Finite Group Databasebeta

← Group #10693941

Character table — Group #10693941

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order12224444344444444666888888881212121212121212121212122466888812121212121224242424242424242424242424242424888888882424242424242424242424242424242488888888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-1-11-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i
χ101111-1-1-1-11-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii
χ111111-1-1-1-11-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−ii
χ121111-1-1-1-11-1-11111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−i
χ131111-1-1-1-11-1-11111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−ii
χ141111-1-1-1-11-1-11111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i
χ151111-1-1-1-11-1-11111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−i
χ161111-1-1-1-11-1-11111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii
χ1722222222222-2-222-2-222200000000222222222222-2-2-2-20000-2-2-2-2-2-2000000000000000000000000000000000000000022-2-222-2-2000000000000
χ1822222222222-2-222-2-222200000000222222222222-2-2-2-20000-2-2-2-2-2-20000000000000000000000000000000000000000-2-222-2-222000000000000
χ19222222222-2-222-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ20222222222-2-222-2-222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222000000002222-2-2-2-2-2-2-2-22222000022-2-2-2-20000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ22222222222-2-2-2-2-2-2-2-2222000000002222-2-2-2-2-2-2-2-22222000022-2-2-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ2322222222-122222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2422222222-122222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2522222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ2622222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2722222222-1-2-222-2-222-1-1-122222222-1-1-1-111111111-2-211-2-2-2-211-1-1-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−300000000000000000000
χ2822222222-1-2-222-2-222-1-1-122222222-1-1-1-111111111-2-211-2-2-2-211-1-1-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−33300000000000000000000
χ2922222222-1-2-222-2-222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-2-211222211-1-1-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−33300000000000000000000
χ3022222222-1-2-222-2-222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-2-211222211-1-1-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−300000000000000000000
χ312222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-22-222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-22-22222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ332222-2-2-2-2222-2-2-2-22222200000000-2-2-2-22222-2-2-2-2-22-2-200002222-2-200000000000000000000000000000000000000000000000022-2-2-2-2220000
χ342222-2-2-2-2222-2-2-2-22222200000000-2-2-2-22222-2-2-2-2-22-2-200002222-2-2000000000000000000000000000000000000000000000000-2-22222-2-20000
χ352222-2-2-2-22-2-2-2-2222222200000000-2-2-2-2-2-2-2-222222-2220000-2-222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ362222-2-2-2-22-2-2-2-2222222200000000-2-2-2-2-2-2-2-222222-2220000-2-222-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-12222-2-2-2-21111-1-1-1-111112-2-1-1-2-2221111-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-12222-2-2-2-21111-1-1-1-111112-2-1-1-2-2221111-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-1-2-2-2-222221111-1-1-1-111112-2-1-122-2-21111-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−300000000000000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-1-2-2-2-222221111-1-1-1-111112-2-1-122-2-21111-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ412222-2-2-2-2-1-2-22222-2-2-1-1-12222-2-2-2-211111111-1-1-1-1-221122-2-2-1-111-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ422222-2-2-2-2-1-2-22222-2-2-1-1-12222-2-2-2-211111111-1-1-1-1-221122-2-2-1-111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ432222-2-2-2-2-1-2-22222-2-2-1-1-1-2-2-2-2222211111111-1-1-1-1-2211-2-222-1-111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ442222-2-2-2-2-1-2-22222-2-2-1-1-1-2-2-2-2222211111111-1-1-1-1-2211-2-222-1-111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ4522-2-22i2i−2i−2i2002-2002i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000002i−2i2-222-2-200002i2i−2i−2i00002−2−i2i22−2−i2i22−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000000000000000
