Finite Group Databasebeta

← Group #13173345

Character table — Group #13173345

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222224444444444444444444444444444448888888888888888888888888888888888889999181818181818181818182727272727272727363636363636545454545454545454545454
order12223444444666333333666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212444422444412121212888888886612121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1iiiiii−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1−i−i−i−i−i−iiiiiii
χ51111111-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111111111-1-111-1-111-1-1-1-111-1-1-1-1
χ61111111-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111
χ71111111-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i11-1-111ii−i−i−i−i−i−iiiii
χ81111111-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiii11-1-111−i−iiiiiii−i−i−i−i
χ911111-1-111-1-1111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1-1-111-1-1
χ1011111-1-111-1-1111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ1111111-1-111-1-1111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1−i−iii−i−iii−i−iii
χ1211111-1-111-1-1111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1ii−i−iii−i−iii−i−i
χ1311111-1-1-1-111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ1411111-1-1-1-111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1
χ1511111-1-1-1-111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-11111−i−i−i−iiiiiii−i−i
χ1611111-1-1-1-111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-11111iiii−i−i−i−i−i−iii
χ171-11-11i−ii−i1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-11-1i−ii−i11-1-111-1-111-1-11-1i−ii−ii−ii−i1-1i−ii−i1-1
χ181-11-11i−ii−i1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-11-1i−ii−i11-1-1-1-111-1-1111-1i−ii−i−ii−ii-11−ii−ii-11
χ191-11-11i−ii−i1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-1-111-11−ii−ii-1-111ii−i−i−i−iii-11−ii−ii-11-11i−i1-11-1−ii
χ201-11-11i−ii−i1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−ii−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-1-111-11−ii−ii-1-111−i−iiiii−i−i-11−ii−ii1-11-1−ii-11-11i−i
χ211-11-11i−i−ii-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−ii-11-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii11-1-1-11i−i−ii11-1-111-1-111-1-1-11i−i−iii−i−ii-11i−i−ii-11
χ221-11-11i−i−ii-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−ii-11-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii11-1-1-11i−i−ii11-1-1-1-111-1-111-11i−i−ii−iii−i1-1−iii−i1-1
χ231-11-11i−i−ii-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−ii-11-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1111-1−iii−i-1-111ii−i−i−i−iii1-1−iii−i-111-1−ii1-1-11i−i
χ241-11-11i−i−ii-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1i−i−ii-11-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1111-1−iii−i-1-111−i−iiiii−i−i1-1−iii−i1-1-11i−i-111-1−ii
χ251-11-11−iii−i-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−i-11-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i11-1-1-11−iii−i11-1-111-1-111-1-1-11−iii−i−iii−i-11−iii−i-11
χ261-11-11−iii−i-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−i-11-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i11-1-1-11−iii−i11-1-1-1-111-1-111-11−iii−ii−i−ii1-1i−i−ii1-1
χ271-11-11−iii−i-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−i-11-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-1111-1i−i−ii-1-111ii−i−i−i−iii1-1i−i−ii1-1-11−ii-111-1i−i
χ281-11-11−iii−i-11-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−iii−i-11-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-1111-1i−i−ii-1-111−i−iiiii−i−i1-1i−i−ii-111-1i−i1-1-11−ii
χ291-11-11−ii−ii1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii11-1-11-1−ii−ii11-1-111-1-111-1-11-1−ii−ii−ii−ii1-1−ii−ii1-1
χ301-11-11−ii−ii1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii11-1-11-1−ii−ii11-1-1-1-111-1-1111-1−ii−iii−ii−i-11i−ii−i-11
χ311-11-11−ii−ii1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-1-111-11i−ii−i-1-111ii−i−i−i−iii-11i−ii−i1-11-1i−i-11-11−ii
χ321-11-11−ii−ii1-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−ii−ii1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-1-111-11i−ii−i-1-111−i−iiiii−i−i-11i−ii−i-11-11−ii1-11-1i−i
χ332222-1222222-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222222222-1-1-1-100000000-1-1-1-1-1-1000000000000
χ342222-1222222-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-2-2111100000000111111000000000000
χ352222-122-2-2-2-2-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-11111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-211112222-2-222-2-2-1-1-1-10000000011-1-111000000000000
χ362222-122-2-2-2-2-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-11111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-222-2-222111100000000-1-111-1-1000000000000
