Finite Group Databasebeta

← Group #10812214

Character table — Group #10812214

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111111111112222222222222222444444444444444444446666666666666666888888888888888888888888888888881212121212121212121212121212121224242424
order122222224444444436666666121212121212121222224444888888888888444444448888888824666666881212121212122424242424242424242424242424242444444444888888884488
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
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ51111111111111111111111111111111111-1-111-1-111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ71111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ911111111111111111111111111111111-1-111-1-1111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1211111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-111111-1-1i−i-1-1-1-111ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i
χ1811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-111111-1-1i−i-1-1-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-11−ii
χ1911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-111111-1-1−ii-1-1-1-111−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-1−ii
χ2011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-111111-1-1−ii-1-1-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-111ii−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−i1-111-1-111−ii-1-111-1-1ii−i−iii−i−i−i−iii−i−iii11-1-1-1-111ii−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−iiiii1-111-1-111−ii-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-11111-1-1−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−iiiii1-111-1-111i−i-1-111-1-1−i−iii−i−iiiii−i−iii−i−i11-1-1-1-111−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−i1-111-1-111i−i-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-11111-1-1ii−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−iiiii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-1-11111−ii11-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-11−ii
χ2611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiii1-1-1-11111−ii11-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1i−i
χ2711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-1-11111i−i11-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii-11i−i
χ2811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i1-1-1-11111i−i11-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1−ii
χ2911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i-11-1-1-1-1-1-1i−i111111ii−i−i−i−iii−i−iiiii−i−i-1-111-1-111−i−iii−i−iii1-1i−i
χ3011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii-11-1-1-1-1-1-1i−i111111ii−i−i−i−iii−i−iiiii−i−i11-1-111-1-1ii−i−iii−i−i-11−ii
χ3111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii-11-1-1-1-1-1-1−ii111111−i−iiiii−i−iii−i−i−i−iii-1-111-1-111ii−i−iii−i−i1-1−ii
χ3211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i-11-1-1-1-1-1-1−ii111111−i−iiiii−i−iii−i−i−i−iii11-1-111-1-1−i−iii−i−iii-11i−i
χ332222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222222222000000000000000022-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ342222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-1-1-1-1-1-1-2-2-1-1-1-1-1-1111111111111111100000000000000000000
χ352222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-222222222-2-2-2-20000000000000000-2-2-1-11111-2-2-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000
χ362222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-1-1111122-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000
χ372222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2222222-2-2-2-222220000000000000000-2-211-1-111-2-211-1-111-1-1-1-11111-1-1-1-1111100000000000000000000
χ382222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000-2-211-1-1112211-1-1111111-1-1-1-11111-1-1-1-100000000000000000000
χ392222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000221111-1-1221111-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ402222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000221111-1-1-2-21111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111112222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000-22-1-1-1-1112i−2i1111-1-1−i−iii−i−iii−i−iii−i−iii00000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111112222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000-22-1-1-1-111−2i2i1111-1-1ii−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−2i2i2i00000000000000002-2-1-111-1-1−2i2i11-1-111−i−iii−i−iiiii−i−iii−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−2i00000000000000002-2-1-111-1-12i−2i11-1-111ii−i−iii−i−i−i−iii−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−2i2i2i2i2i−2i−2i00000000000000002-211-1-1-1-1−2i2i-1-11111−i−iiiii−i−i−i−iiiii−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−2i−2i−2i2i2i00000000000000002-211-1-1-1-12i−2i-1-11111ii−i−i−i−iiiii−i−i−i−iii00000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-222222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000-221111112i−2i-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii00000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-22222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000-22111111−2i2i-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i00000000000000000000
χ492222-2-2-2-222-2-222-2-2222-2-2-2-222222-2-2-2-2002-2002-20000000000002i2i−2i−2i2i2i−2i−2i0000000000002-20000002-200000000000000000000002i−2i2i−2i000000000000
χ502222-2-2-2-222-2-222-2-2222-2-2-2-222222-2-2-2-2002-2002-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000002-20000002-20000000000000000000000−2i2i−2i2i000000000000
χ512222-2-2-2-222-2-222-2-2222-2-2-2-222222-2-2-2-200-2200-220000000000002i2i−2i−2i2i2i−2i−2i000000000000-22000000-220000000000000000000000−2i2i−2i2i000000000000
χ522222-2-2-2-222-2-222-2-2222-2-2-2-222222-2-2-2-200-2200-22000000000000−2i−2i2i2i−2i−2i2i2i000000000000-22000000-2200000000000000000000002i−2i2i−2i000000000000
χ532222-2-2-2-2-2-222-2-222222-2-2-2-22-2-2-2-22222002-200-220000000000002i2i−2i−2i−2i−2i2i2i0000000000002-2000000-2200000000000000000000002i−2i−2i2i000000000000
χ542222-2-2-2-2-2-222-2-222222-2-2-2-22-2-2-2-22222002-200-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000002-2000000-220000000000000000000000−2i2i2i−2i000000000000
χ552222-2-2-2-2-2-222-2-222222-2-2-2-22-2-2-2-2222200-22002-20000000000002i2i−2i−2i−2i−2i2i2i000000000000-220000002-20000000000000000000000−2i2i2i−2i000000000000
χ562222-2-2-2-2-2-222-2-222222-2-2-2-22-2-2-2-2222200-22002-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000-220000002-200000000000000000000002i−2i−2i2i000000000000
χ5722-2-222-2-22i−2i2i−2i2i−2i2i−2i22-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22-22i−2i2i−2i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ5822-2-222-2-22i−2i2i−2i2i−2i2i−2i22-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-22-22−2i2i−2i2i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ5922-2-222-2-22i−2i2i−2i2i−2i2i−2i22-222-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22-22i−2i2i−2i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ6022-2-222-2-22i−2i2i−2i2i−2i2i−2i22-222-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-22-22−2i2i−2i2i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ6122-2-222-2-2−2i2i−2i2i−2i2i−2i2i22-222-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-22-2−2i2i−2i2i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ6222-2-222-2-2−2i2i−2i2i−2i2i−2i2i22-222-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-22-222i−2i2i−2i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.