Finite Group Databasebeta

← Group #13181076

Character table — Group #13181076

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112224444444448888888899121212121212181818242424242424363636545454547272112224444444448888888899121212121212181818242424242424363636545454547272
order123463333666612361212121212122244121212124661212121212122212888866226466666666612661212121212122244121212124661212121212122212888866
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111111111111111111111111111111111111111-1-11-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111
χ4111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1
χ5111-1111111111-111-1-1-1-1-1-1-1-11-111-1-11-1-1111-1-1-11-1111-1-11-1111-1111111111-111-1-1-1-1-1-1-1-11-111-1-11-1-1111-1-1-11-1111-1-11-1
χ6111-1111111111-111-1-1-1-1-1-1-1-11-111-1-11-1-1111-1-1-1-111-1-111-11111-1111111111-111-1-1-1-1-1-1-1-11-111-1-11-1-1111-1-1-1-111-1-111-11
χ7111-1111111111-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-11111-11-1-1111-1111-1111111111-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-11111-11-1-1111-1
χ8111-1111111111-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1111-11111-1-1-11111-1111111111-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1111-11111-1-1-11
χ92222222222222222222222-2-2000000-2-2-200000000-20000002222222222222222222222-2-2000000-2-2-200000000-2000000
χ10222-2222222222-222-2-2-2-2-2-222000000-22200000000-2000000222-2222222222-222-2-2-2-2-2-222000000-22200000000-2000000
χ1122-12-12-1-1222-1-1-1-1-122-1-1-1-12222-1-1-1-12-1-12-1-12-1-100-100000022-12-12-1-1222-1-1-1-1-122-1-1-1-12222-1-1-1-12-1-12-1-12-1-100-1000000
χ1222-12-12-1-1222-1-1-1-1-122-1-1-1-122-2-211112-1-1-211-21100-100000022-12-12-1-1222-1-1-1-1-122-1-1-1-122-2-211112-1-1-211-21100-1000000
χ1322-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-200−i3i3−i3i3-2110−i3i30−i3i300100000022-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-200−i3i3−i3i3-2110−i3i30−i3i3001000000
χ1422-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-200i3−i3i3−i3-2110i3−i30i3−i300100000022-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-200i3−i3i3−i3-2110i3−i30i3−i3001000000
χ1522-1-2-12-1-1222-1-11-1-1-2-211112200−i3i3i3−i3-2-1-10−i3i30i3−i300100000022-1-2-12-1-1222-1-11-1-1-2-211112200−i3i3i3−i3-2-1-10−i3i30i3−i3001000000
χ1622-1-2-12-1-1222-1-11-1-1-2-211112200i3−i3−i3i3-2-1-10i3−i30−i3i300100000022-1-2-12-1-1222-1-11-1-1-2-211112200i3−i3−i3i3-2-1-10i3−i30−i3i3001000000
χ1722-1-2-12-1-1222-1-11-1-1-2-21111-2-22-2-1-1112112-1-1-21100-100000022-1-2-12-1-1222-1-11-1-1-2-21111-2-22-2-1-1112112-1-1-21100-1000000
χ1822-1-2-12-1-1222-1-11-1-1-2-21111-2-2-2211-1-1211-2112-1-100-100000022-1-2-12-1-1222-1-11-1-1-2-21111-2-2-2211-1-1211-2112-1-100-1000000
χ192-220-22222-2-2-2-202-20000002-200000002-2000000000−i2i2−i2i2002-220-22222-2-2-2-202-20000002-200000002-2000000000−i2i2−i2i200
χ202-220-22222-2-2-2-202-20000002-200000002-2000000000i2−i2i2−i2002-220-22222-2-2-2-202-20000002-200000002-2000000000i2−i2i2−i200
χ212-220-22222-2-2-2-202-2000000-220000000-22000000000−i2i2i2−i2002-220-22222-2-2-2-202-2000000-220000000-22000000000−i2i2i2−i200
χ222-220-22222-2-2-2-202-2000000-220000000-22000000000i2−i2−i2i2002-220-22222-2-2-2-202-2000000-220000000-22000000000i2−i2−i2i200
χ2344444111-2-21114-2-2-2111-2-200222222000-1-1-1-1-1-100000000044444111-2-21114-2-2-2111-2-200222222000-1-1-1-1-1-1000000000
χ2444444111-2-21114-2-2-2111-2-200-2-2-2-2-2-200011111100000000044444111-2-21114-2-2-2111-2-200-2-2-2-2-2-2000111111000000000
χ2544444-2-2-211-2-2-24111-2-2-211000000000000000002200000-1-144444-2-2-211-2-2-24111-2-2-211000000000000000002200000-1-1
