Finite Group Databasebeta

← Group #10690633

Character table — Group #10690633

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222234444444444446661212121266121212121212121212124444888888881212121212121212242424242424242424242424242424244444888888888888
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
χ91111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222-2-2-2-222-2-2-2-2222-2-2-2-222-2-2-2-2-2-22222000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222-2-2-2-222-2-2-2-2222-2-2-2-222-2-2-2-2-2-2222200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222-2-2-2-222-2-222-2-222222222222-2-2-2-2-2-2-2-2000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ202222222-2-2-2-222-2-222-2-222222222222-2-2-2-2-2-2-2-200000000-222-20000000000000000-2-22222-2-20000000000000000
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
χ25222222-122-2-2-2-222-2-2-2-2-1-1-11111-1-1111111-1-1-1-1000000002i−2i2i−2i−i3−i3i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ26222222-122-2-2-2-222-2-2-2-2-1-1-11111-1-1111111-1-1-1-1000000002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ27222222-122-2-2-2-222-2-2-2-2-1-1-11111-1-1111111-1-1-1-100000000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ28222222-122-2-2-2-222-2-2-2-2-1-1-11111-1-1111111-1-1-1-100000000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ29222222-1-2-222-2-2-2-2-2-222-1-1-11111-1-111-1-1-1-1111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ30222222-1-2-222-2-2-2-2-2-222-1-1-11111-1-111-1-1-1-1111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ31222222-1-2-222-2-2-2-2-2-222-1-1-11111-1-111-1-1-1-11111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ32222222-1-2-222-2-2-2-2-2-222-1-1-11111-1-111-1-1-1-11111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ33222222-1-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000002-2-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ34222222-1-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000002-2-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ35222222-1-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-11111111100000000-222-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ36222222-1-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-11111111100000000-222-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ372222-2-222222-2-2-2-222-2-2222-2-2-2-2-2-22222-2-222-2-200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ382222-2-222222-2-2-2-222-2-2222-2-2-2-2-2-22222-2-222-2-20000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ392222-2-2222-2-222-2-2-2-2222222222-2-2-2-2-2-22222-2-22-22-2000000002-22-22-22-200000000000000000000000000000000
χ402222-2-2222-2-222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-22-2200000000-22-22-22-2200000000000000000000000000000000
χ412222-2-22-2-2222222-2-2-2-22222222-2-2-2-222-2-2-2-22200002-2-220000000000002-22-2-22-22000000000000000000000000
χ422222-2-22-2-2222222-2-2-2-22222222-2-2-2-222-2-2-2-2220000-222-2000000000000-22-222-22-2000000000000000000000000
χ432222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-222-2-222-2-2222-2-22000000002-22-2-22-2200000000000000000000000000000000
χ442222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-222-2-222-2-222-222-200000000-22-222-22-200000000000000000000000000000000
χ452222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-11100002i−2i2i−2i0000−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii3−33−33−33−30000000000000000
χ462222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-11100002i−2i2i−2i0000i3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii−33−33−33−330000000000000000
χ472222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-1110000−2i2i−2i2i0000−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i−33−33−33−330000000000000000
χ482222-2-2-12222-2-2-2-222-2-2-1-1-1111111-1-1-1-111-1-1110000−2i2i−2i2i0000i3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i3−33−33−33−30000000000000000
