Finite Group Databasebeta

← Group #11771667

Character table — Group #11771667

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11112222222222222222222222222244444444444444444444444444444444444444444444444444444444442424242424242424242424242424242424242424242424243636363636363636
order12442334444466888812121212242424242424242436666688121212121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424668812121616161624242424484848484848484888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i1111iiii−i−i−i−i−i−i−i−iiiii
χ811111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii1111−i−i−i−iiiiiiiii−i−i−i−i
χ911-1-1-1111ii−i−i11i−ii−i-1-1-1-1ii−i−iii−i−i1-1-11-1-11-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1i−ii−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-111i−i-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ1011-1-1-1111ii−i−i11i−ii−i-1-1-1-1ii−i−iii−i−i1-1-11-1-11-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1i−ii−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-111i−i-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ1111-1-1-1111ii−i−i11i−ii−i-1-1-1-1ii−i−iii−i−i1-1-11-1-11-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1i−ii−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-11-1-1−ii11ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ1211-1-1-1111ii−i−i11i−ii−i-1-1-1-1ii−i−iii−i−i1-1-11-1-11-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1i−ii−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-11-1-1−ii11−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ1311-1-1-1111−i−iii11−ii−ii-1-1-1-1−i−iii−i−iii1-1-11-1-11-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−ii−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-111−ii-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1411-1-1-1111−i−iii11−ii−ii-1-1-1-1−i−iii−i−iii1-1-11-1-11-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−ii−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-111−ii-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ1511-1-1-1111−i−iii11−ii−ii-1-1-1-1−i−iii−i−iii1-1-11-1-11-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−ii−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-11-1-1i−i11−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ1611-1-1-1111−i−iii11−ii−ii-1-1-1-1−i−iii−i−iii1-1-11-1-11-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−ii−ii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-11-1-1i−i11ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1722222222222222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222-1222222-1222222-1-1-1-1-1-12222-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-10000-1-1-1-10000000000000000
χ20222222-1222222-1222222-1-1-1-1-1-12222-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-211000011110000000000000000
χ21222222-1222222-1-2-2-2-222-1-11111-2-2-2-2-12-1-1-1-1-2-222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-1-2-211-2-2111111-2-21111111111111100−i3i300−i3i30000−i3i3−i3i30000000000000000
χ22222222-1222222-1-2-2-2-222-1-11111-2-2-2-2-12-1-1-1-1-2-222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-1-1-2-211-2-2111111-2-21111111111111100i3−i300i3−i30000i3−i3i3−i30000000000000000
χ23222222-12-2-2-2-22-1222222-1-1-1-1-1-12222-12-1-1-1-1-2-2-2-2111111-2-21111112-1-1-1-1-122-1-1-2-2111111-2-2111111-1-1-1-1-1-1-1-100−i3i300−i3i30000i3−i3i3−i30000000000000000
χ24222222-12-2-2-2-22-1222222-1-1-1-1-1-12222-12-1-1-1-1-2-2-2-2111111-2-21111112-1-1-1-1-122-1-1-2-2111111-2-2111111-1-1-1-1-1-1-1-100i3−i300i3−i30000−i3i3−i3i30000000000000000
χ25222222-12-2-2-2-22-1-2-2-2-222-1-11111-2-2-2-2-12-1-1-1-122-2-2111111-2-21111112-1-1-1-1-1-2-21122-1-1-1-1-1-122-1-1-1-1-1-11111111122-1-1-2-2-1-1000011110000000000000000
χ26222222-12-2-2-2-22-1-2-2-2-222-1-11111-2-2-2-2-12-1-1-1-122-2-2111111-2-21111112-1-1-1-1-1-2-21122-1-1-1-1-1-122-1-1-1-1-1-111111111-2-21122110000-1-1-1-10000000000000000
χ2722222-1222222-122222-1-1222222-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-100000000
χ2822222-1222222-122222-1-1222222-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-200001111111100000000
χ2922222-1222222-12-2-2-2-2-1-122-2-2-2-21111-1-12-1-1-1-2-2-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-1-111-2-211-2-2111111-2-211111111111100000000000000003−33−33−33−300000000
χ3022222-1222222-12-2-2-2-2-1-122-2-2-2-21111-1-12-1-1-1-2-2-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-1-111-2-211-2-2111111-2-21111111111110000000000000000−33−33−33−3300000000
χ3122222-122-2-2-2-2-122222-1-1222222-1-1-1-1-1-12-1-1-1-2-211-2-2111111-2-21111-12-1-1-1-1-1-12211-2-2111111-2-21111-1-1-1-1-1-1-1-10000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ3222222-122-2-2-2-2-122222-1-1222222-1-1-1-1-1-12-1-1-1-2-211-2-2111111-2-21111-12-1-1-1-1-1-12211-2-2111111-2-21111-1-1-1-1-1-1-1-10000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3322222-122-2-2-2-2-12-2-2-2-2-1-122-2-2-2-21111-1-12-1-1-12211-2-2111111-2-21111-12-1-1-1-111-2-2-1-122-1-1-1-1-1-122-1-1-1-111111111000000002i2i−2i−2i0000−i−i−i−iiiii00000000
