Finite Group Databasebeta

← Group #72342697

Character table — Group #72342697

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111222222222233334444444444666666666688888888888888881212121212121212121216161616161616161616161616161616161616161616161648484848484848484848484848484848
order1244248888888822444416161616161616162488888888366612121212242424242424242444161616161616161612121212242424244848484848484848484848484848484816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ61111111111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ71111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ81111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ911-1-1-1111-1-1ii−i−i11-1-1i−i11-1-1ii−i−i-1111-1-1ii−i−i11-1-111-1-11111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1011-1-1-1111-1-1ii−i−i11-1-1i−i11-1-1ii−i−i-1111-1-1ii−i−i11-1-111-1-11111-1-1-1-1i−i11-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1111-1-1-1111-1-1ii−i−i11-1-1i−i-1-111−i−iii-1111-1-1ii−i−i11-1-111-1-11111-1-1-1-1i−i-1-111−i−iiiii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-1-1-1111-1-1ii−i−i11-1-1i−i-1-111−i−iii-1111-1-1ii−i−i11-1-111-1-11111-1-1-1-1i−i-1-111−i−iiiii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-1-1-1111-1-1−i−iii11-1-1−ii11-1-1−i−iii-1111-1-1−i−iii11-1-111-1-11111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1411-1-1-1111-1-1−i−iii11-1-1−ii11-1-1−i−iii-1111-1-1−i−iii11-1-111-1-11111-1-1-1-1−ii11-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1511-1-1-1111-1-1−i−iii11-1-1−ii-1-111ii−i−i-1111-1-1−i−iii11-1-111-1-11111-1-1-1-1−ii-1-111ii−i−i−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611-1-1-1111-1-1−i−iii11-1-1−ii-1-111ii−i−i-1111-1-1−i−iii11-1-111-1-11111-1-1-1-1−ii-1-111ii−i−i−i−iii−i−iii-1-1-1-11111iiii−i−i−i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1722222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222-2-2-2-22222-2-22222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222-2-2-2-22222-2-2-2-2-2-22222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ21222222-2-2-2-222222222-2-20000000022-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000000000000000
χ22222222-2-2-2-222222222-2-20000000022-2-2-2-22222-1-1-1-1-1-1-1-111111111-2-2000000001111-1-1-1-133−3−333−3−333−3−333−3−30000000000000000
χ23222222-2-2-2-222222222-2-20000000022-2-2-2-22222-1-1-1-1-1-1-1-111111111-2-2000000001111-1-1-1-1−3−333−3−333−3−333−3−3330000000000000000
χ24222222-2-2-2-2-2-2-2-22222220000000022-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222000000002222-2-2-2-200000000000000000000000000000000
χ25222222-2-2-2-2-2-2-2-22222220000000022-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111112200000000-1-1-1-1111133−3−333−3−3−3−333−3−3330000000000000000
χ26222222-2-2-2-2-2-2-2-22222220000000022-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111112200000000-1-1-1-11111−3−333−3−33333−3−333−3−30000000000000000
χ272222-2-200002-22-2222200−i2i2−i2i2−i2i2−i2i2-2-200002-22-222-2-2-2-2220000000000−i2i2−i2i2−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ282222-2-200002-22-2222200−i2i2−i2i2−i2i2−i2i2-2-200002-22-2-1-11111-1-133−3−333−3−300−i2i2−i2i2−i2i2−i2i23−33−3-11-11ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ292222-2-200002-22-2222200−i2i2−i2i2−i2i2−i2i2-2-200002-22-2-1-11111-1-1−3−333−3−33300−i2i2−i2i2−i2i2−i2i2−33−33-11-11ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ302222-2-200002-22-2222200i2−i2i2−i2i2−i2i2−i2-2-200002-22-222-2-2-2-2220000000000i2−i2i2−i2i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ312222-2-200002-22-2222200i2−i2i2−i2i2−i2i2−i2-2-200002-22-2-1-11111-1-133−3−333−3−300i2−i2i2−i2i2−i2i2−i23−33−3-11-11−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ322222-2-200002-22-2222200i2−i2i2−i2i2−i2i2−i2-2-200002-22-2-1-11111-1-1−3−333−3−33300i2−i2i2−i2i2−i2i2−i2−33−33-11-11−