Finite Group Databasebeta

← Group #10729210

Character table — Group #10729210

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11111111111111112222222222222222444444444444666666668888888888888888888888888888888888881212121212121212121212122424242424242424
order12222222222222223666666666666666444444444444444444442222444466666666121212121212121212121212121212121212121244444444444422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111
χ911111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222220000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222200000000-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2000000002222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-200000000-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-20000000022-2-222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-1111100000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-200000000-2-222-2-2221111-1-1-1-11111-1-1-1-111111111-1-1-1-100000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222220000000022-2-2-2-222-1-1-1-1111111111111-1-1-1-11111-1-1-1-100000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222200000000-2-22222-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-1111100000000000000000000
χ252222-2-2-2222-22-2-2-2-222222-2-2-2-2-2-2222-2-20000000000002i2i2i2i−2i−2i−2i−2i002-20000000022-2-2000000000000000000000000000000000000002i−2i
χ262222-2-2-2222-22-2-2-2-222222-2-2-2-2-2-2222-2-20000000000002i2i2i2i−2i−2i−2i−2i00-2200000000-2-22200000000000000000000000000000000000000−2i2i
χ272222-2-2-2222-22-2-2-2-222222-2-2-2-2-2-2222-2-2000000000000−2i−2i−2i−2i2i2i2i2i002-20000000022-2-200000000000000000000000000000000000000−2i2i
χ282222-2-2-2222-22-2-2-2-222222-2-2-2-2-2-2222-2-2000000000000−2i−2i−2i−2i2i2i2i2i00-2200000000-2-222000000000000000000000000000000000000002i−2i
χ29222-22-2-22-2-2-2-2222-2222-2-22222-2-22-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000022-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ30222-22-2-22-2-2-2-2222-2222-2-22222-2-22-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000022-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ31222-22-2-22-2-2-2-2222-2222-2-22222-2-22-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ32222-22-2-22-2-2-2-2222-2222-2-22222-2-22-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ33222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-1111122-2-22i2i−2i−2i2i2i−2i−2i0000000000000000−i3−i3i3i3−i3i3−i3i3-1-111−i−iii−i−iii33−3−333−3−300000000000000000000
χ34222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-1111122-2-22i2i−2i−2i2i2i−2i−2i0000000000000000i3i3−i3−i3i3−i3i3−i3-1-111−i−iii−i−iii−3−333−3−33300000000000000000000
χ35222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-1111122-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−i3−i3i3i3−i3i3−i3i3-1-111ii−i−iii−i−i−3−333−3−33300000000000000000000
χ36222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-1111122-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000i3i3−i3−i3i3−i3i3−i3-1-111ii−i−iii−i−i33−3−333−3−300000000000000000000
χ37222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-11111-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000−i3−i3i3i3i3−i3i3−i311-1-1−i−iiiii−i−i33−3−3−3−33300000000000000000000
χ38222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-11111-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000i3i3−i3−i3−i3i3−i3i311-1-1−i−iiiii−i−i−3−33333−3−300000000000000000000
χ39222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-11111-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000−i3−i3i3i3i3−i3i3−i311-1-1ii−i−i−i−iii−3−33333−3−300000000000000000000
χ40222-22-2-22-2-2-2-2222-2-1-1-111-1-1-1-111-11111-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000i3i3−i3−i3−i3i3−i3i311-1-1ii−i−i−i−iii33−3−3−3−33300000000000000000000
χ4122-22-22-2-2-2-22222-2-222-22222-2-22-2-2-2-22-2000000002i−2i2i−2i000000000000000000000000000000002i−2i2i−2i000000002i2i−2i−2i22-2-2000000000000
χ4222-22-22-2-2-2-22222-2-222-22222-2-22-2-2-2-22-2000000002i−2i2i−2i000000000000000000000000000000002i−2i2i−2i00000000−2i−2i2i2i-2-222000000000000
χ4322-22-22-2-2-2-22222-2-222-22222-2-22-2-2-2-22-200000000−2i2i−2i2i00000000000000000000000000000000−2i2i−2i2i000000002i2i−2i−2i-2-222000000000000
χ4422-22-22-2-2-2-22222-2-222-22222-2-22-2-2-2-22-200000000−2i2i−2i2i00000000000000000000000000000000−2i2i−2i2i00000000−2i−2i2i2i22-2-2000000000000
