Finite Group Databasebeta

← Group #10701750

Character table — Group #10701750

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222222222344444444666666666661212121212121212222266666666888888882424242424242424242424242424242444444444222288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i
χ101111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii−i−iii
χ111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii
χ121111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−iii−i−i
χ131111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii
χ141111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−i
χ151111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i
χ161111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii
χ17222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ18222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ21222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ22222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ2522222222-2-2-2-2222-2-22-22-22222222-2-2-2-2222-2-2-22-200000000000000000000000000000000000022-2-222-2-2000000000000
χ2622222222-2-2-2-2222-2-22-22-22222222-2-2-2-2222-2-2-22-2000000000000000000000000000000000000-2-222-2-222000000000000
χ2722222222-2-2-2-22-2-222-22-222222222-2-2-2-2-2-2-2222-2200000000000000000000000000000000000022-2-2-2-222000000000000
χ2822222222-2-2-2-22-2-222-22-222222222-2-2-2-2-2-2-2222-22000000000000000000000000000000000000-2-22222-2-2000000000000
χ29222-2-22-2-222-2-22222-2-22-2-222-2-2-2-2222-2-222-22-2-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ30222-2-22-2-222-2-22222-2-22-2-222-2-2-2-2222-2-222-22-2-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ31222-2-22-2-222-2-22-2-2-222-22222-2-2-2-2222-2-2-2-22-2222-200000000000000000000000000000000000000000000000000002-2-22
χ32222-2-22-2-222-2-22-2-2-222-22222-2-2-2-2222-2-2-2-22-2222-20000000000000000000000000000000000000000000000000000-222-2
χ33222-2-22-2-2-2-222222-22-2-2-2222-2-2-2-22-2-22222-2-222-2-200000000000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ34222-2-22-2-2-2-222222-22-2-2-2222-2-2-2-22-2-22222-2-222-2-20000000000000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ35222-2-22-2-2-2-2222-2-22-2222-222-2-2-2-22-2-222-2-222-2-22200000000000000002-2-220000000022-2-2-2-22200000000000000000000
χ36222-2-22-2-2-2-2222-2-22-2222-222-2-2-2-22-2-222-2-222-2-2220000000000000000-222-200000000-2-22222-2-200000000000000000000
χ37222-2-22-2-2-2-222-122-22-2-2-22-1-11111-111-1-1-1-111-1-1110000−i3−i3i3i3−i3−i3i3i300002i−2i2i−2i33−3−333−3−3−i−iii−i−iii00000000000000000000
χ38222-2-22-2-2-2-222-122-22-2-2-22-1-11111-111-1-1-1-111-1-1110000−i3−i3i3i3−i3−i3i3i30000−2i2i−2i2i−3−333−3−333ii−i−iii−i−i00000000000000000000
χ39222-2-22-2-2-2-222-122-22-2-2-22-1-11111-111-1-1-1-111-1-1110000i3i3−i3−i3i3i3−i3−i300002i−2i2i−2i−3−333−3−333−i−iii−i−iii00000000000000000000
χ40222-2-22-2-2-2-222-122-22-2-2-22-1-11111-111-1-1-1-111-1-1110000i3i3−i3−i3i3i3−i3−i30000−2i2i−2i2i33−3−333−3−3ii−i−iii−i−i00000000000000000000
χ41222-2-22-2-2-2-222-1-2-22-2222-2-1-11111-111-1-111-1-111-1-10000−i3−i3i3i3i3i3−i3−i300002-2-22−i3−i3i3i3i3i3−i3−i3-1-11111-1-100000000000000000000
χ42222-2-22-2-2-2-222-1-2-22-2222-2-1-11111-111-1-111-1-111-1-10000−i3−i3i3i3i3i3−i3−i30000-222-2i3i3−i3−i3−i3−i3i3i311-1-1-1-11100000000000000000000
