Finite Group Databasebeta

← Group #13157229

Character table — Group #13157229

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222244444444444444444444444444488888888888888888888888888888888888888836363636363636367272216216216216
order12236663333334666666666666666666121226666666666666666666666666612121212121212121212121244441212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i
χ41111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1i−ii−i
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1−ii−ii
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111-1-11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-111-1
χ92222222222222-2222222222222222222-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2002-200002-20000
χ102222222222222-2222222222222222222-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-200-220000-220000
χ11222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-10000
χ12222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111110000
χ13222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-211-2-2-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-122-2-2-1-1-1-1110000
χ14222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-211-2-2-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-2-2221111-1-10000
χ15222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110−i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-2-2-211111111002-2−i3−i3i3i3-110000
χ16222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110−i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-2-2-21111111100-22i3i3−i3−i31-10000
χ17222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-2-2-211111111002-2i3i3−i3−i3-110000
χ18222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-2-2-21111111100-22−i3−i3i3i31-10000
χ1944444441-211-2-2411-2-21111-2-2-2-21-211-2-2444441111-2-2-2-21111-2-2-2-21111-2-2-2-211-2-21111-2-2-2-200000000000000
χ2044444441-211-2-2411-2-21111-2-2-2-21-211-2-244-4-4-4-1-1-1-12222-1-1-1-12222-1-1-1-1222211-2-21111-2-2-2-200000000000000
χ2144444441-211-2-2-411-2-21111-2-2-2-21-211-2-2-4-400033-3-3000033-3-3000033-3-30000-1-122-1-1-1-1222200000000000000
χ2244444441-211-2-2-411-2-21111-2-2-2-21-211-2-2-4-4000-3-3330000-3-3330000-3-3330000-1-122-1-1-1-1222200000000000000
χ234444444-21-2-2114-2-211-2-2-2-21111-21-2-21144444-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-211-2-2-2-2111100000000000000
χ244444444-21-2-2114-2-211-2-2-2-21111-21-2-21144-4-4-42222-1-1-1-12222-1-1-1-12222-1-1-1-1-2-211-2-2-2-2111100000000000000
χ254444444-21-2-211-4-2-211-2-2-2-21111-21-2-211-4-4000000033-3-3000033-3-3000033-3-322-1-12222-1-1-1-100000000000000
χ264444444-21-2-211-4-2-211-2-2-2-21111-21-2-211-4-40000000-3-3330000-3-3330000-3-33322-1-12222-1-1-1-100000000000000
χ27444-2-2-2-21-2−1−3i32−1+3i3211411-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-2-24-2-21111-2-2-2-2−1−3i32−1−3i32−1+3i32−1+3i321111−1+3i32−1+3i32−1−3i32−1−3i32111111-2-2−1−3i32−1−3i32−1+3i32−1+3i32111100000000000000
χ28444-2-2-2-21-2−1−3i32−1+3i3211411-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-2-2-422-1-1-1-122221+3i321+3i321−3i321−3i32-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-111-2-2−1−3i32−1−3i32−1+3i32−1+3i32111100000000000000
