Finite Group Databasebeta

← Group #72244970

Character table — Group #72244970

Order 6912.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size1111111122228888888899999999161616161818181824242424242424242424242424242424484848484848484848484848484848485454545454545454727272727272727272727272727272727272727272727272108108108108108108108108108108108108108108108108108108108108144144144144144144144144
order122244448888366612121212222244442424242488883666121212122424242424242424366612121212242424242424242444444444444466668888121212122424242424242424888888888888888888881212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111-1-1-1-1ii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-111-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ61111-1-1-1-1ii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1-1-1111111−i−iii-1-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ71111-1-1-1-1−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-111-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ81111-1-1-1-1−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1-1-1111111ii−i−i-1-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ911-1-111-1-11-11-111-1-111-1-1-1-111-1-1111-11-11-11-11-1-11-1-11111-1-111-1-11-1-11-1-11111-1-111-1-11111-1-1-1-1i−ii−i11-1-1i−ii−i11-1-111-1-111-1-11-11-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i
χ1011-1-111-1-11-11-111-1-111-1-1-1-111-1-1111-11-11-11-11-1-11-1-11111-1-111-1-11-1-11-1-11111-1-111-1-11111-1-1-1-1−ii−ii11-1-1−ii−ii11-1-111-1-111-1-11-11-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii
χ1111-1-111-1-1-11-1111-1-111-1-1-1-111-1-111-11-11-11-111-1-11-1-111-1-111-1-1111-1-11-1-111-1-111-1-1111111-1-1-1-1i−ii−i11-1-1−ii−ii11-1-1-1-111-1-111-11-11ii−i−iii−i−i−i−iii−i−iiii−ii−i−ii−ii
χ1211-1-111-1-1-11-1111-1-111-1-1-1-111-1-111-11-11-11-111-1-11-1-111-1-111-1-1111-1-11-1-111-1-111-1-1111111-1-1-1-1−ii−ii11-1-1i−ii−i11-1-1-1-111-1-111-11-11−i−iii−i−iiiii−i−iii−i−i−ii−iii−ii−i
χ1311-1-1-1-111i−i−ii11-1-1-1-111-1-11111-1-1i−i−iii−i−ii1-1-1111-1-1ii−i−i−i−iii1-1-1111-1-1ii−i−i−i−iii11-1-1-1-111i−i−ii11-1-1-111-1-1-111ii−i−i−i−iiii−i−iiii−i−i−i−iii-1-11111-1-1i−i−ii-111-1
χ1411-1-1-1-111i−i−ii11-1-1-1-111-1-11111-1-1i−i−iii−i−ii1-1-1111-1-1ii−i−i−i−iii1-1-1111-1-1ii−i−i−i−iii11-1-1-1-111−iii−i11-1-11-1-11-1-111ii−i−i−i−iiii−i−ii−i−iiiii−i−i11-1-1-1-111−iii−i1-1-11
χ1511-1-1-1-111−iii−i11-1-1-1-111-1-11111-1-1−iii−i−iii−i1-1-1111-1-1−i−iiiii−i−i1-1-1111-1-1−i−iiiii−i−i11-1-1-1-111i−i−ii11-1-11-1-11-1-111−i−iiiii−i−i−iii−iii−i−i−i−iii11-1-1-1-111i−i−ii1-1-11
χ1611-1-1-1-111−iii−i11-1-1-1-111-1-11111-1-1−iii−i−iii−i1-1-1111-1-1−i−iiiii−i−i1-1-1111-1-1−i−iiiii−i−i11-1-1-1-111−iii−i11-1-1-111-1-1-111−i−iiiii−i−i−iii−i−i−iiiii−i−i-1-11111-1-1−iii−i-111-1
χ17222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111100001111111111110000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ1922222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111100001111111111110000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ2022222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111222222220000-1-1-1-10000-1-1-1-111111111-2-2-2-2000000000000000000000000
χ2122222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000111100001111-1-1-1-1-1-1-1-10000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ2222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000111100001111-1-1-1-1-1-1-1-10000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ232222-2-2-2-22i2i−2i−2i2222-2-2-2-22222-2-2-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii22-2-222-2-20000-1-1-1-100001111−i−i−i−iiiii2i2i−2i−2i000000000000000000000000