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ332222-2-20000-22-22222200−i2i2−i2i2i2−i2i2−i2-2-20000-22-2222-2-2-2-2220000000000−i2i2−i2i2i2−i2i2−i20000-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ342222-2-20000-22-22222200−i2i2−i2i2i2−i2i2−i2-2-20000-22-22-1-11111-1-133−3−333−3−300−i2i2−i2i2i2−i2i2−i2−33−331-11-1ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ352222-2-20000-22-22222200−i2i2−i2i2i2−i2i2−i2-2-20000-22-22-1-11111-1-1−3−333−3−33300−i2i2−i2i2i2−i2i2−i23−33−31-11-1ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ362222-2-20000-22-22222200i2−i2i2−i2−i2i2−i2i2-2-20000-22-2222-2-2-2-2220000000000i2−i2i2−i2−i2i2−i2i20000-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ372222-2-20000-22-22222200i2−i2i2−i2−i2i2−i2i2-2-20000-22-22-1-11111-1-133−3−333−3−300i2−i2i2−i2−i2i2−i2i2−33−331-11-1−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ382222-2-20000-22-22222200i2−i2i2−i2−i2i2−i2i2-2-20000-22-22-1-11111-1-1−3−333−3−33300i2−i2i2−i2−i2i2−i2i23−33−31-11-1−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ3922-2-22-200002i−2i−2i2i22-2-200−i2i2i2−i22−2−222-200002i−2i−2i2i2222-2-2-2-20000000000−i2i2i2−i22−2−2200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ4022-2-22-200002i−2i−2i2i22-2-200−i2i2i2−i22−2−222-200002i−2i−2i2i-1-1-1-1111133−3−3−3−33300−i2i2i2−i22−2−22i3−i3−i3i3−iii−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ4122-2-22-200002i−2i−2i2i22-2-200−i2i2i2−i22−2−222-200002i−2i−2i2i-1-1-1-11111−3−33333−3−300−i2i2i2−i22−2−22−i3i3i3−i3−iii−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ4222-2-22-200002i−2i−2i2i22-2-200i2−i2−i2i2−222−22-200002i−2i−2i2i2222-2-2-2-20000000000i2−i2−i2i2−222−200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ4322-2-22-200002i−2i−2i2i22-2-200i2−i2−i2i2−222−22-200002i−2i−2i2i-1-1-1-1111133−3−3−3−33300i2−i2−i2i2−222−2i3−i3−i3i3−iii−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ4422-2-22-200002i−2i−2i2i22-2-200i2−i2−i2i2−222−22-200002i−2i−2i2i-1-1-1-11111−3−33333−3−300i2−i2−i2i2−222−2−i3i3i3−i3−iii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ4522-2-22-20000−2i2i2i−2i22-2-200−i2i2i2−i2−222−22-20000−2i2i2i−2i2222-2-2-2-20000000000−i2i2i2−i2−222−20000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ4622-2-22-20000−2i2i2i−2i22-2-200−i2i2i2−i2−222−22-20000−2i2i2i−2i-1-1-1-1111133−3−3−3−33300−i2i2i2−i2−222−2−i3i3i3−i3i−i−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ4722-2-22-20000−2i2i2i−2i22-2-200−i2i2i2−i2−222−22-20000−2i2i2i−2i-1-1-1-11111−3−33333−3−300−i2i2i2−i2−222−2i3−i3−i3i3i−i−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ4822-2-22-20000−2i2i2i−2i22-2-200i2−i2−i2i22−2−222-20000−2i2i2i−2i2222-2-2-2-20000000000i2−i2−i2i22−2−220000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ4922-2-22-20000−2i2i2i−2i22-2-200i2−i2−i2i22−2−222-20000−2i2i2i−2i-1-1-1-1111133−3−3−3−33300i2−i2−i2i22−2−22−i3i3i3−i3i−i−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ5022-2-22-20000−2i2i2i−2i22-2-200i2−i2−i2i22−2−222-20000−2i2i2i−2i-1-1-1-11111−3−33333−3−300i2−i2−i2i22−2−22i3−i3−i3i3i−i−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ5122-2-2-2222-2-22i2i−2i−2i22-2-22i−2i22-2-22i2i−2i−2i-2222-2-22i2i−2i−2i-1-111-1-111-1-1-1-111112i−2i22-2-22i2i−2i−2i−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii0000000000000000
χ5222-2-2-2222-2-22i2i−2i−2i22-2-22i−2i-2-222−2i−2i2i2i-2222-2-22i2i−2i−2i-1-111-1-111-1-1-1-111112i−2i-2-222−2i−2i2i2i−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ5322-2-2-2222-2-2−2i−2i2i2i22-2-2−2i2i22-2-2−2i−2i2i2i-2222-2-2−2i−2i2i2i-1-111-1-111-1-1-1-11111−2i2i22-2-2−2i−2i2i2iii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ5422-2-2-2222-2-2−2i−2i2i2i22-2-2−2i2i-2-2222i2i−2i−2i-2222-2-2−2i−2i2i2i-1-111-1-111-1-1-1-11111−2i2i-2-2222i2i−2i−2iii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii0000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.