Finite Group Databasebeta

← Group #13167027

Character table — Group #13167027

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order122344612123333666661212121212121212123666666612121212121212122222446666121212122446612126666661212121212126888812242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ51111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-111-1-111111-1-1-1111-1-1-1-1ii−i−i1ii−i−iii−i−i
χ61111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-111-1-111111-1-1-1111-1-1-1-1−i−iii1−i−iii−i−iii
χ71111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-111-1-111-1-1-1111-1-1-1111-1ii−i−i1ii−i−i−i−iii
χ81111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-111-1-111-1-1-1111-1-1-1111-1−i−iii1−i−iiiii−i−i
χ911-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-11111i−ii−i1i−ii−ii−ii−i
χ1011-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-11111−ii−ii1−ii−ii−ii−ii
χ1111-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-11i−ii−i1i−ii−i−ii−ii
χ1211-111-11111111-11111-1111111-1-11-1-1-1-1-1-111-1-1-111-1-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-11−ii−ii1−ii−iii−ii−i
χ1311-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-1111111-1-11111-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ1411-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-1111111-1-11111-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1-1-111-11-111-1-111-1
χ1511-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-11111-1-111-1-1-1-11111-11-111-1-1-1-1-1-1-1-1111111-11-1-1111-1-11-111-1
χ1611-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-11111-1-111-1-1-1-11111-11-111-1-1-1-1-1-1-1-1111111-1-111-11-111-11-1-11
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-2000000000000-20000-200000000
χ182222-2-22-2-2222222222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2220000000000002-2-222-2-200000000000020000-200000000
χ19222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-1-10000-100000000
χ20222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-211-10000-100000000
χ21222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i310000100000000
χ22222-122-1-1-122-1-1-122-1-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i310000100000000
χ23222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-2111111220000−i3i3i3−i3−i3i3i3−i32-2-2-1-1110−i3i30i3−i30−i3i30i3−i3-10000100000000
χ24222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-2111111220000i3−i3−i3i3i3−i3−i3i32-2-2-1-1110i3−i30−i3i30i3−i30−i3i3-10000100000000
χ25222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-2111111-2-22-22-2-1-111-1-111-22211-1-12-1-1-2112-1-1-21110000-100000000
χ26222-1-2-2-11122-1-1-122-1-11-2-21111-2-2-122-1-1-1-1-1-2-2111111-2-2-22-2211-1-111-1-1-22211-1-1-2112-1-1-2112-1-110000-100000000
χ2722-222-22222222-22222-2222222-2-22-2-2-2-2-2-222-2-2-222-2-222000000000000-2-222222000000000000-20000-200000000
χ2822-22-222-2-22222-222222-2-2-2-2-2-2222-2-2-2-2-2-22-2222-2-222-2-20000000000002-22-2-22200000000000020000-200000000
χ2922-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111220000−i3i3i3−i3i3−i3−i3i3-2-22-1-1-1-10−i3i30i3−i30i3−i30−i3i310000100000000
χ3022-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111220000i3−i3−i3i3−i3i3i3−i3-2-22-1-1-1-10i3−i30−i3i30−i3i30i3−i310000100000000
χ3122-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111-2-22-2-22-1-11111-1-122-211112-1-1-211-2112-1-1-10000-100000000
χ3222-2-12-2-1-1-122-1-1122-1-1122-1-1-1-1-2-2-1-2-21111-12-211-1-111-2-2-222-211-1-1-1-11122-21111-2112-1-12-1-1-211-10000-100000000
χ3322-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-12222-2-2-1-1-1-11111-22-2-1-1112-1-12-1-1-211-21110000-100000000
χ3422-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-122-2-2221111-1-1-1-1-22-2-1-111-211-2112-1-12-1-110000-100000000
χ3522-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-1-2-20000−i3i3−i3i3i3−i3i3−i32-2211-1-10−i3i30−i3i30i3−i30i3−i3-10000100000000
χ3622-2-1-22-11122-1-1122-1-1-1-2-2111122-1-2-21111-1-22-1-111-1-1-2-20000i3−i3i3−i3−i3i3−i3i32-2211-1-10i3−i30i3−i30−i3i30−i3i3-10000100000000
