Finite Group Databasebeta

← Group #10801258

Character table — Group #10801258

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111111111112222222222222222444444444444444444446666666666666666888888888888888888888888888888881212121212121212121212121212121224242424
order1222222244444444366666661212121212121212444444448888888888882222444488888888246688121212121212121212122424242424242424242424242424242422444444888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ5111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1
χ911111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111
χ1011111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-11111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-111i−i11-1-111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1i−i
χ1811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii1-111i−i11-1-111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-11111−i−iii−i−iii-11−ii
χ1911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1-111−ii11-1-111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1−ii
χ2011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i1-111−ii11-1-111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11i−i
χ2111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111ii−i−iii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i-11-1-1−ii11-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-1-111-1-111ii−i−i−i−iii-11−ii
χ2211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111ii−i−iii−i−i−i−iii-1-1-1-11111−i−i−i−iiiii-11-1-1−ii11-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii11-1-111-1-1−i−iiiii−i−i1-1i−i
χ2311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−iii−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiii-11-1-1i−i11-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111−i−iiiii−i−i-11i−i
χ2411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−iii−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−i-11-1-1i−i11-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i11-1-111-1-1ii−i−i−i−iii1-1−ii
χ2511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-11-1-1i−i-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1ii−i−i−i−iii-11i−i
χ2611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-11-1-1i−i-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111−i−iiiii−i−i1-1−ii
χ2711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11-1-1−ii-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1−i−iiiii−i−i-11−ii
χ2811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-11-1-1−ii-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111ii−i−i−i−iii1-1i−i
χ2911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiii1-111−ii-1-111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-11111ii−i−iii−i−i1-1−ii
χ3011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i-1-1-1-11111iiii−i−i−i−i1-111−ii-1-111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i1111-1-1-1-1−i−iii−i−iii-11i−i
χ3111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i1-111i−i-1-111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-11111−i−iii−i−iii1-1i−i
χ3211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iii-1-1-1-11111−i−i−i−iiiii1-111i−i-1-111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii1111-1-1-1-1ii−i−iii−i−i-11−ii
χ332222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222222222000000000000000022-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ342222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-1-1-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ352222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-222222222-2-2-2-20000000000000000-2-211-2-2-1-1-1-1111111-1-1-1-11111-1-1-1-1111100000000000000000000
χ362222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-21122-1-1-1-11111111111-1-1-1-11111-1-1-1-100000000000000000000
χ372222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-211221111-1-1-1-111-1-1-1-1-1-1-1-11111111100000000000000000000
χ382222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2222222220000000000000000-2-211-2-21111-1-1-1-11111111111-1-1-1-1-1-1-1-100000000000000000000