χ2644444-2-2-211-2-2-24111-2-2-21100000000000000000-2-2000001144444-2-2-211-2-2-24111-2-2-21100000000000000000-2-20000011
χ27444-44111-2-2111-4-2-22-1-1-122002-222-2-2000-1-1-1111000000000444-44111-2-2111-4-2-22-1-1-122002-222-2-2000-1-1-1111000000000
χ28444-44111-2-2111-4-2-22-1-1-12200-22-2-222000111-1-1-1000000000444-44111-2-2111-4-2-22-1-1-12200-22-2-222000111-1-1-1000000000
χ29444-44-2-2-211-2-2-2-411-1222-1-1000000000000000002-200000-11444-44-2-2-211-2-2-2-411-1222-1-1000000000000000002-200000-11
χ30444-44-2-2-211-2-2-2-411-1222-1-100000000000000000-22000001-1444-44-2-2-211-2-2-2-411-1222-1-100000000000000000-22000001-1
χ3144-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i32110022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i3200000000044-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i32110022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i32000000000
χ3244-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i321100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i3200000000044-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i321100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i32000000000
χ3344-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i32110022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i3200000000044-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i32110022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i32000000000
χ3444-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i321100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i3200000000044-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i321100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i32000000000
χ3544-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-1002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i3200000000044-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-1002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i32000000000
χ3644-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i3200000000044-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i32000000000
χ3744-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-1002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i3200000000044-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-1002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i32000000000
χ3844-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i3200000000044-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i32000000000
χ394-4-2024-2-24-4-4220-220000004-40000000-220000000000000004-4-2024-2-24-4-4220-220000004-40000000-22000000000000000
χ404-4-2024-2-24-4-4220-22000000-4400000002-20000000000000004-4-2024-2-24-4-4220-22000000-4400000002-2000000000000000
χ4188-48-4-42222-422-4-1-12-422-1-10000000000000000000000000088-48-4-42222-422-4-1-12-422-1-100000000000000000000000000
χ4288-4-8-4-42222-4224-1-1-24-2-2110000000000000000000000000088-4-8-4-42222-4224-1-1-24-2-21100000000000000000000000000
χ438-880-8222-44-2-2-20-44000000000000000000000000000000008-880-8222-44-2-2-20-4400000000000000000000000000000000
χ448-880-8-4-4-42-244402-2000000000000000000000000000000008-880-8-4-4-42-244402-200000000000000000000000000000000
χ458-8-4042−1−3i3−1+3i3-44-21+3i31−3i302-2000000000000000000000000000000008-8-4042−1−3i3−1+3i3-44-21+3i31−3i302-200000000000000000000000000000000
χ468-8-4042−1+3i3−1−3i3-44-21−3i31+3i302-2000000000000000000000000000000008-8-4042−1+3i3−1−3i3-44-21−3i31+3i302-200000000000000000000000000000000
χ478-8-404-4222-24-2-20-11000033−33000000000000000000000000008-8-404-4222-24-2-20-11000033−3300000000000000000000000000
