400000000000000000000000000000000000000000000000022−2200−222200000000000000
χ884-44-444-4-40000400000000-44-444-4-4000000000000000000000000000000000000000000000000−22220022−2200000000000000
χ894-4-444-44-44-44-4-24-4444-4-4-422-2-222-2-22-22-22-222-2-2200000000000000000000000000000000000000000000000000000000
χ904-4-444-44-44-44-4-2-44-4-4-444422-2-222-2-22-222-22-2-222-200000000000000000000000000000000000000000000000000000000
χ914-4-4-4-44444-4-44-24-44-4-44-442222-2-2-2-222-2-22-22-222-200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-44444-4-44-2-44-444-44-42222-2-2-2-222-22-22-22-2-2200000000000000000000000000000000000000000000000000000000
χ9388-88-88-8-80000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-8-880000-400000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-8-8-880000-4000000004-4-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-88-888-8-80000-4000000004-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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