χ242222-2-2-2-22i2i−2i−2i2222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii00000000000011110000-1-1-1-1iiii−i−i−i−i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ252222-2-2-2-22i2i−2i−2i2222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii00000000000011110000-1-1-1-1iiii−i−i−i−i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ262222-2-2-2-2−2i−2i2i2i2222-2-2-2-22222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i22-2-222-2-20000-1-1-1-100001111iiii−i−i−i−i−2i−2i2i2i000000000000000000000000
χ272222-2-2-2-2−2i−2i2i2i2222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i00000000000011110000-1-1-1-1−i−i−i−iiiii0000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ282222-2-2-2-2−2i−2i2i2i2222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i00000000000011110000-1-1-1-1−i−i−i−iiiii0000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ2922-2-222-2-22-22-222-2-222-2-222-2-222-2-22-22-2-22-22-111-111-1-1-1-111-1-111-111-111-1-1-1-111-1-11100000000000011-1-1000011-1-111-1-111-1-100002−2−222−2−222−2−222−2−2200000000
χ3022-2-222-2-22-22-222-2-222-2-222-2-222-2-22-22-2-22-22-111-111-1-1-1-111-1-111-111-111-1-1-1-111-1-11100000000000011-1-1000011-1-111-1-111-1-10000−222−2−222−2−222−2−222−200000000
χ3122-2-222-2-22-22-222-2-222-2-2-2-222-2-2222-22-22-22-2-111-111-1-1-1-111-1-111-111-111-1-1-1-111-1-1112222-2-2-2-20000-1-1110000-1-111-1-111-1-1112-22-2000000000000000000000000
χ3222-2-222-2-2-22-2222-2-222-2-222-2-222-2-2-22-222-22-2-111-111-1-111-1-111-1-1-111-111-1-111-1-111-1-100000000000011-1-1000011-1-1-1-111-1-11100002−2−222−2−22−222−2−222−200000000
χ3322-2-222-2-2-22-2222-2-222-2-222-2-222-2-2-22-222-22-2-111-111-1-111-1-111-1-1-111-111-1-111-1-111-1-100000000000011-1-1000011-1-1-1-111-1-1110000−222−2−222−22−2−222−2−2200000000
χ3422-2-222-2-2-22-2222-2-222-2-2-2-222-2-222-22-22-22-22-111-111-1-111-1-111-1-1-111-111-1-111-1-111-1-12222-2-2-2-20000-1-1110000-1-11111-1-111-1-1-22-22000000000000000000000000
χ3522-2-2-2-2222i−2i−2i2i22-2-2-2-22222-2-2-2-2222i−2i−2i2i−2i2i2i−2i-111-1-1-111−i−iiiii−i−i-111-1-1-111−i−iiiii−i−i00000000000011-1-10000-1-111ii−i−i−i−iii00002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ3622-2-2-2-2222i−2i−2i2i22-2-2-2-22222-2-2-2-2222i−2i−2i2i−2i2i2i−2i-111-1-1-111−i−iiiii−i−i-111-1-1-111−i−iiiii−i−i00000000000011-1-10000-1-111ii−i−i−i−iii0000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ3722-2-2-2-2222i−2i−2i2i22-2-2-2-222-2-22222-2-22i−2i−2i2i2i−2i−2i2i-111-1-1-111−i−iiiii−i−i-111-1-1-111−i−iiiii−i−i22-2-2-2-2220000-1-111000011-1-1−i−iiiii−i−i2i−2i−2i2i000000000000000000000000
χ3822-2-2-2-222−2i2i2i−2i22-2-2-2-22222-2-2-2-222−2i2i2i−2i2i−2i−2i2i-111-1-1-111ii−i−i−i−iii-111-1-1-111ii−i−i−i−iii00000000000011-1-10000-1-111−i−iiiii−i−i00002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ3922-2-2-2-222−2i2i2i−2i22-2-2-2-22222-2-2-2-222−2i2i2i−2i2i−2i−2i2i-111-1-1-111ii−i−i−i−iii-111-1-1-111ii−i−i−i−iii00000000000011-1-10000-1-111−i−iiiii−i−i0000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ4022-2-2-2-222−2i2i2i−2i22-2-2-2-222-2-22222-2-2−2i2i2i−2i−2i2i2i−2i-111-1-1-111ii−i−i−i−iii-111-1-1-111ii−i−i−i−iii22-2-2-2-2220000-1-111000011-1-1ii−i−i−i−iii−2i2i2i−2i000000000000000000000000
χ412-22-22i−2i2i−2i00002-22-22i−2i2i−2i2-22-22i−2i2i−2i0000000022-2-22i−2i2i−2i0000000022-2-22i−2i2i−2i000000002-22i−2i2-22i−2i00002-22-200002i−2i2i−2i000000000000000000000000000000000000
χ422-22-22i−2i2i−2i00002-22-22i−2i2i−2i2-22-22i−2i2i−2i00000000-1-111−ii−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13-1-111−ii−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132-22i−2i2-22i−2i0000-11-110000−ii−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000000000000000
