Finite Group Databasebeta

← Group #10702247

Character table — Group #10702247

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111111111111222222222222222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444424242424242424242424242424242424
order1222222222222222344444444666666666666666121212121212121212121212121212124444444488888888888888881212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424242222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ10111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-111−i−iii
χ11111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−i-1-111−i−iii
χ12111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iii11-1-1ii−i−i
χ13111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii11-1-1−i−iii
χ14111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-111ii−i−i
χ15111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ16111111-1-1-1-1-11-11-1-11111-1-1-11-1111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111110000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111112222-2-2-2-20000000000000000-1-1-1-11111-1-1-1-111113333−3−3−3−33333−3−3−3−33333−3−3−3−33333−3−3−3−30000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111112222-2-2-2-20000000000000000-1-1-1-11111-1-1-1-11111−3−3−3−33333−3−3−3−33333−3−3−3−33333−3−3−3−333330000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222200000000000000001111-1-1-1-11111-1-1-1-13333−3−3−3−33333−3−3−3−3−3−3−3−33333−3−3−3−333330000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222200000000000000001111-1-1-1-11111-1-1-1-1−3−3−3−33333−3−3−3−333333333−3−3−3−33333−3−3−3−30000000000000000
χ27222222-2-2-2-2-22-22-2-22-2-2-2222-22222222-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222-2-2222i2i−2i−2i−2i−2i2i2i00000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ28222222-2-2-2-2-22-22-2-22-2-2-2222-22222222-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ29222222-2-2-2-2-22-22-2-2-1222-2-2-22-2-1-1-1-1-1-1111111-111-1-1-1-1-1-1111111-1-1112i2i−2i−2i2i2i−2i−2i2222-2-2-2-22i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ30222222-2-2-2-2-22-22-2-2-1222-2-2-22-2-1-1-1-1-1-1111111-111-1-1-1-1-1-1111111-1-1112i2i−2i−2i2i2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ31222222-2-2-2-2-22-22-2-2-1222-2-2-22-2-1-1-1-1-1-1111111-111-1-1-1-1-1-1111111-1-111−2i−2i2i2i−2i−2i2i2i2222-2-2-2-2−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ32222222-2-2-2-2-22-22-2-2-1222-2-2-22-2-1-1-1-1-1-1111111-111-1-1-1-1-1-1111111-1-111−2i−2i2i2i−2i−2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ33222222-2-2-2-2-22-22-2-2-1-2-2-2222-22-1-1-1-1-1-1111111-111111111-1-1-1-1-1-111-1-12i2i−2i−2i−2i−2i2i2i0000000000000000−i−i−i−iiiiiiiii−i−i−i−i3333−3−3−3−3−3−3−3−33333i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000000000000000
χ34222222-2-2-2-2-22-22-2-2-1-2-2-2222-22-1-1-1-1-1-1111111-111111111-1-1-1-1-1-111-1-12i2i−2i−2i−2i−2i2i2i0000000000000000−i−i−i−iiiiiiiii−i−i−i−i−3−3−3−333333333−3−3−3−3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000000000000000
χ35222222-2-2-2-2-22-22-2-2-1-2-2-2222-22-1-1-1-1-1-1111111-111111111-1-1-1-1-1-111-1-1−2i−2i2i2i2i2i−2i−2i0000000000000000iiii−i−i−i−i−i−i−i−iiiii3333−3−3−3−3−3−3−3−33333−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000000000000000
χ36222222-2-2-2-2-22-22-2-2-1-2-2-2222-22-1-1-1-1-1-1111111-111111111-1-1-1-1-1-111-1-1−2i−2i2i2i2i2i−2i−2i0000000000000000iiii−i−i−i−i−i−i−i−iiiii−3−3−3−333333333−3−3−3−3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000000000000000
χ372222-2-2222-2-2-2-2-2-22200000000222-2-2-2222-2-2-2-22-200000000000000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−22i2i−2i−2i00002i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i222−2−222−2−222−2−222−2−20000000000000000
χ382222-2-2222-2-2-2-2-2-22200000000222-2-2-2222-2-2-2-22-200000000000000002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−2222i2i−2i−2i00002i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2−222−2−222−2−222−2−2220000000000000000
χ392222-2-2222-2-2-2-2-2-22200000000222-2-2-2222-2-2-2-22-20000000000000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−222−2i−2i2i2i0000−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2−222−2−222−2−222−2−2220000000000000000
χ402222-2-2222-2-2-2-2-2-22200000000222-2-2-2222-2-2-2-22-20000000000000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−2−2i−2i2i2i0000−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i222−2−222−2−222−2−222−2−20000000000000000
χ412222-2-2222-2-2-2-2-2-22-100000000-1-1-1111-1-1-11111-11333−3−3−3333−3−3−33−33−32i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−2−i−iii−i3−i3i3i3−i−iii−i3−i3i3i3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70000000000000000
χ422222-2-2222-2-2-2-2-2-22-100000000-1-1-1111-1-1-11111-11333−3−3−3333−3−3−33−33−32i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−222−i−iii−i3−i3i3i3−i−iii−i3−i3i3i3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70000000000000000
χ432222-2-2222-2-2-2-2-2-22-100000000-1-1-1111-1-1-11111-11333−3−3−3333−3−3−33−33−3−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−222ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70000000000000000
χ442222-2-2222-2-2-2-2-2-22-100000000-1-1-1111-1-1-11111-11333−3−3−3333−3−3−33−33−3−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−2ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70000000000000000
χ452222-2-2222-2-2-2-2-2-22-100000000-1-1-1111-1-1-11111-11−3−3−3333−3−3−3333−33−332i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−2−i−iiii3i3−i3−i3−i−iiii3i3−i3−i3ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230000000000000000
χ462222-2-2222-2-2-2-2-2-22-100000000-1-1-1111-1-1-11111-11−3−3−3333−3−3−3333−33−332i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−222−i−iiii3i3−i3−i3−i−iiii3i3−i3−i3−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.