Finite Group Databasebeta

← Group #10690717

Character table — Group #10690717

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222234444444444446661212121266121212121212121212124444888888881212121212121212242424242424242424242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ91111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222-2-2-2-222-2-2-2-222222222222-2-2-2-2-2-2-2-22-22-20000000022-2-222-2-200000000000000000000000000000000
χ18222222222-2-2-2-222-2-2-2-222222222222-2-2-2-2-2-2-2-2-22-2200000000-2-222-2-22200000000000000000000000000000000
χ192222222-2-2-2-2-2-2-2-22222222-2-2-2-222-2-2-2-2-2-222222-2-220000000022-2-2-2-22200000000000000000000000000000000
χ202222222-2-2-2-2-2-2-2-22222222-2-2-2-222-2-2-2-2-2-22222-222-200000000-2-22222-2-200000000000000000000000000000000
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
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
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
χ25222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-22-200000000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ26222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-22-200000000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ27222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-220000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ28222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-220000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ29222222-1-2-22222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-1111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ30222222-1-2-22222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-1111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ31222222-1-2-22222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-11111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ32222222-1-2-22222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-11111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ33222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-12-2-2200000000-1-11111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ34222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-12-2-2200000000-1-11111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ35222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-222-20000000011-1-1-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ36222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-222-20000000011-1-1-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ372222-2-222222-2-2-2-222-2-2222-2-2-2-2-2-22222-2-222-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382222-2-222222-2-2-2-222-2-2222-2-2-2-2-2-22222-2-222-2-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392222-2-2222-2-222-2-2-2-222222-2-2-2-2-2-222-2-222-2-22200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ402222-2-2222-2-222-2-2-2-222222-2-2-2-2-2-222-2-222-2-2220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ412222-2-22-2-222-2-222-2-2222222222-2-2-2-222-2-2-2-222000000002-2-2200000000000000002-22-2-22-220000000000000000
χ422222-2-22-2-222-2-222-2-2222222222-2-2-2-222-2-2-2-22200000000-222-20000000000000000-22-222-22-20000000000000000
χ432222-2-22-2-2-2-2222222-2-22222222-2-2-2-2-2-22222-2-200002-2-220000000000002-22-2-22-22000000000000000000000000
χ442222-2-22-2-2-2-2222222-2-22222222-2-2-2-2-2-22222-2-20000-222-2000000000000-22-222-22-2000000000000000000000000
χ452222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-111000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i33−3−333−3−33−ii−ii−ii−ii0000000000000000
χ462222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-111000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−333−3−333−3−ii−ii−ii−ii0000000000000000
χ472222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-11100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−333−3−333−3i−ii−ii−ii−i0000000000000000
χ482222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-11100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i33−3−333−3−33i−ii−ii−ii−i0000000000000000
χ492222-2-2-122-2-222-2-2-2-222-1-1-1111111-1-111-1-111-1-100002i−2i2i−2i0000−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii3−3−333−3−330000000000000000
χ502222-2-2-122-2-222-2-2-2-222-1-1-1111111-1-111-1-111-1-100002i−2i2i−2i0000i3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii−333−3−333−30000000000000000
χ512222-2-2-122-2-222-2-2-2-222-1-1-1111111-1-111-1-111-1-10000−2i2i−2i2i0000−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i−333−3−333−30000000000000000
