Finite Group Databasebeta

← Group #10690635

Character table — Group #10690635

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222344444444444466666661212121212121212121212124444444488881212121212121212121212121212121224242424242424248888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222-2-2-2-222-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ18222222222-2-2-2-222-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222-2-2-2-2-2-2-2-222222222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000000000002-2-22
χ202222222-2-2-2-2-2-2-2-222222222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000-222-2
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-1-1-11111-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-12222-2-2-2-222-2-2-1-1-1-1-1-1-1-111111111-1-1-1-111110000000000000000
χ26222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ27222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ28222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1-2-2-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-222222-2-2-2-222-2-2-2-2-2-222222-2-222-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ302222-2-222222-2-2-2-222-2-2-2-2-2-222222-2-222-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ312222-2-2222-2-222-2-2-2-222-2-2-2-222222-2-2-2-222-2-2222-2002-200000022-2-2000022-2-20000000000000000000000000000
χ322222-2-2222-2-222-2-2-2-222-2-2-2-222222-2-2-2-222-2-222-2200-22000000-2-2220000-2-2220000000000000000000000000000
χ332222-2-22-2-222-2-222-2-222-2-2-2-2222-2-222-2-22222-2-2000000000000000000000000000000000000000000002-2-220000
χ342222-2-22-2-222-2-222-2-222-2-2-2-2222-2-222-2-22222-2-200000000000000000000000000000000000000000000-222-20000
χ352222-2-22-2-2-2-2222222-2-2-2-2-2-2222-2-22222-2-2-2-2222-200-2200000022-2-20000-2-2220000000000000000000000000000
χ362222-2-22-2-2-2-2222222-2-2-2-2-2-2222-2-22222-2-2-2-222-22002-2000000-2-222000022-2-20000000000000000000000000000
χ372222-2-2-122-2-222-2-2-2-2221111-1-1-1-1-11111-1-111-1-12-2002-2000000-1-111−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ382222-2-2-122-2-222-2-2-2-2221111-1-1-1-1-11111-1-111-1-12-2002-2000000-1-111i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ392222-2-2-122-2-222-2-2-2-2221111-1-1-1-1-11111-1-111-1-1-2200-2200000011-1-1−i3−i3i3i311-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ402222-2-2-122-2-222-2-2-2-2221111-1-1-1-1-11111-1-111-1-1-2200-2200000011-1-1i3i3−i3−i311-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ412222-2-2-1-2-2-2-2222222-2-21111-1-1-111-1-1-1-11111-1-12-200-22000000-1-111−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ422222-2-2-1-2-2-2-2222222-2-21111-1-1-111-1-1-1-11111-1-12-200-22000000-1-111i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ432222-2-2-1-2-2-2-2222222-2-21111-1-1-111-1-1-1-11111-1-1-22002-200000011-1-1−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ442222-2-2-1-2-2-2-2222222-2-21111-1-1-111-1-1-1-11111-1-1-22002-200000011-1-1i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ452-2-222-222i−2i2-22-22i−2i2i−2i2i−2i22-2-2-2-222i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ462-2-222-222i−2i2-22-22i−2i2i−2i2i−2i22-2-2-2-222i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ472-2-222-222i−2i-22-222i−2i−2i2i−2i2i22-2-2-2-222i−2i2i−2i−2i2i−2i2i-22-22002i−2i002-2000000002i−2i2i−2i00002-22-2000000000000000000000000