χ29444-2-2-2-21-2−1−3i32−1+3i3211-411-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211220−2i32i333-3-30000−3−i32−3−i323−i323−i32i3i3i3i3−3+i32−3+i323+i323+i32−i3−i3−i3−i3-1-1221+3i321+3i321−3i321−3i32-1-1-1-100000000000000
χ30444-2-2-2-21-2−1−3i32−1+3i3211-411-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i32112202i3−2i3-3-33300003+i323+i32−3+i32−3+i32−i3−i3−i3−i33−i323−i32−3−i32−3−i32i3i3i3i3-1-1221+3i321+3i321−3i321−3i32-1-1-1-100000000000000
χ31444-2-2-2-21-2−1+3i32−1−3i3211411-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-2-24-2-21111-2-2-2-2−1+3i32−1+3i32−1−3i32−1−3i321111−1−3i32−1−3i32−1+3i32−1+3i32111111-2-2−1+3i32−1+3i32−1−3i32−1−3i32111100000000000000
χ32444-2-2-2-21-2−1+3i32−1−3i3211411-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-2-2-422-1-1-1-122221−3i321−3i321+3i321+3i32-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-111-2-2−1+3i32−1+3i32−1−3i32−1−3i32111100000000000000
χ33444-2-2-2-21-2−1+3i32−1−3i3211-411-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211220−2i32i3-3-33300003−i323−i32−3−i32−3−i32i3i3i3i33+i323+i32−3+i32−3+i32−i3−i3−i3−i3-1-1221−3i321−3i321+3i321+3i32-1-1-1-100000000000000
χ34444-2-2-2-21-2−1+3i32−1−3i3211-411-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i32112202i3−2i333-3-30000−3+i32−3+i323+i323+i32−i3−i3−i3−i3−3−i32−3−i323−i323−i32i3i3i3i3-1-1221−3i321−3i321+3i321+3i32-1-1-1-100000000000000
χ35444-2-2-2-2-2111−1−3i32−1+3i324-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2-24-2-2-2-2-2-211111111−1−3i32−1−3i32−1+3i32−1+3i321111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i3200000000000000
χ36444-2-2-2-2-2111−1−3i32−1+3i324-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2-2-4222222-1-1-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-11−3i321−3i321+3i321+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i3200000000000000
χ37444-2-2-2-2-2111−1−3i32−1+3i32-4-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32220−2i32i3000033-3-3i3i3i3i3−3−i32−3−i323−i323−i32−i3−i3−i3−i3−3+i32−3+i323+i323+i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i3200000000000000
χ38444-2-2-2-2-2111−1−3i32−1+3i32-4-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i322202i3−2i30000-3-333−i3−i3−i3−i33+i323+i32−3+i32−3+i32i3i3i3i33−i323−i32−3−i32−3−i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i3200000000000000
χ39444-2-2-2-2-2111−1+3i32−1−3i324-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2-24-2-2-2-2-2-211111111−1+3i32−1+3i32−1−3i32−1−3i321111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i3200000000000000
χ40444-2-2-2-2-2111−1+3i32−1−3i324-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2-2-4222222-1-1-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-11+3i321+3i321−3i321−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i3200000000000000
χ41444-2-2-2-2-2111−1+3i32−1−3i32-4-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32220−2i32i30000-3-333i3i3i3i33−i323−i32−3−i32−3−i32−i3−i3−i3−i33+i323+i32−3+i32−3+i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i3200000000000000
χ42444-2-2-2-2-2111−1+3i32−1−3i32-4-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i322202i3−2i3000033-3-3−i3−i3−i3−i3−3+i32−3+i323+i323+i32i3i3i3i3−3−i32−3−i323−i323−i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i3200000000000000