χ4522-2-222-2-2222-2-2-22-222-2-2-2-2-2222-2-2222-20000000000002i2i−2i−2i2i2i−2i−2i00002-200000000000000000000002-22-20000000000000000002i−2i0000
χ4622-2-222-2-2222-2-2-22-222-2-2-2-2-2222-2-2222-20000000000002i2i−2i−2i2i2i−2i−2i0000-220000000000000000000000-22-22000000000000000000−2i2i0000
χ4722-2-222-2-2222-2-2-22-222-2-2-2-2-2222-2-2222-2000000000000−2i−2i2i2i−2i−2i2i2i00002-200000000000000000000002-22-2000000000000000000−2i2i0000
χ4822-2-222-2-2222-2-2-22-222-2-2-2-2-2222-2-2222-2000000000000−2i−2i2i2i−2i−2i2i2i0000-220000000000000000000000-22-220000000000000000002i−2i0000
χ4922-2-2-2-22-222-2-222-2222-2-2-222-2-2-22-222-22000000002-2-2222-2-2-2-2220000000000000000000000002-2-22000000000000000022-2-200000000
χ5022-2-2-2-22-222-2-222-2222-2-2-222-2-2-22-222-22000000002-2-22-2-22222-2-20000000000000000000000002-2-220000000000000000-2-22200000000
χ5122-2-2-2-22-222-2-222-2222-2-2-222-2-2-22-222-2200000000-222-222-2-2-2-222000000000000000000000000-222-20000000000000000-2-22200000000
χ5222-2-2-2-22-222-2-222-2222-2-2-222-2-2-22-222-2200000000-222-2-2-22222-2-2000000000000000000000000-222-2000000000000000022-2-200000000
χ532-222-2-2-2-22-22-22-2222-222-22-22-2-2-2-22-22200002-22-2000000000000000000000000000000002-22-20000000000002-22-200002-22-200000000
χ542-222-2-2-2-22-22-22-2222-222-22-22-2-2-2-22-22200002-22-2000000000000000000000000000000002-22-2000000000000-22-220000-22-2200000000
χ552-222-2-2-2-22-22-22-2222-222-22-22-2-2-2-22-2220000-22-2200000000000000000000000000000000-22-220000000000002-22-20000-22-2200000000
χ562-222-2-2-2-22-22-22-2222-222-22-22-2-2-2-22-2220000-22-2200000000000000000000000000000000-22-22000000000000-22-2200002-22-200000000
χ572-22-22-2-2-2-2222-22-222-22-22-22-22-2-2-2-22220000000000002-22-22-22-20000002-20000000000000000000000002-22-20000000000002-2000000
χ582-22-22-2-2-2-2222-22-222-22-22-22-22-2-2-2-22220000000000002-22-22-22-2000000-22000000000000000000000000-22-22000000000000-22000000
χ592-22-22-2-2-2-2222-22-222-22-22-22-22-2-2-2-2222000000000000-22-22-22-220000002-20000000000000000000000002-22-2000000000000-22000000
χ602-22-22-2-2-2-2222-22-222-22-22-22-22-2-2-2-2222000000000000-22-22-22-22000000-22000000000000000000000000-22-220000000000002-2000000
χ612-22-2-222-2-22-222-22-22-22-222-22-222-2-22-2-200002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i000000000000000000002i−2i−2i2i00000000000000002-22-2000000000000
χ622-22-2-222-2-22-222-22-22-22-222-22-222-2-22-2-200002i−2i−2i2i0000−2i2i−2i2i2i−2i2i−2i000000000000000000002i−2i−2i2i0000000000000000-22-22000000000000
χ632-22-2-222-2-22-222-22-22-22-222-22-222-2-22-2-20000−2i2i2i−2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000−2i2i2i−2i0000000000000000-22-22000000000000
χ642-22-2-222-2-22-222-22-22-22-222-22-222-2-22-2-20000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000−2i2i2i−2i00000000000000002-22-2000000000000
χ652-2-222-222-222-22-2-2-22-2-22-22-2-22-222-222-22-22-2000000002i−2i−2i2i2i−2i−2i2i00000000000000002-22-200000000000000002i−2i−2i2i0000000000000000
χ662-2-222-222-222-22-2-2-22-2-22-22-2-22-222-222-22-22-200000000−2i2i2i−2i−2i2i2i−2i00000000000000002-22-20000000000000000−2i2i2i−2i0000000000000000
χ672-2-222-222-222-22-2-2-22-2-22-22-2-22-222-222-2-22-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000-22-220000000000000000−2i2i2i−2i0000000000000000
χ682-2-222-222-222-22-2-2-22-2-22-22-2-22-222-222-2-22-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000-22-2200000000000000002i−2i−2i2i0000000000000000
χ692-2-22-22-22-22-2-2-22222-2-22-2-222-22-22-22-220000000000002-2-22-222-22-20000002-22-200000000000000000000000000000000000000002-200
χ702-2-22-22-22-22-2-2-22222-2-22-2-222-22-22-22-220000000000002-2-22-222-2-22000000-22-220000000000000000000000000000000000000000-2200
χ712-2-22-22-22-22-2-2-22222-2-22-2-222-22-22-22-22000000000000-222-22-2-222-20000002-22-20000000000000000000000000000000000000000-2200
χ722-2-22-22-22-22-2-2-22222-2-22-2-222-22-22-22-22000000000000-222-22-2-22-22000000-22-2200000000000000000000000000000000000000002-200
χ732-2-2-222-222-2-222-2-222-2-2-222-2-222-222-2-222-2-22000000000000000000000000000000002-2-22000000000000000000002-2-22-222-200000000
χ742-2-2-222-222-2-222-2-222-2-2-222-2-222-222-2-222-2-22000000000000000000000000000000002-2-2200000000000000000000-222-22-2-2200000000
