Finite Group Databasebeta

← Group #10701899

Character table — Group #10701899

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111111111111222222222222222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444424242424242424242424242424242424
order1222222222222222344444444666666666666666121212121212121212121212121212124444444488888888888888881212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424242222222244444444
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
χ911111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1211111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1311111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1411111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1511111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000000002222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
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
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-222-2-20000000000000000-1-1-1-11111-1-1-1-111113333−3−3−3−33333−3−3−3−33333−3−3−3−33333−3−3−3−30000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-222-2-20000000000000000-1-1-1-11111-1-1-1-11111−3−3−3−33333−3−3−3−33333−3−3−3−33333−3−3−3−333330000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222-2-22200000000000000001111-1-1-1-11111-1-1-1-13333−3−3−3−33333−3−3−3−3−3−3−3−33333−3−3−3−333330000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222-2-22200000000000000001111-1-1-1-11111-1-1-1-1−3−3−3−33333−3−3−3−333333333−3−3−3−33333−3−3−3−30000000000000000
χ2722222-2-2-2-2-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22222222222-2-2-2-22200000000000000002222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2822222-2-2-2-2-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-222222222-2-22222-2-20000000000000000-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ2922222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ3022222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ3122222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ3222222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ3322222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-111111111-1-1-111111111-1-1-1-1-1-1-1-122-2-2-2-2220000000000000000-1-1-1-111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000000000000000
χ3422222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-111111111-1-1-111111111-1-1-1-1-1-1-1-122-2-2-2-2220000000000000000-1-1-1-111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000000000000000
χ3522222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-111111111-1-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-200000000000000001111-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000000000000000
χ3622222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-111111111-1-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-200000000000000001111-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000000000000000
χ37222-2-22222-2-22-2-2-2-220000000022-2-22222-2-2-2-22-2-20000000000000000002-2002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000022-2-2000022-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ38222-2-22222-2-22-2-2-2-220000000022-2-22222-2-2-2-22-2-20000000000000000002-2002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000022-2-2000022-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ39222-2-22222-2-22-2-2-2-220000000022-2-22222-2-2-2-22-2-2000000000000000000-2200-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-2-2220000-2-222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ40222-2-22222-2-22-2-2-2-220000000022-2-22222-2-2-2-22-2-2000000000000000000-2200-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-2-2220000-2-222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ41222-2-22222-2-22-2-2-2-2-100000000-1-111-1-1-1-11111-1113333−3−3−3−333−3−333−3−3002-2002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i233−3−3-1-11133−3−3-1-111ζ5+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
χ42222-2-22222-2-22-2-2-2-2-100000000-1-111-1-1-1-11111-1113333−3−3−3−333−3−333−3−3002-2002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i233−3−3-1-11133−3−3-1-111−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
χ43222-2-22222-2-22-2-2-2-2-100000000-1-111-1-1-1-11111-1113333−3−3−3−333−3−333−3−300-2200-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−3−33311-1-1−3−33311-1-1ζ5+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
χ44222-2-22222-2-22-2-2-2-2-100000000-1-111-1-1-1-11111-1113333−3−3−3−333−3−333−3−300-2200-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−3−33311-1-1−3−33311-1-1−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
χ45222-2-22222-2-22-2-2-2-2-100000000-1-111-1-1-1-11111-111−3−3−3−33333−3−333−3−333002-2002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−3−333-1-111−3−333-1-111ζ13+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
χ46222-2-22222-2-22-2-2-2-2-100000000-1-111-1-1-1-11111-111−3−3−3−33333−3−333−3−333002-2002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−3−333-1-111−3−333-1-111−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.