χ392222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000022-1-1-2-211111111-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ402222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022-1-12211111111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000002-2-1-12i−2i-1-111-1-11111−i−iii−i−iii−i−iii−i−iii00000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000002-2-1-1−2i2i-1-111-1-11111ii−i−iii−i−iii−i−iii−i−i00000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000-2211−2i2i-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i00000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000-22112i−2i-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii00000000000000000000
χ4522222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-22222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000-22112i−2i11-1-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−i00000000000000000000
χ4622222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-22222-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000-2211−2i2i11-1-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iii00000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000002-2-1-1−2i2i11-1-111-1-111−i−iiiii−i−iii−i−i−i−iii00000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000002-2-1-12i−2i11-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i00000000000000000000
χ49222-2-2-2-2222-2-2-2-222222-2-2-2-2222-2-2-2-2222i−2i2i−2i00000000000000000000000022-2-222-2-20000002i−2i2i−2i0000000000000000000000000000002i−2i2i−2i00000000
χ50222-2-2-2-2222-2-2-2-222222-2-2-2-2222-2-2-2-2222i−2i2i−2i000000000000000000000000-2-222-2-2220000002i−2i2i−2i000000000000000000000000000000−2i2i−2i2i00000000
χ51222-2-2-2-2222-2-2-2-222222-2-2-2-2222-2-2-2-222−2i2i−2i2i00000000000000000000000022-2-222-2-2000000−2i2i−2i2i000000000000000000000000000000−2i2i−2i2i00000000
χ52222-2-2-2-2222-2-2-2-222222-2-2-2-2222-2-2-2-222−2i2i−2i2i000000000000000000000000-2-222-2-222000000−2i2i−2i2i0000000000000000000000000000002i−2i2i−2i00000000
χ53222-2-2-2-22-2-22222-2-2222-2-2-2-22-2-22222-2-22i−2i−2i2i0000000000000000000000002i2i−2i−2i−2i−2i2i2i0000002i−2i−2i2i000000000000000000000000000000-222-200000000
χ54222-2-2-2-22-2-22222-2-2222-2-2-2-22-2-22222-2-22i−2i−2i2i000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000002i−2i−2i2i0000000000000000000000000000002-2-2200000000
χ55222-2-2-2-22-2-22222-2-2222-2-2-2-22-2-22222-2-2−2i2i2i−2i0000000000000000000000002i2i−2i−2i−2i−2i2i2i000000−2i2i2i−2i0000000000000000000000000000002-2-2200000000
χ56222-2-2-2-22-2-22222-2-2222-2-2-2-22-2-22222-2-2−2i2i2i−2i000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000−2i2i2i−2i000000000000000000000000000000-222-200000000
χ5722-222-2-2-22i−2i2i2i−2i−2i2i−2i22-222-2-2-22i−2i2i2i−2i−2i2i−2i00002-22i−2i00000000000022-2-22i2i−2i−2i0000000000000000002-22i−2i0000000000000000002-200002i−2i000000000000
χ5822-222-2-2-22i−2i2i2i−2i−2i2i−2i22-222-2-2-22i−2i2i2i−2i−2i2i−2i00002-22i−2i000000000000-2-222−2i−2i2i2i0000000000000000002-22i−2i000000000000000000-220000−2i2i000000000000
χ5922-222-2-2-22i−2i2i2i−2i−2i2i−2i22-222-2-2-22i−2i2i2i−2i−2i2i−2i0000-22−2i2i00000000000022-2-22i2i−2i−2i000000000000000000-22−2i2i000000000000000000-220000−2i2i000000000000
χ6022-222-2-2-22i−2i2i2i−2i−2i2i−2i22-222-2-2-22i−2i2i2i−2i−2i2i−2i0000-22−2i2i000000000000-2-222−2i−2i2i2i000000000000000000-22−2i2i0000000000000000002-200002i−2i000000000000
χ6122-222-2-2-2−2i2i−2i−2i2i2i−2i2i22-222-2-2-2−2i2i−2i−2i2i2i−2i2i00002-2−2i2i00000000000022-2-2−2i−2i2i2i0000000000000000002-2−2i2i0000000000000000002-20000−2i2i000000000000
χ6222-222-2-2-2−2i2i−2i−2i2i2i−2i2i22-222-2-2-2−2i2i−2i−2i2i2i−2i2i00002-2−2i2i000000000000-2-2222i2i−2i−2i0000000000000000002-2−2i2i000000000000000000-2200002i−2i000000000000
χ6322-222-2-2-2−2i2i−2i−2i2i2i−2i2i22-222-2-2-2−2i2i−2i−2i2i2i−2i2i0000-222i−2i00000000000022-2-2−2i−2i2i2i000000000000000000-222i−2i000000000000000000-2200002i−2i000000000000
χ6422-222-2-2-2−2i2i−2i−2i2i2i−2i2i22-222-2-2-2−2i2i−2i−2i2i2i−2i2i0000-222i−2i000000000000-2-2222i2i−2i−2i000000000000000000-222i−2i0000000000000000002-20000−2i2i000000000000
χ652-222-22-2-22i−2i2i−2i2i−2i−2i2i2-222-22-2-22i−2i2i−2i2i−2i−2i2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22-22i−2i2i−2i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.