χ488-8-404-4222-24-2-20-110000−3333000000000000000000000000008-8-404-4222-24-2-20-110000−333300000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ50111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ51111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111111-1-1-11111-1-1
χ52111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111111-1-1-1-1-111
χ53111-1111111111-111-1-1-1-1-1-1-1-11-111-1-11-1-1111-1-1-11-1111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-11-1-111111111-11-1-111-111-1-1-1111-11-1-1-111-11
χ54111-1111111111-111-1-1-1-1-1-1-1-11-111-1-11-1-1111-1-1-1-111-1-111-11-1-1-11-1-1-1-1-1-1-1-1-11-1-111111111-11-1-111-111-1-1-11111-1-111-1-11-1
χ55111-1111111111-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-11111-11-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-11-1-1111111111-111-1-1-111111-1-1-1-11-111-1-1-11
χ56111-1111111111-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1111-11111-1-1-11-1-1-11-1-1-1-1-1-1-1-1-11-1-1111111111-111-1-1-111111-1-1-11-1-1-1-1111-1
χ572222222222222222222222-2-2000000-2-2-200000000-2000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222000000222000000002000000
χ58222-2222222222-222-2-2-2-2-2-222000000-22200000000-2000000-2-2-22-2-2-2-2-2-2-2-2-22-2-2222222-2-20000002-2-2000000002000000
χ5922-12-12-1-1222-1-1-1-1-122-1-1-1-12222-1-1-1-12-1-12-1-12-1-100-1000000-2-21-21-211-2-2-211111-2-21111-2-2-2-21111-211-211-211001000000
χ6022-12-12-1-1222-1-1-1-1-122-1-1-1-122-2-211112-1-1-211-21100-1000000-2-21-21-211-2-2-211111-2-21111-2-222-1-1-1-1-2112-1-12-1-1001000000
χ6122-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-200−i3i3−i3i3-2110−i3i30−i3i3001000000-2-21-21-211-2-2-211111-2-211112200i3−i3i3−i32-1-10i3−i30i3−i300-1000000
χ6222-12-12-1-1222-1-1-1-1-122-1-1-1-1-2-200i3−i3i3−i3-2110i3−i30i3−i3001000000-2-21-21-211-2-2-211111-2-211112200−i3i3−i3i32-1-10−i3i30−i3i300-1000000
χ6322-1-2-12-1-1222-1-11-1-1-2-211112200−i3i3i3−i3-2-1-10−i3i30i3−i3001000000-2-2121-211-2-2-211-11122-1-1-1-1-2-200i3−i3−i3i32110i3−i30−i3i300-1000000
χ6422-1-2-12-1-1222-1-11-1-1-2-211112200i3−i3−i3i3-2-1-10i3−i30−i3i3001000000-2-2121-211-2-2-211-11122-1-1-1-1-2-200−i3i3i3−i32110−i3i30i3−i300-1000000
χ6522-1-2-12-1-1222-1-11-1-1-2-21111-2-22-2-1-1112112-1-1-21100-1000000-2-2121-211-2-2-211-11122-1-1-1-122-2211-1-1-2-1-1-2112-1-1001000000
χ6622-1-2-12-1-1222-1-11-1-1-2-21111-2-2-2211-1-1211-2112-1-100-1000000-2-2121-211-2-2-211-11122-1-1-1-1222-2-1-111-2-1-12-1-1-211001000000
χ672-220-22222-2-2-2-202-20000002-200000002-2000000000−i2i2−i2i200-22-202-2-2-2-222220-22000000-220000000-22000000000i2−i2i2−i200
χ682-220-22222-2-2-2-202-20000002-200000002-2000000000i2−i2i2−i200-22-202-2-2-2-222220-22000000-220000000-22000000000−i2i2−i2i200
χ692-220-22222-2-2-2-202-2000000-220000000-22000000000−i2i2i2−i200-22-202-2-2-2-222220-220000002-200000002-2000000000i2−i2−i2i200
χ702-220-22222-2-2-2-202-2000000-220000000-22000000000i2−i2−i2i200-22-202-2-2-2-222220-220000002-200000002-2000000000−i2i2i2−i200
χ7144444111-2-21114-2-2-2111-2-200222222000-1-1-1-1-1-1000000000-4-4-4-4-4-1-1-122-1-1-1-4222-1-1-12200-2-2-2-2-2-2000111111000000000
χ7244444111-2-21114-2-2-2111-2-200-2-2-2-2-2-2000111111000000000-4-4-4-4-4-1-1-122-1-1-1-4222-1-1-12200222222000-1-1-1-1-1-1000000000
χ7344444-2-2-211-2-2-24111-2-2-211000000000000000002200000-1-1-4-4-4-4-4222-1-1222-4-1-1-1222-1-100000000000000000-2-20000011
χ7444444-2-2-211-2-2-24111-2-2-21100000000000000000-2-20000011-4-4-4-4-4222-1-1222-4-1-1-1222-1-1000000000000000002200000-1-1
χ75444-44111-2-2111-4-2-22-1-1-122002-222-2-2000-1-1-1111000000000-4-4-44-4-1-1-122-1-1-1422-2111-2-200-22-2-222000111-1-1-1000000000
χ76444-44111-2-2111-4-2-22-1-1-12200-22-2-222000111-1-1-1000000000-4-4-44-4-1-1-122-1-1-1422-2111-2-2002-222-2-2000-1-1-1111000000000