χ432-22-22i−2i2i−2i00002-22-22i−2i2i−2i2-22-22i−2i2i−2i00000000-1-111−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13-1-111−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ132-22i−2i2-22i−2i0000-11-110000−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000000000000000
χ442-22-2−2i2i−2i2i00002-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000000022-2-2−2i2i−2i2i0000000022-2-2−2i2i−2i2i000000002-2−2i2i2-2−2i2i00002-22-20000−2i2i−2i2i000000000000000000000000000000000000
χ452-22-2−2i2i−2i2i00002-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000-1-111i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23-1-111i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ232-2−2i2i2-2−2i2i0000-11-110000i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000000000000000
χ462-22-2−2i2i−2i2i00002-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000-1-111i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23-1-111i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232-2−2i2i2-2−2i2i0000-11-110000i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000000000000000
χ472-2-222i−2i−2i2i00002-2-222i−2i−2i2i-222-2−2i2i2i−2i000000002-22-2−2i2i2i−2i000000002-22-2−2i2i2i−2i000000002-22i−2i-22−2i2i00002-2-2200002i−2i−2i2i000000000000000000000000000000000000
χ482-2-222i−2i−2i2i00002-2-222i−2i−2i2i-222-2−2i2i2i−2i00000000-11-11i−i−ii−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13-11-11i−i−ii−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ132-22i−2i-22−2i2i0000-111-10000−iii−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000000000000000
χ492-2-222i−2i−2i2i00002-2-222i−2i−2i2i-222-2−2i2i2i−2i00000000-11-11i−i−iiζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13-11-11i−i−iiζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ132-22i−2i-22−2i2i0000-111-10000−iii−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000000000000000
χ502-2-22−2i2i2i−2i00002-2-22−2i2i2i−2i-222-22i−2i−2i2i000000002-22-22i−2i−2i2i000000002-22-22i−2i−2i2i000000002-2−2i2i-222i−2i00002-2-220000−2i2i2i−2i000000000000000000000000000000000000
χ512-2-22−2i2i2i−2i00002-2-22−2i2i2i−2i-222-22i−2i−2i2i00000000-11-11−iii−iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23-11-11−iii−iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ232-2−2i2i-222i−2i0000-111-10000i−i−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000000000000000
χ522-2-22−2i2i2i−2i00002-2-22−2i2i2i−2i-222-22i−2i−2i2i00000000-11-11−iii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23-11-11−iii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ232-2−2i2i-222i−2i0000-111-10000i−i−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000000000000000000
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χ12516-16-161616i−16i−16i16i0000-222-2−2i2i2i−2i0000000000000000-22-222i−2i−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ131-11-1−iii−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000000000000000000000000000000
χ12616-16-1616−16i16i16i−16i0000-222-22i−2i−2i2i00000000000000004-44-44i−4i−4i4i00000000-22-22−2i2i2i−2i00000000000000000000000000000000000000000000000000000000000000000000
χ12716-16-1616−16i16i16i−16i0000-222-22i−2i−2i2i0000000000000000-22-22−2i2i2i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ13−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ231-11-1i−i−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000000000000000000000000000000
χ12816-16-1616−16i16i16i−16i0000-222-22i−2i−2i2i0000000000000000-22-22−2i2i2i−2i−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ231-11-1i−i−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000000000000000000000000000000

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