χ752-2-2-222-222-2-222-2-222-2-2-222-2-222-222-2-22-222-200000000000000000000000000000000-222-2000000000000000000002-2-222-2-2200000000
χ762-2-2-222-222-2-222-2-222-2-2-222-2-222-222-2-22-222-200000000000000000000000000000000-222-200000000000000000000-222-2-222-200000000
χ774444-4-4-4444-44-4-4-4-4-2-2-2-2-2222222-2-2-22200000000000000000000004-400000000-2-2220000000000000000000000000000000000000000
χ784444-4-4-4444-44-4-4-4-4-2-2-2-2-2222222-2-2-2220000000000000000000000-440000000022-2-20000000000000000000000000000000000000000
χ79444-4-4444-4-44-4-4-4-44444-4-4-4-4-4-4444-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ80444-4-4444-4-44-4-4-4-44-2-2-2222222-2-2-222-2-200000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ81444-4-4444-4-44-4-4-4-44-2-2-2222222-2-2-222-2-2000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ8244-444-44-4-4-4-44-4-44444-444-4-444-44-4-4-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ8344-444-44-4-4-4-44-4-444-2-22-2-222-2-22-22222-200000000000000000000000000000000000000000000000023−23−2323000000000000000000000000
χ8444-444-44-4-4-4-44-4-444-2-22-2-222-2-22-22222-2000000000000000000000000000000000000000000000000−232323−23000000000000000000000000
χ8544-44-44-4-4-4-44444-4-4-2-22-2-2-2-222-22222-22000000004i−4i4i−4i00000000000000000000000000000000−2i2i−2i2i0000000000000000000000000000
χ8644-44-44-4-4-4-44444-4-4-2-22-2-2-2-222-22222-2200000000−4i4i−4i4i000000000000000000000000000000002i−2i2i−2i0000000000000000000000000000
χ8744-4-444-4-4444-4-4-44-4-2-222222-2-2-222-2-2-220000000000000000000000004-40000000000000000000000-22-22000000000000000000000000
χ8844-4-444-4-4444-4-4-44-4-2-222222-2-2-222-2-2-22000000000000000000000000-4400000000000000000000002-22-2000000000000000000000000
χ8944-4-4-4-44-444-4-444-44-2-2222-2-2222-22-2-22-2000000004-4-4400000000000000000000000000000000-222-20000000000000000000000000000
χ9044-4-4-4-44-444-4-444-44-2-2222-2-2222-22-2-22-200000000-444-4000000000000000000000000000000002-2-220000000000000000000000000000
χ914-444444-44-4-4-4-44-4-44-444-4-44-4444-44-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ924-444444-44-4-4-4-44-4-4-22-2-222-22-2-2-22-2222000000000000000000000000000000000000000000000000000023−23−232300000000000000000000
χ934-444444-44-4-4-4-44-4-4-22-2-222-22-2-2-22-22220000000000000000000000000000000000000000000000000000−232323−2300000000000000000000
χ944-444-4-4-4-44-44-44-444-22-2-22-22-22222-22-2-200004-44-400000000000000000000000000000000-22-2200000000000000000000000000000000
χ954-444-4-4-4-44-44-44-444-22-2-22-22-22222-22-2-20000-44-44000000000000000000000000000000002-22-200000000000000000000000000000000
χ964-44-44-4-4-4-4444-44-44-22-22-22-22-22222-2-2-2000000000000000000000000004-4000000000000000000000000-22-2200000000000000000000
χ974-44-44-4-4-4-4444-44-44-22-22-22-22-22222-2-2-200000000000000000000000000-440000000000000000000000002-22-200000000000000000000
χ984-44-4-444-4-44-444-44-4-22-22-2-22-22-2-222-22200004i−4i−4i4i00000000000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ994-44-4-444-4-44-444-44-4-22-22-2-22-22-2-222-2220000−4i4i4i−4i000000000000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ1004-4-444-444-444-44-4-4-4-222-22-222-22-2-22-2-224-44-400000000000000000000000000000000-22-22000000000000000000000000000000000000
χ1014-4-444-444-444-44-4-4-4-222-22-222-22-2-22-2-22-44-44000000000000000000000000000000002-22-2000000000000000000000000000000000000
χ1024-4-44-44-44-44-4-4-4444-222-222-2-22-22-22-22-2000000000000000000004-4000000-22-2200000000000000000000000000000000000000000000
χ1034-4-44-44-44-44-4-4-4444-222-222-2-22-22-22-22-200000000000000000000-440000002-22-200000000000000000000000000000000000000000000
χ1044-4-4-444-444-4-444-4-44-2222-2-222-2-22-2-222-24-4-4400000000000000000000000000000000-222-2000000000000000000000000000000000000
χ1054-4-4-444-444-4-444-4-44-2222-2-222-2-22-2-222-2-444-4000000000000000000000000000000002-2-22000000000000000000000000000000000000
χ1064-4-4-4-4-4444-444-444-44-4-4-44-444-4-4444-44-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1074-4-4-4-4-4444-444-444-4-2222-22-2-222-2-2-22-220000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ1084-4-4-4-4-4444-444-444-4-2222-22-2-222-2-2-22-2200000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000000

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