Finite Group Databasebeta

← Group #13166221

Character table — Group #13166221

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222288888888888888888888888899999999999918181818181818181818181818181818181818181818181818181818181854545454545454545454545454545454
order122234466612121212333666666666121212121212121212121212222244444444444444666612121212121212121212121212121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ511111111111111111111111111111111111111-1-1-1-1ii−i−iii−i−i-1-1ii−i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13
χ611111111111111111111111111111111111111-1-1-1-1ii−i−iii−i−i-1-1ii−i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13
χ711111111111111111111111111111111111111-1-1-1-1−i−iii−i−iii-1-1−i−iii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23
χ811111111111111111111111111111111111111-1-1-1-1−i−iii−i−iii-1-1−i−iii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23
χ911111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ1411111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ1511111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ1611111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1711-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-11-11-11-11-1i−ii−ii−i1-11-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ1811-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-11-11-11-11-1i−ii−ii−i1-11-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii-11−ii
χ1911-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-1-11-11-11-11i−i−ii−ii1-11-1ii−i−i-1-111−i−iii-1-111−i−iiii−i-11i−i-11−ii1-1−ii1-1
χ2011-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-1-11-11-11-11i−i−ii−ii1-11-1ii−i−i-1-111−i−iii-1-111−i−iii−ii1-1−ii1-1i−i-11i−i-11
χ2111-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-11i−i−iii−i−ii−ii-111-1-11-11−i−iiiii−i−i-1-111−i−iii11-1-1ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ2211-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-11i−i−iii−i−ii−ii-111-1-11-11−i−iiiii−i−i-1-111−i−iii11-1-1−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ2311-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-11−iii−i−iii−i−ii1-1-11-11-11−i−iii−i−iii11-1-1ii−i−i-1-111−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13
χ2411-1-11i−i1-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-11−iii−i−iii−i−ii1-1-11-11-11−i−iii−i−iii11-1-1ii−i−i-1-111ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13
χ2511-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-11-11-11-11-1−ii−ii−ii1-11-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii
χ2611-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-11-11-11-11-1−ii−ii−ii1-11-1−i−iii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i-11i−i
χ2711-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-1-11-11-11-11−iii−ii−i1-11-1−i−iii-1-111ii−i−i-1-111ii−i−ii−i1-1i−i1-1−ii-11−ii-11
χ2811-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-1-11-11-11-11−iii−ii−i1-11-1−i−iii-1-111ii−i−i-1-111ii−i−i−ii-11−ii-11i−i1-1i−i1-1
χ2911-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-11i−i−iii−i−iii−i1-1-11-11-11ii−i−iii−i−i11-1-1−i−iii-1-111ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23
χ3011-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-11i−i−iii−i−iii−i1-1-11-11-11ii−i−iii−i−i11-1-1−i−iii-1-111−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23
χ3111-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-11−iii−i−iii−ii−i-111-1-11-11ii−i−i−i−iii-1-111ii−i−i11-1-1−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ3211-1-11−ii1-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-11−iii−i−iii−ii−i-111-1-11-11ii−i−i−i−iii-1-111ii−i−i11-1-1ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ332222-122-1-1-1-1-1-1-12-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ342222-122-1-1-1-1-1-1-12-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-12222-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ352222-122-1-1-1-1-1-1-12-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-22i2i−2i−2i11111111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ362222-122-1-1-1-1-1-1-12-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2−2i−2i2i2i11111111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ372222-1-2-2-1-1-111112-1-12-1-12-1-12-1-1-2-21111-2-21111222222222222-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ382222-1-2-2-1-1-111112-1-12-1-12-1-12-1-1-2-21111-2-211112222-2-2-2-2-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ392222-1-2-2-1-1-111112-1-12-1-12-1-12-1-1-2-21111-2-21111-2-2-2-22i2i−2i−2i2i2i−2i−2i22−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ402222-1-2-2-1-1-111112-1-12-1-12-1-12-1-1-2-21111-2-21111-2-2-2-2−2i−2i2i2i−2i−2i2i2i222i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ4122-2-2-12i−2i-111−i−iii2-1-12-1-1-211-2112i2i−i−i−i−i−2i−2iiiii2-22-22-22-22-22-22i−2i2i−2i2i−2i-11-11−i−iii-1-111−i−iii-1-111−i−iii0000000000000000
χ4222-2-2-12i−2i-111−i−iii2-1-12-1-1-211-2112i2i−i−i−i−i−2i−2iiiii2-22-2-22-22-22-222i−2i−2i2i−2i2i-11-11−i−iii11-1-1ii−i−i11-1-1ii−i−i0000000000000000
χ4322-2-2-12i−2i-111−i−iii2-1-12-1-1-211-2112i2i−i−i−i−i−2i−2iiiii-22-222i−2i−2i2i2i−2i−2i2i−2i2i-222-21-11-1ii−i−i−i−iii11-1-1ii−i−i-1-1110000000000000000
χ4422-2-2-12i−2i-111−i−iii2-1-12-1-1-211-2112i2i−i−i−i−i−2i−2iiiii-22-22−2i2i2i−2i−2i2i2i−2i−2i2i2-2-221-11-1ii−i−iii−i−i-1-111−i−iii11-1-10000000000000000
χ4522-2-2-1−2i2i-111ii−i−i2-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i2-22-22-22-22-22-2−2i2i−2i2i−2i2i-11-11ii−i−i-1-111ii−i−i-1-111ii−i−i0000000000000000
χ4622-2-2-1−2i2i-111ii−i−i2-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i2-22-2-22-22-22-22−2i2i2i−2i2i−2i-11-11ii−i−i11-1-1−i−iii11-1-1−i−iii0000000000000000
χ4722-2-2-1−2i2i-111ii−i−i2-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i-22-222i−2i−2i2i2i−2i−2i2i2i−2i2-2-221-11-1−i−iii−i−iii-1-111ii−i−i11-1-10000000000000000
χ4822-2-2-1−2i2i-111ii−i−i2-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i-22-22−2i2i2i−2i−2i2i2i−2i2i−2i-222-21-11-1−i−iiiii−i−i11-1-1−i−iii-1-1110000000000000000
χ492-22-2200-22-20000222-2-2-2222-2-2-20000000000002-2-222i2i−2i−2i−2i−2i2i2i0000002-2-2200002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ502-22-2200-22-20000222-2-2-2222-2-2-20000000000002-2-22−2i−2i2i2i2i2i−2i−2i0000002-2-220000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ512-22-2200-22-20000222-2-2-2222-2-2-2000000000000-222-22222-2-2-2-2000000-222-200002-22-20000-22-2200000000000000000000
χ522-22-2200-22-20000222-2-2-2222-2-2-2000000000000-222-2-2-2-2-22222000000-222-20000-22-2200002-22-200000000000000000000
χ532-22-2-1001-113−33−32-1-1-2112-1-1-2110033−3−30033−3−32-2-222i2i−2i−2i−2i−2i2i2i000000-111-13−33−3−ii−ii−i3i3−i3i3−ii−ii−i3i3−i3i30000000000000000
χ542-22-2-1001-113−33−32-1-1-2112-1-1-2110033−3−30033−3−32-2-22−2i−2i2i2i2i2i−2i−2i000000-111-13−33−3i−ii−ii3−i3i3−i3i−ii−ii3−i3i3−i30000000000000000
χ552-22-2-1001-113−33−32-1-1-2112-1-1-2110033−3−30033−3−3-222-22222-2-2-2-20000001-1-11−33−33-11-11−33−331-11-13−33−30000000000000000
χ562-22-2-1001-113−33−32-1-1-2112-1-1-2110033−3−30033−3−3-222-2-2-2-2-222220000001-1-11−33−331-11-13−33−3-11-11−33−330000000000000000
χ572-22-2-1001-11−33−332-1-1-2112-1-1-21100−3−33300−3−3332-2-222i2i−2i−2i−2i−2i2i2i000000-111-1−33−33−ii−iii3−i3i3−i3−ii−iii3−i3i3−i30000000000000000
χ582-22-2-1001-11−33−332-1-1-2112-1-1-21100−3−33300−3−3332-2-22−2i−2i2i2i2i2i−2i−2i000000-111-1−33−33i−ii−i−i3i3−i3i3i−ii−i−i3i3−i3i30000000000000000
χ592-22-2-1001-11−33−332-1-1-2112-1-1-21100−3−33300−3−333-222-22222-2-2-2-20000001-1-113−33−3-11-113−33−31-11-1−33−330000000000000000
χ602-22-2-1001-11−33−332-1-1-2112-1-1-21100−3−33300−3−333-222-2-2-2-2-222220000001-1-113−33−31-11-1−33−33-11-113−33−30000000000000000
χ612-2-22200-2-220000222-2-2-2-2-2-222200000000000022-2-22i−2i−2i2i−2i2i2i−2i00000022-2-200002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ622-2-22200-2-220000222-2-2-2-2-2-222200000000000022-2-2−2i2i2i−2i2i−2i−2i2i00000022-2-20000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ632-2-22200-2-220000222-2-2-2-2-2-2222000000000000-2-2222-22-2-22-22000000-2-22200002-2-220000-222-200000000000000000000
χ642-2-22200-2-220000222-2-2-2-2-2-2222000000000000-2-222-22-222-22-2000000-2-2220000-222-200002-2-2200000000000000000000
χ652-2-22-10011-1−i3i3i3−i32-1-1-211-2112-1-100−i3−i3i3i300i3i3−i3−i322-2-22i−2i−2i2i−2i2i2i−2i000000-1-111−i3i3i3−i3−iii−i−333−3−iii−i−333−30000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.