χ4344-44-4-441-211-2-20-1-122-1-1-1-122221-211-2-200000−i3i3−i3i300−2i32i3−i3i3−i3i300−2i32i3−i3i3−i3i300−2i32i33-3003-33-3000000000000000000
χ4444-44-4-441-211-2-20-1-122-1-1-1-122221-211-2-200000−i3i3i3−i3−2i32i300−i3i3i3−i3−2i32i300−i3i3i3−i3−2i32i300-3300-33-33000000000000000000
χ4544-44-4-441-211-2-20-1-122-1-1-1-122221-211-2-200000i3−i3−i3i32i3−2i300i3−i3−i3i32i3−2i300i3−i3−i3i32i3−2i300-3300-33-33000000000000000000
χ4644-44-4-441-211-2-20-1-122-1-1-1-122221-211-2-200000i3−i3i3−i3002i3−2i3i3−i3i3−i3002i3−2i3i3−i3i3−i3002i3−2i33-3003-33-3000000000000000000
χ4744-44-4-444444440-4-4-4-4-4-4-4-4-4-4-4-44444440000000000000000000000000000000000000000000000000000000
χ4844-44-4-44-21-2-211022-1-12222-1-1-1-1-21-2-2110000000−2i32i3−i3i3i3−i300−2i32i3−i3i3i3−i300−2i32i3−i3i3i3−i3003-300003-33-300000000000000
χ4944-44-4-44-21-2-211022-1-12222-1-1-1-1-21-2-21100000002i3−2i3i3−i3−i3i3002i3−2i3i3−i3−i3i3002i3−2i3i3−i3−i3i3003-300003-33-300000000000000
χ5044-44-4-44-21-2-211022-1-12222-1-1-1-1-21-2-21100000−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i300-330000-33-3300000000000000
χ5144-44-4-44-21-2-211022-1-12222-1-1-1-1-21-2-211000002i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i300-330000-33-3300000000000000
χ5244-4-222-21-2−1−3i32−1+3i32110-1-1221+3i321+3i321−3i321−3i32-1-1-1-11-2−1−3i32−1+3i3211−2i32i3000−i3i3−i3i300−2i32i33+i32−3−i32−3+i323−i323-3i3−i3−3+i323−i323+i32−3−i32-33i3−i33-300−3−i323+i32−3+i323−i32−i3i3i3−i300000000000000
χ5344-4-222-21-2−1−3i32−1+3i32110-1-1221+3i321+3i321−3i321−3i32-1-1-1-11-2−1−3i32−1+3i3211−2i32i3000i3−i3i3−i3002i3−2i3−3−i323+i323−i32−3+i32-33−i3i33−i32−3+i32−3−i323+i323-3−i3i33-300−3−i323+i32−3+i323−i32−i3i3i3−i300000000000000
χ5444-4-222-21-2−1−3i32−1+3i32110-1-1221+3i321+3i321−3i321−3i32-1-1-1-11-2−1−3i32−1+3i32112i3−2i3000−i3i3i3−i3−2i32i3003+i32−3−i323−i32−3+i32i3−i33-3−3+i323−i32−3−i323+i32i3−i3-33-33003+i32−3−i323−i32−3+i32i3−i3−i3i300000000000000
χ5544-4-222-21-2−1−3i32−1+3i32110-1-1221+3i321+3i321−3i321−3i32-1-1-1-11-2−1−3i32−1+3i32112i3−2i3000i3−i3−i3i32i3−2i300−3−i323+i32−3+i323−i32−i3i3-333−i32−3+i323+i32−3−i32−i3i33-3-33003+i32−3−i323−i32−3+i32i3−i3−i3i300000000000000
χ5644-4-222-21-2−1+3i32−1−3i32110-1-1221−3i321−3i321+3i321+3i32-1-1-1-11-2−1+3i32−1−3i3211−2i32i3000−i3i3i3−i3−2i32i300−3+i323−i32−3−i323+i32i3−i3-333+i32−3−i323−i32−3+i32i3−i33-3-33003−i32−3+i323+i32−3−i32−i3i3i3−i300000000000000
χ5744-4-222-21-2−1+3i32−1−3i32110-1-1221−3i321−3i321+3i321+3i32-1-1-1-11-2−1+3i32−1−3i3211−2i32i3000i3−i3−i3i32i3−2i3003−i32−3+i323+i32−3−i32−i3i33-3−3−i323+i32−3+i323−i32−i3i3-33-33003−i32−3+i323+i32−3−i32−i3i3i3−i300000000000000
χ5844-4-222-21-2−1+3i32−1−3i32110-1-1221−3i321−3i321+3i321+3i32-1-1-1-11-2−1+3i32−1−3i32112i3−2i3000−i3i3−i3i300−2i32i3−3+i323−i323+i32−3−i32-33i3−i33+i32−3−i32−3+i323−i323-3i3−i33-300−3+i323−i32−3−i323+i32i3−i3−i3i300000000000000
χ5944-4-222-21-2−1+3i32−1−3i32110-1-1221−3i321−3i321+3i321+3i32-1-1-1-11-2−1+3i32−1−3i32112i3−2i3000i3−i3i3−i3002i3−2i33−i32−3+i32−3−i323+i323-3−i3i3−3−i323+i323−i32−3+i32-33−i3i33-300−3+i323−i32−3−i323+i32i3−i3−i3i300000000000000
χ6044-4-222-244-2-2-2-20-4-4-4-42222222244-2-2-2-2−2i32i30000000000000000000000000000000−2i32i32i3−2i32i3−2i3−2i32i300000000000000