χ374444444441-2-2-241-2-2-24-2-2-2-2-2-21111-2-2-21111-2-2-21111000000000000000000000000000000000022220-1-1-1-10000
χ384444444441-2-2-241-2-2-24-2-2-2-2-2-21111-2-2-21111-2-2-211110000000000000000000000000000000000-2-2-2-2011110000
χ39444444444-21114-21114111111-2-2-2-2111-2-2-2-2111-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ40444444444-21114-21114111111-2-2-2-2111-2-2-2-2111-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ414444-4-44-4-41-2-2-241-2-2-2-4222222-1-111-2-2-2111-1222-1-1-1-100000000000000000000000000000000002i2i−2i−2i0−i−iii0000
χ424444-4-44-4-41-2-2-241-2-2-2-4222222-1-111-2-2-2111-1222-1-1-1-10000000000000000000000000000000000−2i−2i2i2i0ii−i−i0000
χ434444-4-44-4-4-21114-2111-4-1-1-1-1-1-122-2-2111-2-2-22-1-1-12222002-22-222-2-222-2-20000000-1-1-1111-1-1-111100000000000000
χ444444-4-44-4-4-21114-2111-4-1-1-1-1-1-122-2-2111-2-2-22-1-1-1222200-22-22-2-222-2-2220000000111-1-1-1111-1-1-100000000000000
χ45444-244-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-21−1−3i32−1+3i32111-21−1−3i32−1+3i321111002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ46444-244-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-21−1−3i32−1+3i32111-21−1−3i32−1+3i32111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ47444-244-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-21−1+3i32−1−3i32111-21−1+3i32−1−3i321111002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ48444-244-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-21−1+3i32−1−3i32111-21−1+3i32−1−3i32111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ49444-2-4-4-222-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322-1-11+3i321+3i321−3i321−3i32221-21−1−3i32−1+3i321112-11+3i321−3i32-1-1-1-1002-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i30000000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i3200000000000000
χ50444-2-4-4-222-21−1−3i32−1+3i32-2-21−1−3i32−1+3i322-1-11+3i321+3i321−3i321−3i32221-21−1−3i32−1+3i321112-11+3i321−3i32-1-1-1-100-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i300000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i3200000000000000
χ51444-2-4-4-222-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322-1-11−3i321−3i321+3i321+3i32221-21−1+3i32−1−3i321112-11−3i321+3i32-1-1-1-1002-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i30000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i3200000000000000
χ52444-2-4-4-222-21−1+3i32−1−3i32-2-21−1+3i32−1−3i322-1-11−3i321−3i321+3i321+3i32221-21−1+3i32−1−3i321112-11−3i321+3i32-1-1-1-100-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i300000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i3200000000000000
χ5344-444-44441-2-2-2-41-2-2-2-4-2-2-2-2-2-2-1-11-1222-1-11122211-1-100000000000000000000000000000000002i−2i2i−2i0−ii−ii0000
χ5444-444-44441-2-2-2-41-2-2-2-4-2-2-2-2-2-2-1-11-1222-1-11122211-1-10000000000000000000000000000000000−2i2i−2i2i0i−ii−i0000
χ5544-444-4444-2111-4-2111-411111122-22-1-1-122-2-2-1-1-1-2-222002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ5644-444-4444-2111-4-2111-411111122-22-1-1-122-2-2-1-1-1-2-22200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ5744-44-444-4-41-2-2-2-41-2-2-24222222111-1222-1-11-1-2-2-2-1-11100000000000000000000000000000000002-2-220-111-10000
χ5844-44-444-4-41-2-2-2-41-2-2-24222222111-1222-1-11-1-2-2-2-1-1110000000000000000000000000000000000-222-201-1-110000
χ5944-44-444-4-4-2111-4-21114-1-1-1-1-1-1-2-2-22-1-1-122-2211122-2-20022-2-22222-2-2-2-20000000-1-1-1-1-1-111111100000000000000
χ6044-44-444-4-4-2111-4-21114-1-1-1-1-1-1-2-2-22-1-1-122-2211122-2-200-2-222-2-2-2-222220000000111111-1-1-1-1-1-100000000000000
χ6144-4-24-4-2-2-2-21−1−3i32−1+3i322-21−1−3i32−1+3i32211−1−3i32−1−3i32−1+3i32−1+3i322212-11+3i321−3i32-1-11-2-11+3i321−3i3211-1-1002-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i3200000000000000
χ6244-4-24-4-2-2-2-21−1−3i32−1+3i322-21−1−3i32−1+3i32211−1−3i32−1−3i32−1+3i32−1+3i322212-11+3i321−3i32-1-11-2-11+3i321−3i3211-1-100-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3200000000000000