χ43222-2-22-2-2-2-222-1-2-22-2222-2-1-11111-111-1-111-1-111-1-10000i3i3−i3−i3−i3−i3i3i300002-2-22i3i3−i3−i3−i3−i3i3i3-1-11111-1-100000000000000000000
χ44222-2-22-2-2-2-222-1-2-22-2222-2-1-11111-111-1-111-1-111-1-10000i3i3−i3−i3−i3−i3i3i30000-222-2−i3−i3i3i3i3i3−i3−i311-1-1-1-11100000000000000000000
χ452-2-2222-2-22-22-222-2222-2-2-2-2-222-2-222-22-22-2-222-22-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ462-2-2222-2-22-22-222-2222-2-2-2-2-222-2-222-22-22-2-222-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ472-2-2222-2-22-22-22-22-2-2-2222-2-222-2-222-22-2-222-2-22-220000000000000000000000000000000000000000000000002-2-220000
χ482-2-2222-2-22-22-22-22-2-2-2222-2-222-2-222-22-2-222-2-22-22000000000000000000000000000000000000000000000000-222-20000
χ492-2-2222-2-2-22-2222-2-2-222-22-2-222-2-22-22-222-2-2-2-22220000000000002-22-200002-22-22-22-20000000000000000000000000000
χ502-2-2222-2-2-22-2222-2-2-222-22-2-222-2-22-22-222-2-2-2-2222000000000000-22-220000-22-22-22-220000000000000000000000000000
χ512-2-2222-2-2-22-222-2222-2-22-2-2-222-2-22-22-22-22222-2-2-20000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ522-2-2222-2-2-22-222-2222-2-22-2-2-222-2-22-22-22-22222-2-2-2000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ532-2-2222-2-2-22-22-12-2-2-222-2211-1-111-11-11-1-11111-1-1-10000−i3i3−i3i3−i3i3−i3i32-22-20000-11-11-11-11−i3i3−i3i3−i3i3−i3i300000000000000000000
χ542-2-2222-2-2-22-22-12-2-2-222-2211-1-111-11-11-1-11111-1-1-10000−i3i3−i3i3−i3i3−i3i3-22-2200001-11-11-11-1i3−i3i3−i3i3−i3i3−i300000000000000000000
χ552-2-2222-2-2-22-22-12-2-2-222-2211-1-111-11-11-1-11111-1-1-10000i3−i3i3−i3i3−i3i3−i32-22-20000-11-11-11-11i3−i3i3−i3i3−i3i3−i300000000000000000000
χ562-2-2222-2-2-22-22-12-2-2-222-2211-1-111-11-11-1-11111-1-1-10000i3−i3i3−i3i3−i3i3−i3-22-2200001-11-11-11-1−i3i3−i3i3−i3i3−i3i300000000000000000000
χ572-2-2222-2-2-22-22-1-2222-2-22-211-1-111-11-11-11-1-1-1-11110000−i3i3−i3i3i3−i3i3−i32i−2i−2i2i0000−ii−iii−ii−i3−33−3−33−3300000000000000000000
χ582-2-2222-2-2-22-22-1-2222-2-22-211-1-111-11-11-11-1-1-1-11110000−i3i3−i3i3i3−i3i3−i3−2i2i2i−2i0000i−ii−i−ii−ii−33−333−33−300000000000000000000
χ592-2-2222-2-2-22-22-1-2222-2-22-211-1-111-11-11-11-1-1-1-11110000i3−i3i3−i3−i3i3−i3i32i−2i−2i2i0000−ii−iii−ii−i−33−333−33−300000000000000000000
χ602-2-2222-2-2-22-22-1-2222-2-22-211-1-111-11-11-11-1-1-1-11110000i3−i3i3−i3−i3i3−i3i3−2i2i2i−2i0000i−ii−i−ii−ii3−33−3−33−3300000000000000000000
χ612-2-2-2-22222-2-2222-22-2-2-222-2-2-2-22222-2-222-222-22-2-22-22-22-2-222-2-2200000000000000000000000000000000000000000000
χ622-2-2-2-22222-2-2222-22-2-2-222-2-2-2-22222-2-222-222-22-2-2-22-22-222-2-222-200000000000000000000000000000000000000000000
χ632-2-2-2-22222-2-222-22-2222-2-2-2-2-2-22222-2-22-22-2-22-2222-2-222-2-22-222-200000000000000000000000000000000000000000000
χ642-2-2-2-22222-2-222-22-2222-2-2-2-2-2-22222-2-22-22-2-22-222-222-2-222-22-2-2200000000000000000000000000000000000000000000
χ652-2-2-2-22222-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1-11-1112-22-2-111-1-111-1000000003−3−333−3−333−3−333−3−3300000000000000000000
χ662-2-2-2-22222-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1-11-1112-22-2-111-1-111-100000000−333−3−333−3−333−3−333−300000000000000000000
χ672-2-2-2-22222-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1-11-111-22-221-1-111-1-11000000003−3−333−3−33−333−3−333−300000000000000000000