χ482-2-222-222i−2i-22-222i−2i−2i2i−2i2i22-2-2-2-222i−2i2i−2i−2i2i−2i2i-22-2200−2i2i00-2200000000−2i2i−2i2i0000-22-22000000000000000000000000
χ492-2-222-22−2i2i2-22-2−2i2i−2i2i−2i2i22-2-2-2-22−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ502-2-222-22−2i2i2-22-2−2i2i−2i2i−2i2i22-2-2-2-22−2i2i−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ512-2-222-22−2i2i-22-22−2i2i2i−2i2i−2i22-2-2-2-22−2i2i−2i2i2i−2i2i−2i-22-22002i−2i00-22000000002i−2i2i−2i0000-22-22000000000000000000000000
χ522-2-222-22−2i2i-22-22−2i2i2i−2i2i−2i22-2-2-2-22−2i2i−2i2i2i−2i2i−2i-22-2200−2i2i002-200000000−2i2i−2i2i00002-22-2000000000000000000000000
χ532-2-222-2-12i−2i-22-222i−2i−2i2i−2i2i-1-11111-1−ii−iii−ii−i1-11-1002i−2i002-200003−33−3−ii−ii−i3i3−i3i3-11-11−i3i3−i3i33−33−30000000000000000
χ542-2-222-2-12i−2i-22-222i−2i−2i2i−2i2i-1-11111-1−ii−iii−ii−i1-11-1002i−2i002-20000−33−33−ii−iii3−i3i3−i3-11-11i3−i3i3−i3−33−330000000000000000
χ552-2-222-2-12i−2i-22-222i−2i−2i2i−2i2i-1-11111-1−ii−iii−ii−i1-11-100−2i2i00-2200003−33−3i−ii−i−i3i3−i3i31-11-1i3−i3i3−i3−33−330000000000000000
χ562-2-222-2-12i−2i-22-222i−2i−2i2i−2i2i-1-11111-1−ii−iii−ii−i1-11-100−2i2i00-220000−33−33i−ii−ii3−i3i3−i31-11-1−i3i3−i3i33−33−30000000000000000
χ572-2-222-2-1−2i2i-22-22−2i2i2i−2i2i−2i-1-11111-1i−ii−i−ii−ii1-11-1002i−2i00-2200003−33−3−ii−iii3−i3i3−i31-11-1−i3i3−i3i3−33−330000000000000000
χ582-2-222-2-1−2i2i-22-22−2i2i2i−2i2i−2i-1-11111-1i−ii−i−ii−ii1-11-1002i−2i00-220000−33−33−ii−ii−i3i3−i3i31-11-1i3−i3i3−i33−33−30000000000000000
χ592-2-222-2-1−2i2i-22-22−2i2i2i−2i2i−2i-1-11111-1i−ii−i−ii−ii1-11-100−2i2i002-200003−33−3i−ii−ii3−i3i3−i3-11-11i3−i3i3−i33−33−30000000000000000
χ602-2-222-2-1−2i2i-22-22−2i2i2i−2i2i−2i-1-11111-1i−ii−i−ii−ii1-11-100−2i2i002-20000−33−33i−ii−i−i3i3−i3i3-11-11−i3i3−i3i3−33−330000000000000000
χ612-2-22-2222i−2i2-2-22−2i2i2i−2i−2i2i-2-222-2-222i−2i−2i2i2i−2i−2i2i2-2-22000000002-22i−2i00000000000000002-2-222i−2i−2i2i0000000000000000
χ622-2-22-2222i−2i2-2-22−2i2i2i−2i−2i2i-2-222-2-222i−2i−2i2i2i−2i−2i2i2-2-2200000000-22−2i2i0000000000000000-222-2−2i2i2i−2i0000000000000000
χ632-2-22-2222i−2i-222-2−2i2i−2i2i2i−2i-2-222-2-222i−2i−2i2i−2i2i2i−2i-222-2000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ642-2-22-2222i−2i-222-2−2i2i−2i2i2i−2i-2-222-2-222i−2i−2i2i−2i2i2i−2i-222-20000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ652-2-22-222−2i2i2-2-222i−2i−2i2i2i−2i-2-222-2-22−2i2i2i−2i−2i2i2i−2i2-2-22000000002-2−2i2i00000000000000002-2-22−2i2i2i−2i0000000000000000