χ77444-44-2-2-211-2-2-2-411-1222-1-1000000000000000002-200000-11-4-4-44-4222-1-12224-1-11-2-2-21100000000000000000-22000001-1
χ78444-44-2-2-211-2-2-2-411-1222-1-100000000000000000-22000001-1-4-4-44-4222-1-12224-1-11-2-2-211000000000000000002-200000-11
χ7944-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i32110022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i32000000000-4-42-42-11+3i321−3i3222-11+3i321−3i322-1-12-11+3i321−3i32-1-100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i32000000000
χ8044-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211-21−1−3i32−1+3i321100-2-21+i31−i31+i31−i30001−1−i32−1+i321−1−i32−1+i32000000000-4-42-42-11+3i321−3i3222-11+3i321−3i322-1-12-11+3i321−3i32-1-10022−1−i3−1+i3−1−i3−1+i3000-11+i321−i32-11+i321−i32000000000
χ8144-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i32110022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i32000000000-4-42-42-11−3i321+3i3222-11−3i321+3i322-1-12-11−3i321+3i32-1-100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i32000000000
χ8244-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211-21−1+3i32−1−3i321100-2-21−i31+i31−i31+i30001−1+i32−1−i321−1+i32−1−i32000000000-4-42-42-11−3i321+3i3222-11−3i321+3i322-1-12-11−3i321+3i32-1-10022−1+i3−1−i3−1+i3−1−i3000-11−i321+i32-11−i321+i32000000000
χ8344-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-1002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i32000000000-4-4242-11+3i321−3i3222-11+3i321−3i32-2-1-1-21−1−3i32−1+3i321100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i32000000000
χ8444-2-4-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322112-11+3i321−3i32-1-100-221+i31−i3−1−i3−1+i30001−1−i32−1+i32-11+i321−i32000000000-4-4242-11+3i321−3i3222-11+3i321−3i32-2-1-1-21−1−3i32−1+3i3211002-2−1−i3−1+i31+i31−i3000-11+i321−i321−1−i32−1+i32000000000
χ8544-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-1002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i32000000000-4-4242-11−3i321+3i3222-11−3i321+3i32-2-1-1-21−1+3i32−1−3i321100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i32000000000
χ8644-2-4-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322112-11−3i321+3i32-1-100-221−i31+i3−1+i3−1−i30001−1+i32−1−i32-11−i321+i32000000000-4-4242-11−3i321+3i3222-11−3i321+3i32-2-1-1-21−1+3i32−1−3i3211002-2−1+i3−1−i31−i31+i3000-11−i321+i321−1+i32−1−i32000000000
χ874-4-2024-2-24-4-4220-220000004-40000000-22000000000000000-4420-2-422-444-2-202-2000000-4400000002-2000000000000000
χ884-4-2024-2-24-4-4220-22000000-4400000002-2000000000000000-4420-2-422-444-2-202-20000004-40000000-22000000000000000
χ8988-48-4-42222-422-4-1-12-422-1-100000000000000000000000000-8-84-844-2-2-2-24-2-2411-24-2-21100000000000000000000000000
χ9088-4-8-4-42222-4224-1-1-24-2-21100000000000000000000000000-8-84844-2-2-2-24-2-2-4112-422-1-100000000000000000000000000
χ918-880-8222-44-2-2-20-4400000000000000000000000000000000-88-808-2-2-24-422204-400000000000000000000000000000000
χ928-880-8-4-4-42-244402-200000000000000000000000000000000-88-808444-22-4-4-40-2200000000000000000000000000000000
χ938-8-4042−1−3i3−1+3i3-44-21+3i31−3i302-200000000000000000000000000000000-8840-4-21+3i31−3i34-42−1−3i3−1+3i30-2200000000000000000000000000000000
χ948-8-4042−1+3i3−1−3i3-44-21−3i31+3i302-200000000000000000000000000000000-8840-4-21−3i31+3i34-42−1+3i3−1−3i30-2200000000000000000000000000000000
χ958-8-404-4222-24-2-20-11000033−3300000000000000000000000000-8840-44-2-2-22-42201-10000−333300000000000000000000000000
χ968-8-404-4222-24-2-20-110000−333300000000000000000000000000-8840-44-2-2-22-42201-1000033−3300000000000000000000000000

Here i is the imaginary unit (i² = −1).