χ682-2-2-2-22222-2-22-12-22-2-2-2221111-1-1-1-111-1-11-1-11-111-22-221-1-111-1-1100000000−333−3−333−33−3−333−3−3300000000000000000000
χ692-2-2-2-22222-2-22-1-22-2222-2-21111-1-1-1-111-11-111-11-1-12-2-22-111-11-1-1100000000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ702-2-2-2-22222-2-22-1-22-2222-2-21111-1-1-1-111-11-111-11-1-12-2-22-111-11-1-1100000000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ712-2-2-2-22222-2-22-1-22-2222-2-21111-1-1-1-111-11-111-11-1-1-222-21-1-11-111-100000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ722-2-2-2-22222-2-22-1-22-2222-2-21111-1-1-1-111-11-111-11-1-1-222-21-1-11-111-100000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ732-2-2-2-2222-222-222-2-22-222-2-2-2-2-2222-222-22-22-22-2-22000000000000000000000000000000000000000000002-22-200000000
χ742-2-2-2-2222-222-222-2-22-222-2-2-2-2-2222-222-22-22-22-2-2200000000000000000000000000000000000000000000-22-2200000000
χ752-2-2-2-2222-222-22-222-22-2-22-2-2-2-2222-222-2-22-22-222-2000000000000000000000000000000000000000000002-2-2200000000
χ762-2-2-2-2222-222-22-222-22-2-22-2-2-2-2222-222-2-22-22-222-200000000000000000000000000000000000000000000-222-200000000
χ7744444444-4-4-4-4-244-4-44-44-4-2-2-2-2-2-2-22222-2-2-2222-2200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-444-44-44-2-2-2-2-2-2-22222222-2-2-22-200000000000000000000000000000000000000000000000000000000
χ79444-4-44-4-444-4-4-2444-4-44-4-4-2-22222-2-2-222-2-22-2222-200000000000000000000000000000000000000000000000000000000
χ80444-4-44-4-444-4-4-2-4-4-444-444-2-22222-2-2-22222-22-2-2-2200000000000000000000000000000000000000000000000000000000
χ8144-44-4-44-400004000000004-44-44-4-4000000000000000000000000000000000000000000000000004-40000000000000000
χ8244-44-4-44-400004000000004-44-44-4-400000000000000000000000000000000000000000000000000-440000000000000000
χ8344-4-44-4-4400004000000004-4-44-44-400000000000000000000000000000000000000000000000000004-400000000000000
χ8444-4-44-4-4400004000000004-4-44-44-40000000000000000000000000000000000000000000000000000-4400000000000000
χ854-444-4-4-440000400000000-444-4-44-40000000000000000000000000000000000000000000000000000004-4000000000000
χ864-444-4-4-440000400000000-444-4-44-4000000000000000000000000000000000000000000000000000000-44000000000000
χ874-44-44-44-40000400000000-44-444-4-40000000000000000000000000000000000000000000000004-4000000000000000000
χ884-44-44-44-40000400000000-44-444-4-4000000000000000000000000000000000000000000000000-44000000000000000000
χ894-4-4444-4-44-44-4-24-4444-4-4-422-2-222-2-22-22-222-2-22-2200000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-44-44-4-2-44-4-4-444422-2-222-2-22-222-2-222-22-200000000000000000000000000000000000000000000000000000000
χ914-4-4-4-4444-444-4-24-4-44-444-42222-2-2-22-2-22-22-22-222-200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-444-4-2-444-44-4-442222-2-2-22-2-222-22-22-2-2200000000000000000000000000000000000000000000000000000000
χ9388-88-8-88-80000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-8-880000-400000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-8-8-880000-4000000004-4-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-88-88-88-80000-4000000004-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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