χ6344-4-24-4-2-2-2-21−1+3i32−1−3i322-21−1+3i32−1−3i32211−1+3i32−1+3i32−1−3i32−1−3i322212-11−3i321+3i32-1-11-2-11−3i321+3i3211-1-1002-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i3200000000000000
χ6444-4-24-4-2-2-2-21−1+3i32−1−3i322-21−1+3i32−1−3i32211−1+3i32−1+3i32−1−3i32−1−3i322212-11−3i321+3i32-1-11-2-11−3i321+3i3211-1-100-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3200000000000000
χ6544-4-2-44-222-21−1−3i32−1+3i322-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-2-212-11+3i321−3i32-1-1121−1−3i32−1+3i32-1-1110022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ6644-4-2-44-222-21−1−3i32−1+3i322-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-2-212-11+3i321−3i32-1-1121−1−3i32−1+3i32-1-11100-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i300000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i3200000000000000
χ6744-4-2-44-222-21−1+3i32−1−3i322-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-2-212-11−3i321+3i32-1-1121−1+3i32−1−3i32-1-1110022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ6844-4-2-44-222-21−1+3i32−1−3i322-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-2-212-11−3i321+3i32-1-1121−1+3i32−1−3i32-1-11100-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i300000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i3200000000000000
χ694-40400-40044440-4-4-4-40000000004000000-4000000004-40000000000000004-40000000000000000000000000000
χ704-40400-40044440-4-4-4-40000000004000000-400000000-44000000000000000-440000000000000000000000000000
χ714-40-200223−2344-2-20-4-42200023−2323−2300-20000002000023−23004-4000000000000000-2223−2300000000000000000000000000
χ724-40-200223−2344-2-20-4-42200023−2323−2300-20000002000023−2300-440000000000000002-2−232300000000000000000000000000
χ734-40-2002−232344-2-20-4-422000−2323−232300-200000020000−2323004-4000000000000000-22−232300000000000000000000000000
χ744-40-2002−232344-2-20-4-422000−2323−232300-200000020000−232300-440000000000000002-223−2300000000000000000000000000
χ75888-488-4-4-42-422-42-422-4-4-4222222-12-422-1-1-12-422-1-1-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-4442-422-42-422444-2-2-2-2-2-2-12-422-1-1-1-24-2-2111100000000000000000000000000000000000000000000000
χ7788-8-48-8-4-4-42-42242-4224-4-42222-2-2-1-24-2-211-124-2-2-1-11100000000000000000000000000000000000000000000000
χ7888-8-4-88-4442-42242-422-444-2-2-2-222-1-24-2-211-1-2-42211-1-100000000000000000000000000000000000000000000000
χ798-80800-8002-4-4-40-244400000006i−6i2000000-20000006i−6i00000000000000000000000000000000000000000000000
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χ818-80800-800-422204-2-2-206i−6i6i−6i−6i6i00-400000040000000000000000000000000000000000000000000000000000000
χ828-80800-800-422204-2-2-20−6i6i−6i6i6i−6i00-400000040000000000000000000000000000000000000000000000000000000
χ838-80-400443−432-4220-24-2-2000−2323−23236i−6i-10000−3i33i3100003−3−3i3i00000000000000000000000000000000000000000000000
χ848-80-400443−432-4220-24-2-2000−2323−2323−6i6i-100003i3−3i3100003−33i−3i00000000000000000000000000000000000000000000000
χ858-80-400443−43-42−1−3i3−1+3i304-21+3i31−3i306i−6i2ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ11002000000-20000−23230000000000000000000000000000000000000000000000000
χ868-80-400443−43-42−1+3i3−1−3i304-21−3i31+3i30−6i6i−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ11002000000-20000−23230000000000000000000000000000000000000000000000000
χ878-80-4004−43432-4220-24-2-200023−2323−236i−6i-100003i3−3i310000−33−3i3i00000000000000000000000000000000000000000000000
χ888-80-4004−43432-4220-24-2-200023−2323−23−6i6i-10000−3i33i310000−333i−3i00000000000000000000000000000000000000000000000
χ898-80-4004−4343-42−1−3i3−1+3i304-21+3i31−3i30−6i6i−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ11002000000-2000023−230000000000000000000000000000000000000000000000000
χ908-80-4004−4343-42−1+3i3−1−3i304-21−3i31+3i306i−6i4ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ11002000000-2000023−230000000000000000000000000000000000000000000000000

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