χ3422222-122-2-2-2-2-12-2-2-2-2-1-122-2-2-2-21111-1-12-1-1-12211-2-2111111-2-21111-12-1-1-1-111-2-2-1-122-1-1-1-1-1-122-1-1-1-11111111100000000−2i−2i2i2i0000iiii−i−i−i−i00000000
χ352222-222-200002222-2-222222222-2-2-2-22-2-22-2-2000000000000000000-2-2-2-22222-2-2000000000000000022-2-222-2-2000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ362222-222-200002222-2-222222222-2-2-2-22-2-22-2-2000000000000000000-2-2-2-22222-2-2000000000000000022-2-222-2-2000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ372222-222-2000022-2-2222222-2-2-2-222222-2-22-2-2000000000000000000-2-2-2-222-2-2220000000000000000-2-222-2-2220000000000000000000000002−22−2−22−22
χ382222-222-2000022-2-2222222-2-2-2-222222-2-22-2-2000000000000000000-2-2-2-222-2-2220000000000000000-2-222-2-222000000000000000000000000−22−222−22−2
χ3922-2-2222-20000222i−2i−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i222222000000000000000000-2-2-2-2-2-22i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ4022-2-2222-20000222i−2i−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i222222000000000000000000-2-2-2-2-2-22i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ4122-2-2222-2000022−2i2i2i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i222222000000000000000000-2-2-2-2-2-2−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ4222-2-2222-2000022−2i2i2i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i222222000000000000000000-2-2-2-2-2-2−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ4322-2-2-22222i2i−2i−2i22−2i2i−2i2i-2-2-2-2−2i−2i2i2i−2i−2i2i2i2-2-22-2-2-222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2222-2-2−2i2i−2i2i-2-2-2-2-2-2-2-222222222−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ4422-2-2-2222−2i−2i2i2i222i−2i2i−2i-2-2-2-22i2i−2i−2i2i2i−2i−2i2-2-22-2-2-22−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2222-2-22i−2i2i−2i-2-2-2-2-2-2-2-2222222222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ4522-2-2-22-122i2i−2i−2i2-12i−2i2i−2i-2-211−i−iii2i2i−2i−2i-1-21-1112-22i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-1112i−2i−ii22-1-1-1-1-1-1-2-2111111−i−i−i−iiiii2-2-1-12i−2i110000−i−iii0000000000000000
χ4622-2-2-22-122i2i−2i−2i2-12i−2i2i−2i-2-211−i−iii2i2i−2i−2i-1-21-1112-22i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-1112i−2i−ii22-1-1-1-1-1-1-2-2111111−i−i−i−iiiii-2211−2i2i-1-10000ii−i−i0000000000000000
χ4722-2-2-22-122i2i−2i−2i2-1−2i2i−2i2i-2-211ii−i−i−2i−2i2i2i-1-21-111-222i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-111−2i2ii−i-2-211111122-1-1-1-1-1-1iiii−i−i−i−i00−i3i300i3−i300003−3−330000000000000000
χ4822-2-2-22-122i2i−2i−2i2-1−2i2i−2i2i-2-211ii−i−i−2i−2i2i2i-1-21-111-222i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-111−2i2ii−i-2-211111122-1-1-1-1-1-1iiii−i−i−i−i00i3−i300−i3i30000−333−30000000000000000
χ4922-2-2-22-12−2i−2i2i2i2-12i−2i2i−2i-2-211−i−iii2i2i−2i−2i-1-21-111-22−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-1112i−2i−ii-2-211111122-1-1-1-1-1-1−i−i−i−iiiii00−i3i300i3−i30000−333−30000000000000000
χ5022-2-2-22-12−2i−2i2i2i2-12i−2i2i−2i-2-211−i−iii2i2i−2i−2i-1-21-111-22−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-1112i−2i−ii-2-211111122-1-1-1-1-1-1−i−i−i−iiiii00i3−i300−i3i300003−3−330000000000000000
χ5122-2-2-22-12−2i−2i2i2i2-1−2i2i−2i2i-2-211ii−i−i−2i−2i2i2i-1-21-1112-2−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-111−2i2ii−i22-1-1-1-1-1-1-2-2111111iiii−i−i−i−i2-2-1-1−2i2i110000ii−i−i0000000000000000
χ5222-2-2-22-12−2i−2i2i2i2-1−2i2i−2i2i-2-211ii−i−i−2i−2i2i2i-1-21-1112-2−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-111−2i2ii−i22-1-1-1-1-1-1-2-2111111iiii−i−i−i−i-22112i−2i-1-10000−i−iii0000000000000000
χ5322-2-2-2-1222i2i−2i−2i-122i−2i2i−2i11-2-22i2i−2i−2i−i−iii-11-2-1112-2−i−i2i2i−i−i−i−iii−2i−2iiiii-12-1-111−ii2i−2i-1-122-1-1-1-111-2-21111−i−i−i−iiiii000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000
χ5422-2-2-2-1222i2i−2i−2i-122i−2i2i−2i11-2-22i2i−2i−2i−i−iii-11-2-1112-2−i−i2i2i−i−i−i−iii−2i−2iiiii-12-1-111−ii2i−2i-1-122-1-1-1-111-2-21111−i−i−i−iiiii00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000
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χ1154-4−4i4i0-2-202−2i−2+2i2+2i−2−2i2200002i−2i2i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13100-1-3300−1+i1−i−1+i1−i2+i−2−i−1−2i1+2i−1−i1+i−1−i1+i−1+2i1−2i2−i−2+i003i−3i−ii00006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000
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χ1204-4−4i4i0-2-20−2+2i2−2i−2−2i2+2i2200002i−2i2i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13100-13-3001−i−1+i1−i−1+i1+2i−1−2i−2−i2+i1+i−1−i1+i−1−i−2+i2−i1−2i−1+2i00−3i3i−ii00006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.