χ522222-2-2-122-2-222-2-2-2-222-1-1-1111111-1-111-1-111-1-10000−2i2i−2i2i0000i3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i3−3−333−3−330000000000000000
χ532222-2-2-1-2-222-2-222-2-222-1-1-1-1-1-1-11111-1-11111-1-1000000002-2-22−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3-11-111-11-10000000000000000
χ542222-2-2-1-2-222-2-222-2-222-1-1-1-1-1-1-11111-1-11111-1-1000000002-2-22i3−i3i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3-11-111-11-10000000000000000
χ552222-2-2-1-2-222-2-222-2-222-1-1-1-1-1-1-11111-1-11111-1-100000000-222-2−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i3i3−i31-11-1-11-110000000000000000
χ562222-2-2-1-2-222-2-222-2-222-1-1-1-1-1-1-11111-1-11111-1-100000000-222-2i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i3−i3i31-11-1-11-110000000000000000
χ572222-2-2-1-2-2-2-2222222-2-2-1-1-1-1-1-1-1111111-1-1-1-11100002-2-220000−i3i3i3−i3i3−i3−i3i3-11-111-11-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ582222-2-2-1-2-2-2-2222222-2-2-1-1-1-1-1-1-1111111-1-1-1-11100002-2-220000i3−i3−i3i3−i3i3i3−i3-11-111-11-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ592222-2-2-1-2-2-2-2222222-2-2-1-1-1-1-1-1-1111111-1-1-1-1110000-222-20000−i3i3i3−i3i3−i3−i3i31-11-1-11-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ602222-2-2-1-2-2-2-2222222-2-2-1-1-1-1-1-1-1111111-1-1-1-1110000-222-20000i3−i3−i3i3−i3i3i3−i31-11-1-11-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ612-22-22-222i−2i2-22-22i−2i2i−2i2i−2i-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ622-22-22-222i−2i2-22-22i−2i2i−2i2i−2i-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ632-22-22-222i−2i-22-222i−2i−2i2i−2i2i-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ642-22-22-222i−2i-22-222i−2i−2i2i−2i2i-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ652-22-22-22−2i2i2-22-2−2i2i−2i2i−2i2i-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ662-22-22-22−2i2i2-22-2−2i2i−2i2i−2i2i-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ672-22-22-22−2i2i-22-22−2i2i2i−2i2i−2i-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ682-22-22-22−2i2i-22-22−2i2i2i−2i2i−2i-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ692-22-2-2222i−2i2-2-22−2i2i2i−2i−2i2i-22-2−2i−2i2i2i-222i−2i2-2-222i−2i−2i2i0000000000000000000000000000000000002-22i−2i000000000000
χ702-22-2-2222i−2i2-2-22−2i2i2i−2i−2i2i-22-2−2i−2i2i2i-222i−2i2-2-222i−2i−2i2i000000000000000000000000000000000000-22−2i2i000000000000
χ712-22-2-2222i−2i-222-2−2i2i−2i2i2i−2i-22-2−2i−2i2i2i-222i−2i-222-2−2i2i2i−2i00000000000000000000000000000000000000002-22i−2i00000000
χ722-22-2-2222i−2i-222-2−2i2i−2i2i2i−2i-22-2−2i−2i2i2i-222i−2i-222-2−2i2i2i−2i0000000000000000000000000000000000000000-22−2i2i00000000
χ732-22-2-222−2i2i2-2-222i−2i−2i2i2i−2i-22-22i2i−2i−2i-22−2i2i2-2-22−2i2i2i−2i0000000000000000000000000000000000002-2−2i2i000000000000
χ742-22-2-222−2i2i2-2-222i−2i−2i2i2i−2i-22-22i2i−2i−2i-22−2i2i2-2-22−2i2i2i−2i000000000000000000000000000000000000-222i−2i000000000000
χ752-22-2-222−2i2i-222-22i−2i2i−2i−2i2i-22-22i2i−2i−2i-22−2i2i-222-22i−2i−2i2i00000000000000000000000000000000000000002-2−2i2i00000000
χ762-22-2-222−2i2i-222-22i−2i2i−2i−2i2i-22-22i2i−2i−2i-22−2i2i-222-22i−2i−2i2i0000000000000000000000000000000000000000-222i−2i00000000
χ774-44-44-4-24i−4i4-44-44i−4i4i−4i4i−4i2-22−2i−2i2i2i-22−2i2i-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ784-44-44-4-24i−4i-44-444i−4i−4i4i−4i4i2-22−2i−2i2i2i-22−2i2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ794-44-44-4-2−4i4i4-44-4−4i4i−4i4i−4i4i2-222i2i−2i−2i-222i−2i-22-222i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ804-44-44-4-2−4i4i-44-44−4i4i4i−4i4i−4i2-222i2i−2i−2i-222i−2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ814-44-4-44-24i−4i4-4-44−4i4i4i−4i−4i4i2-222i2i−2i−2i2-2−2i2i-222-2−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ824-44-4-44-24i−4i-444-4−4i4i−4i4i4i−4i2-222i2i−2i−2i2-2−2i2i2-2-222i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ834-44-4-44-2−4i4i4-4-444i−4i−4i4i4i−4i2-22−2i−2i2i2i2-22i−2i-222-22i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ844-44-4-44-2−4i4i-444-44i−4i4i−4i−4i4i2-22−2i−2i2i2i2-22i−2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ8588-8-80080000000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4000000000000-444−4i34i3−4i34i30000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-4000000000000-4444i3−4i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ888-8-88008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-400000000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800-400000000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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