χ4622-2-22i2i−2i−2i2002-2002i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000002i−2i2-222-2-200002i2i−2i−2i0000−22i2−i2−22i2−i2−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000000000000000
χ4722-2-22i2i−2i−2i2002-2002i−2i2-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000002i−2i2-2-2-2220000−2i−2i2i2i00002−2−i2i2−22i2−i22−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000000000000000
χ4822-2-22i2i−2i−2i2002-2002i−2i2-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000002i−2i2-2-2-2220000−2i−2i2i2i0000−22i2−i22−2−i2i2−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000000000000000
χ4922-2-22i2i−2i−2i-1002-2002i−2i-11122-2-22i2i−2i−2i−i−iii−i3−i3i3i333−3−300−i3i300003−3−ii-11-1-11133−3−3−i−iii−i3−i3i3i32−2−i2i22−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000
χ5022-2-22i2i−2i−2i-1002-2002i−2i-11122-2-22i2i−2i−2i−i−iii−i3−i3i3i333−3−300−i3i300003−3−ii-11-1-11133−3−3−i−iii−i3−i3i3i3−22i2−i2−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000
χ5122-2-22i2i−2i−2i-1002-2002i−2i-11122-2-22i2i−2i−2i−i−iiii3i3−i3−i3−3−33300i3−i30000−33−ii-11-1-111−3−333−i−iiii3i3−i3−i32−2−i2i22−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000
χ5222-2-22i2i−2i−2i-1002-2002i−2i-11122-2-22i2i−2i−2i−i−iiii3i3−i3−i3−3−33300i3−i30000−33−ii-11-1-111−3−333−i−iiii3i3−i3−i3−22i2−i2−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000
χ5322-2-22i2i−2i−2i-1002-2002i−2i-111-2-222−2i−2i2i2i−i−iii−i3−i3i3i333−3−300−i3i300003−3−ii-1111-1-1−3−333ii−i−ii3i3−i3−i32−2−i2i2−22i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000
χ5422-2-22i2i−2i−2i-1002-2002i−2i-111-2-222−2i−2i2i2i−i−iii−i3−i3i3i333−3−300−i3i300003−3−ii-1111-1-1−3−333ii−i−ii3i3−i3−i3−22i2−i22−2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000
χ5522-2-22i2i−2i−2i-1002-2002i−2i-111-2-222−2i−2i2i2i−i−iiii3i3−i3−i3−3−33300i3−i30000−33−ii-1111-1-133−3−3ii−i−i−i3−i3i3i32−2−i2i2−22i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000
χ5622-2-22i2i−2i−2i-1002-2002i−2i-111-2-222−2i−2i2i2i−i−iiii3i3−i3−i3−3−33300i3−i30000−33−ii-1111-1-133−3−3ii−i−i−i3−i3i3i3−22i2−i22−2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000
χ5722-2-2−2i−2i2i2i2002-200−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000−2i2i2-222-2-20000−2i−2i2i2i00002−2i2−i22−2i2−i22−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000000000000000
χ5822-2-2−2i−2i2i2i2002-200−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000−2i2i2-222-2-20000−2i−2i2i2i0000−22−i2i2−22−i2i2−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000000000000000
χ5922-2-2−2i−2i2i2i2002-200−2i2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000−2i2i2-2-2-22200002i2i−2i−2i00002−2i2−i2−22−i2i22−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000000000000000
χ6022-2-2−2i−2i2i2i2002-200−2i2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000−2i2i2-2-2-22200002i2i−2i−2i0000−22−i2i22−2i2−i2−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000000000000000
χ6122-2-2−2i−2i2i2i-1002-200−2i2i-11122-2-2−2i−2i2i2iii−i−i−i3−i3i3i3−3−33300−i3i30000−33i−i-11-1-111−3−333ii−i−i−i3−i3i3i32−2i2−i22−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000
χ6222-2-2−2i−2i2i2i-1002-200−2i2i-11122-2-2−2i−2i2i2iii−i−i−i3−i3i3i3−3−33300−i3i30000−33i−i-11-1-111−3−333ii−i−i−i3−i3i3i3−22−i2i2−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.