χ662-2-22-222−2i2i2-2-222i−2i−2i2i2i−2i-2-222-2-22−2i2i2i−2i−2i2i2i−2i2-2-2200000000-222i−2i0000000000000000-222-22i−2i−2i2i0000000000000000
χ672-2-22-222−2i2i-222-22i−2i2i−2i−2i2i-2-222-2-22−2i2i2i−2i2i−2i−2i2i-222-20000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ682-2-22-222−2i2i-222-22i−2i2i−2i−2i2i-2-222-2-22−2i2i2i−2i2i−2i−2i2i-222-2000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ692-2-22-22-12i−2i2-2-22−2i2i2i−2i−2i2i11-1-111-1−iii−i−iii−i-111-1000000002-22i−2i3−3−333−3−33−i3i3i3−i3−i3i3i3−i3-111-1−iii−i0000000000000000
χ702-2-22-22-12i−2i2-2-22−2i2i2i−2i−2i2i11-1-111-1−iii−i−iii−i-111-1000000002-22i−2i−333−3−333−3i3−i3−i3i3i3−i3−i3i3-111-1−iii−i0000000000000000
χ712-2-22-22-12i−2i2-2-22−2i2i2i−2i−2i2i11-1-111-1−iii−i−iii−i-111-100000000-22−2i2i3−3−33−333−3−i3i3i3−i3i3−i3−i3i31-1-11i−i−ii0000000000000000
χ722-2-22-22-12i−2i2-2-22−2i2i2i−2i−2i2i11-1-111-1−iii−i−iii−i-111-100000000-22−2i2i−333−33−3−33i3−i3−i3i3−i3i3i3−i31-1-11i−i−ii0000000000000000
χ732-2-22-22-1−2i2i2-2-222i−2i−2i2i2i−2i11-1-111-1i−i−iii−i−ii-111-1000000002-2−2i2i3−3−333−3−33i3−i3−i3i3i3−i3−i3i3-111-1i−i−ii0000000000000000
χ742-2-22-22-1−2i2i2-2-222i−2i−2i2i2i−2i11-1-111-1i−i−iii−i−ii-111-1000000002-2−2i2i−333−3−333−3−i3i3i3−i3−i3i3i3−i3-111-1i−i−ii0000000000000000
χ752-2-22-22-1−2i2i2-2-222i−2i−2i2i2i−2i11-1-111-1i−i−iii−i−ii-111-100000000-222i−2i3−3−33−333−3i3−i3−i3i3−i3i3i3−i31-1-11−iii−i0000000000000000
χ762-2-22-22-1−2i2i2-2-222i−2i−2i2i2i−2i11-1-111-1i−i−iii−i−ii-111-100000000-222i−2i−333−33−3−33−i3i3i3−i3i3−i3−i3i31-1-11−iii−i0000000000000000
χ77444444-244-4-4-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ78444444-2-4-4-4-4-4-4-4-44444-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000000000000000
χ794444-4-4-24444-4-4-4-444-4-42222-2-2-2-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ804444-4-4-2-4-444-4-444-4-4442222-2-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ814-4-444-4-24i−4i4-44-44i−4i4i−4i4i−4i-2-22222-2−2i2i−2i2i−2i2i−2i2i-22-220000000000000000000000000000000000000000000000000000
χ824-4-444-4-2−4i4i4-44-4−4i4i−4i4i−4i4i-2-22222-22i−2i2i−2i2i−2i2i−2i-22-220000000000000000000000000000000000000000000000000000
χ834-4-44-44-24i−4i-444-4−4i4i−4i4i4i−4i22-2-222-2−2i2i2i−2i2i−2i−2i2i2-2-220000000000000000000000000000000000000000000000000000
χ844-4-44-44-2−4i4i-444-44i−4i4i−4i−4i4i22-2-222-22i−2i−2i2i−2i2i2i−2i2-2-220000000000000000000000000000000000000000000000000000
χ8588-8-800800000000000000008-8-80000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4000000000000−4i34i3−4i34i3-4440000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000000000004i3−4i34i3−4i3-4440000000000000000000000000000000000000000000000000000000000000000
χ888-88-80080000000000000000-88-80000000000000000000000000000000000000000000000000000000000000000
χ898-88-800-4000000000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000000
χ908-88-800-40000000000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.