χ492222-2-2-122-2-222-2-2-2-222-1-1-1-1-1-1-1111111-1-1-1-1112-22-200000000-11-11-11-11−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ502222-2-2-122-2-222-2-2-2-222-1-1-1-1-1-1-1111111-1-1-1-1112-22-200000000-11-11-11-11i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ512222-2-2-122-2-222-2-2-2-222-1-1-1-1-1-1-1111111-1-1-1-111-22-22000000001-11-11-11-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ522222-2-2-122-2-222-2-2-2-222-1-1-1-1-1-1-1111111-1-1-1-111-22-22000000001-11-11-11-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ532222-2-2-1-2-2222222-2-2-2-2-1-1-1-1-1-1-11111-1-11111-1-100002-2-220000−i3i3i3−i3i3−i3−i3i3-11-111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ542222-2-2-1-2-2222222-2-2-2-2-1-1-1-1-1-1-11111-1-11111-1-100002-2-220000i3−i3−i3i3−i3i3i3−i3-11-111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ552222-2-2-1-2-2222222-2-2-2-2-1-1-1-1-1-1-11111-1-11111-1-10000-222-20000−i3i3i3−i3i3−i3−i3i31-11-1-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ562222-2-2-1-2-2222222-2-2-2-2-1-1-1-1-1-1-11111-1-11111-1-10000-222-20000i3−i3−i3i3−i3i3i3−i31-11-1-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ572222-2-2-1-2-2-2-2-2-2222222-1-1-1111111-1-111-1-111-1-12-2-2200000000-11-111-11-13−3−33−333−33−3−33−333−30000000000000000
χ582222-2-2-1-2-2-2-2-2-2222222-1-1-1111111-1-111-1-111-1-12-2-2200000000-11-111-11-1−333−33−3−33−333−33−3−330000000000000000
χ592222-2-2-1-2-2-2-2-2-2222222-1-1-1111111-1-111-1-111-1-1-222-2000000001-11-1-11-113−3−33−333−3−333−33−3−330000000000000000
χ602222-2-2-1-2-2-2-2-2-2222222-1-1-1111111-1-111-1-111-1-1-222-2000000001-11-1-11-11−333−33−3−333−3−33−333−30000000000000000
χ612-2-222-222i−2i2-22i−2i2i−2i2i−2i2-2-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ622-2-222-222i−2i2-22i−2i2i−2i2i−2i2-2-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ632-2-222-222i−2i-22−2i2i2i−2i−2i2i-22-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i0000000000000000000000000000000000002i−2i2-2000000000000
χ642-2-222-222i−2i-22−2i2i2i−2i−2i2i-22-22-2−2i−2i2i2i2-2−2i2i-22-222i−2i2i−2i000000000000000000000000000000000000−2i2i-22000000000000
χ652-2-222-22−2i2i2-2−2i2i−2i2i−2i2i2-2-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ662-2-222-22−2i2i2-2−2i2i−2i2i−2i2i2-2-22-2−2i−2i2i2i2-2−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ672-2-222-22−2i2i-222i−2i−2i2i2i−2i-22-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i0000000000000000000000000000000000002i−2i-22000000000000
χ682-2-222-22−2i2i-222i−2i−2i2i2i−2i-22-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i000000000000000000000000000000000000−2i2i2-2000000000000
χ692-2-22-2222i−2i2-2−2i2i−2i2i2i−2i-22-22-2−2i−2i2i2i-222i−2i2-2-222i−2i−2i2i00000000000000000000000000000000000000002-22i−2i00000000
χ702-2-22-2222i−2i2-2−2i2i−2i2i2i−2i-22-22-2−2i−2i2i2i-222i−2i2-2-222i−2i−2i2i0000000000000000000000000000000000000000-22−2i2i00000000
χ712-2-22-2222i−2i-222i−2i−2i2i−2i2i2-2-22-22i2i−2i−2i-22−2i2i-222-22i−2i−2i2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ722-2-22-2222i−2i-222i−2i−2i2i−2i2i2-2-22-22i2i−2i−2i-22−2i2i-222-22i−2i−2i2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ732-2-22-222−2i2i2-22i−2i2i−2i−2i2i-22-22-22i2i−2i−2i-22−2i2i2-2-22−2i2i2i−2i00000000000000000000000000000000000000002-2−2i2i00000000
χ742-2-22-222−2i2i2-22i−2i2i−2i−2i2i-22-22-22i2i−2i−2i-22−2i2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000-222i−2i00000000
χ752-2-22-222−2i2i-22−2i2i2i−2i2i−2i2-2-22-2−2i−2i2i2i-222i−2i-222-2−2i2i2i−2i000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ762-2-22-222−2i2i-22−2i2i2i−2i2i−2i2-2-22-2−2i−2i2i2i-222i−2i-222-2−2i2i2i−2i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ774-4-444-4-24i−4i4-44i−4i4i−4i4i−4i4-42-22−2i−2i2i2i-22−2i2i-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ784-4-444-4-24i−4i-44−4i4i4i−4i−4i4i-442-222i2i−2i−2i-222i−2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ794-4-444-4-2−4i4i4-4−4i4i−4i4i−4i4i4-42-222i2i−2i−2i-222i−2i-22-222i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ804-4-444-4-2−4i4i-444i−4i−4i4i4i−4i-442-22−2i−2i2i2i-22−2i2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ814-4-44-44-24i−4i4-4−4i4i−4i4i4i−4i-442-222i2i−2i−2i2-2−2i2i-222-2−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ824-4-44-44-24i−4i-444i−4i−4i4i−4i4i4-42-22−2i−2i2i2i2-22i−2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ834-4-44-44-2−4i4i4-44i−4i4i−4i−4i4i-442-22−2i−2i2i2i2-22i−2i-222-22i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ844-4-44-44-2−4i4i-44−4i4i4i−4i4i−4i4-42-222i2i−2i−2i2-2−2i2i2-2-222i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8588-8-8008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-400000000000044-443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-400000000000044-4−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-88-80080000000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ898-88-800-4000000000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-88-800-4000000000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000

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