χ6144-4-222-244-2-2-2-20-4-4-4-42222222244-2-2-2-22i3−2i300000000000000000000000000000002i3−2i3−2i32i3−2i32i32i3−2i300000000000000
χ6244-4-222-2-2111−1−3i32−1+3i32022-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2111−1−3i32−1+3i32−2i32i3000−2i32i300i3−i3i3−i3i3−i3-33−3−i323+i323−i32−3+i32i3−i33-33−i32−3+i32−3−i323+i3200-33i3−i3−i3i33+i32−3−i323−i32−3+i3200000000000000
χ6344-4-222-2-2111−1−3i32−1+3i32022-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2111−1−3i32−1+3i32−2i32i30002i3−2i300−i3i3−i3i3−i3i33-33+i32−3−i32−3+i323−i32−i3i3-33−3+i323−i323+i32−3−i3200-33i3−i3−i3i33+i32−3−i323−i32−3+i3200000000000000
χ6444-4-222-2-2111−1−3i32−1+3i32022-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2111−1−3i32−1+3i322i3−2i300000−2i32i3−i3i3i3−i3-33i3−i33+i32−3−i323−i32−3+i323-3i3−i3−3+i323−i32−3−i323+i32003-3−i3i3i3−i3−3−i323+i32−3+i323−i3200000000000000
χ6544-4-222-2-2111−1−3i32−1+3i32022-1-1-1-1-1-11+3i321+3i321−3i321−3i32-2111−1−3i32−1+3i322i3−2i3000002i3−2i3i3−i3−i3i33-3−i3i3−3−i323+i32−3+i323−i32-33−i3i33−i32−3+i323+i32−3−i32003-3−i3i3i3−i3−3−i323+i32−3+i323−i3200000000000000
χ6644-4-222-2-2111−1+3i32−1−3i32022-1-1-1-1-1-11−3i321−3i321+3i321+3i32-2111−1+3i32−1−3i32−2i32i300000−2i32i3−i3i3i3−i33-3i3−i3−3+i323−i32−3−i323+i32-33i3−i33+i32−3−i323−i32−3+i32003-3i3−i3−i3i3−3+i323−i32−3−i323+i3200000000000000
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χ704-40400-44444440000000000000-4-4-4-4-4-4000000000000000000000000000000000000000002i−2i002i−2i2i−2i000000
χ714-40400-44444440000000000000-4-4-4-4-4-400000000000000000000000000000000000000000−2i2i00−2i2i−2i2i000000
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χ754-40-22i3−2i3244-2-2-2-2000002i3−2i32i3−2i32i3−2i32i3−2i3-4-4222200000000000000000000000000000000000000000−2i2i00−2ζ112ζ11−2ζ72ζ7000000
χ768-80800-82-422-4-406-6006-6-660000-24-2-2440000000000000000000000000000000000000000000000000000000
χ778-80800-82-422-4-40-6600-666-60000-24-2-2440000000000000000000000000000000000000000000000000000000
χ788-80800-8-42-4-4220006-600006-6-664-244-2-20000000000000000000000000000000000000000000000000000000
χ798-80800-8-42-4-422000-660000-666-64-244-2-20000000000000000000000000000000000000000000000000000000
χ808-80-4−4i34i342-4−1−3i3−1+3i32206-600−3−i33+i33−i3−3+i32i3−2i32i3−2i3-241+3i31−3i3-2-20000000000000000000000000000000000000000000000000000000
χ818-80-4−4i34i342-4−1+3i3−1−3i3220-66003−i3−3+i3−3−i33+i32i3−2i32i3−2i3-241−3i31+3i3-2-20000000000000000000000000000000000000000000000000000000
χ828-80-4−4i34i34-4222−1−3i3−1+3i30006-62i3−2i32i3−2i3−3−i33+i33−i3−3+i34-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000
χ838-80-4−4i34i34-4222−1+3i3−1−3i3000-662i3−2i32i3−2i33−i3−3+i3−3−i33+i34-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000
χ848-80-44i3−4i342-4−1−3i3−1+3i3220-66003+i3−3−i3−3+i33−i3−2i32i3−2i32i3-241+3i31−3i3-2-20000000000000000000000000000000000000000000000000000000
χ858-80-44i3−4i342-4−1+3i3−1−3i32206-600−3+i33−i33+i3−3−i3−2i32i3−2i32i3-241−3i31+3i3-2-20000000000000000000000000000000000000000000000000000000
χ868-80-44i3−4i34-4222−1−3i3−1+3i3000-66−2i32i3−2i32i33+i3−3−i3−3+i33−i34-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000
χ878-80-44i3−4i34-4222−1+3i3−1−3i30006-6−2i32i3−2i32i3−3+i33−i33+i3−3−i34-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.