χ372222-1-2-222-2-2-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-111-1-111-2-21111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-12222-2-2-2-222-1-1-1-1000000001111-1-1000000000000
χ382222-1-2-222-2-2-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-111-1-111-2-21111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-22222-2-2111100000000-1-1-1-111000000000000
χ392222-1-2-2-2-222-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-11111-1-122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-21111222222-2-2-2-2-1-1-1-100000000-1-11111000000000000
χ402222-1-2-2-2-222-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-11111-1-122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-21111-2-2-2-2-2-2222211110000000011-1-1-1-1000000000000
χ4122-2-220000002-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000002i−2i2i−2i0000002i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ4222-2-220000002-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000002i−2i2i−2i0000002i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ4322-2-220000002-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000−2i2i−2i2i000000−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ4422-2-220000002-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000−2i2i−2i2i000000−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ452-22-2-12i−2i2i−2i2-21-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111−ii−ii-1122-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii22-2-22-22i−2i2i−2i-1-11100000000-11−ii−ii000000000000
χ462-22-2-12i−2i2i−2i2-21-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111−ii−ii-1122-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii-2-222-22−2i2i−2i2i11-1-1000000001-1i−ii−i000000000000
χ472-22-2-12i−2i−2i2i-221-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111−iii−i1-1-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i22-2-2-222i−2i−2i2i-1-111000000001-1−iii−i000000000000
χ482-22-2-12i−2i−2i2i-221-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111−iii−i1-1-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-2-2222-2−2i2i2i−2i11-1-100000000-11i−i−ii000000000000
χ492-22-2-1−2i2i2i−2i-221-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111i−i−ii1-1-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii22-2-2-22−2i2i2i−2i-1-111000000001-1i−i−ii000000000000
χ502-22-2-1−2i2i2i−2i-221-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111i−i−ii1-1-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-2-2222-22i−2i−2i2i11-1-100000000-11−iii−i000000000000
χ512-22-2-1−2i2i−2i2i2-21-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111i−ii−i-1122-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i22-2-22-2−2i2i−2i2i-1-11100000000-11i−ii−i000000000000
χ522-22-2-1−2i2i−2i2i2-21-1122-1-1-1-1-2-2111122-1-1-1-1-2-21111i−ii−i-1122-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i-2-222-222i−2i2i−2i11-1-1000000001-1−ii−ii000000000000
χ532-2-222000000-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i−2i2i0000002i−2i−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ542-2-222000000-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i−2i2i0000002i−2i−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ552-2-222000000-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i2i−2i000000−2i2i2i−2i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ562-2-222000000-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i2i−2i000000−2i2i2i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ57444444444444441-211-2-21-211-2-21-211-2-21-211-2-24444441-211-2-21-211-2-21-211-2-21-211-2-21-211-2-21-211-2-20000000000000000000000000000000000000000
χ5844444444444444-21-2-211-21-2-211-21-2-211-21-2-211444444-21-2-211-21-2-211-21-2-211-21-2-211-21-2-211-21-2-2110000000000000000000000000000000000000000
χ594444444-4-4-4-44441-211-2-21-211-2-21-211-2-21-211-2-244-4-4-4-4-12-1-122-12-1-1221-211-2-21-211-2-2-12-1-122-12-1-1220000000000000000000000000000000000000000
χ604444444-4-4-4-4444-21-2-211-21-2-211-21-2-211-21-2-21144-4-4-4-42-122-1-12-122-1-1-21-2-211-21-2-2112-122-1-12-122-1-10000000000000000000000000000000000000000
χ6144444-4-444-4-44441-211-2-21-211-2-21-211-2-21-211-2-2-4-444-4-4-12-1-122-12-1-122-12-1-122-12-1-1221-211-2-21-211-2-20000000000000000000000000000000000000000
χ6244444-4-444-4-4444-21-2-211-21-2-211-21-2-211-21-2-211-4-444-4-42-122-1-12-122-1-12-122-1-12-122-1-1-21-2-211-21-2-2110000000000000000000000000000000000000000
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χ1208-8-88-400000044-4-4222−1+3i3−1−3i3-4222−1+3i3−1−3i34-2-2-21−3i31+3i34-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000

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