Finite Group Databasebeta

← Group #13181091

Character table — Group #13181091

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222224444444444444444448888888888888888991212121212121212121212121818181818181824242424242424242424242436363636363672727272108108108108
order1223446121233336666612121212121212121236666666121212121212121222224466661212121224466121266666612121212121222446126612124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-111-1-111-1-11-1-111-1-1111-1-1-1111-1-1-11-11-11-11-11-111-1-1
χ61111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-111-1-111-1-11-1-111-1-1111-1-1-1111-1-1-1-11-111-1-11-11-1-111
χ71111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-11-1-111-1-1111-1-111-1-1-1-1-1111-1-1-11111-11-11-11-11-1-1-111
χ81111-1-11-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-11-1-111-1-1111-1-111-1-1-1-1-1111-1-1-1111-11-111-1-11-1111-1-1
χ911-111-11111111-11111-1111111-1-11-1-1-1-1-1-11-1-1-1111-1-1111-1-1111-1-1-1-111-11-11111111-1-1-1-1-1-111111-1-1-1-111-1-11-11-1
χ1011-111-11111111-11111-1111111-1-11-1-1-1-1-1-11-1-1-1111-1-1111-1-1111-1-1-1-111-11-11111111-1-1-1-1-1-1111-1-111-1-1-1-111-11-11
χ1111-111-11111111-11111-1111111-1-11-1-1-1-1-1-11-1-1-1111-1-111-111-1-1-11111-1-1-11-11111-1-1-1111111-1-1-111-1-1-1-111-1-1-11-11
χ1211-111-11111111-11111-1111111-1-11-1-1-1-1-1-11-1-1-1111-1-111-111-1-1-11111-1-1-11-11111-1-1-1111111-1-1-1-1-111-1-1-1-1111-11-1
χ1311-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1111111-1-11111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-11-1-11-111-1-111-1-11
χ1411-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1111111-1-11111-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-111-1-11-111-1-111-1
χ1511-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-11111-1-1111-1-1-1-1-1-1-1-11111111-1-11-111-1-11-111-1
χ1611-11-111-1-11111-111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-11111-1-1111-1-1-1-1-1-1-1-1111111-111-1-11-111-11-1-11
χ172222222222222222222222222222222222222222222-2-2000000000000-2-2-2-2-2-2-20000000000000000-2-200000000
χ182222-2-22-2-2222222222-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000000000-222-2-2220000000000000000-2200000000
χ19222-122-1-1-12-1-12-12-1-12-122-1-1-1-122-12-1-12-1-1-12-1-12-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-12-1-12-1-10000-1-100000000
χ20222-122-1-1-12-1-12-12-1-12-122-1-1-1-122-12-1-12-1-1-12-1-12-1-1-1-122-2-2-2-211111111222-1-1-1-1-211-211-211-2110000-1-100000000
χ21222-122-1-1-12-1-12-12-1-12-122-1-1-1-122-12-1-12-1-1-12-1-12-1-1-1-1-2-20000−i3i3−i3i3−i3i3−i3i3-2-2-211110−i3i30−i3i30−i3i30−i3i300001100000000
χ22222-122-1-1-12-1-12-12-1-12-122-1-1-1-122-12-1-12-1-1-12-1-12-1-1-1-1-2-20000i3−i3i3−i3i3−i3i3−i3-2-2-211110i3−i30i3−i30i3−i30i3−i300001100000000
χ23222-1-2-2-1112-1-12-12-1-121-2-21111-2-2-12-1-12-1-1-1-211-21111222-22-2-1-111-1-1112-2-2-1-1112-1-1-2112-1-1-2110000-1100000000
χ24222-1-2-2-1112-1-12-12-1-121-2-21111-2-2-12-1-12-1-1-1-211-2111122-22-2211-1-111-1-12-2-2-1-111-2112-1-1-2112-1-10000-1100000000
χ25222-1-2-2-1112-1-12-12-1-121-2-21111-2-2-12-1-12-1-1-1-211-21111-2-20000−i3i3i3−i3−i3i3i3−i3-22211-1-10−i3i30i3−i30−i3i30i3−i300001-100000000
χ26222-1-2-2-1112-1-12-12-1-121-2-21111-2-2-12-1-12-1-1-1-211-21111-2-20000i3−i3−i3i3i3−i3−i3i3-22211-1-10i3−i30−i3i30i3−i30−i3i300001-100000000
χ2722-222-22222222-22222-2222222-2-22-2-2-2-2-2-22-2-2-2222-2-2-2-20000000000002-22-2-2-2-200000000000000002200000000
χ2822-22-222-2-22222-222222-2-2-2-2-2-2222-2-2-2-2-2-22222-2-2-222-2-200000000000022-2-2-22200000000000000002-200000000
χ2922-2-12-2-1-1-12-1-1212-1-12122-1-1-1-1-2-2-1-211-211-1-2112-1-111222-2-22-1-11111-1-1-22-2-1-1-1-12-1-1-211-2112-1-100001100000000
χ3022-2-12-2-1-1-12-1-1212-1-12122-1-1-1-1-2-2-1-211-211-1-2112-1-11122-222-211-1-1-1-111-22-2-1-1-1-1-2112-1-12-1-1-21100001100000000
χ3122-2-12-2-1-1-12-1-1212-1-12122-1-1-1-1-2-2-1-211-211-1-2112-1-111-2-20000−i3i3i3−i3i3−i3−i3i32-2211110−i3i30i3−i30i3−i30−i3i30000-1-100000000
χ3222-2-12-2-1-1-12-1-1212-1-12122-1-1-1-1-2-2-1-211-211-1-2112-1-111-2-20000i3−i3−i3i3−i3i3i3−i32-2211110i3−i30−i3i30−i3i30i3−i30000-1-100000000
χ3322-2-1-22-1112-1-1212-1-12-1-2-2111122-1-211-211-12-1-1-211-1-12222-2-2-1-1-1-11111-2-22-1-1112-1-12-1-1-211-21100001-100000000
χ3422-2-1-22-1112-1-1212-1-12-1-2-2111122-1-211-211-12-1-1-211-1-122-2-2221111-1-1-1-1-2-22-1-111-211-2112-1-12-1-100001-100000000
χ3522-2-1-22-1112-1-1212-1-12-1-2-2111122-1-211-211-12-1-1-211-1-1-2-20000−i3i3−i3i3i3−i3i3−i322-211-1-10−i3i30−i3i30i3−i30i3−i30000-1100000000
χ3622-2-1-22-1112-1-1212-1-12-1-2-2111122-1-211-211-12-1-1-211-1-1-2-20000i3−i3i3−i3−i3i3−i3i322-211-1-10i3−i30i3−i30−i3i30−i3i30000-1100000000
χ37444444444111-24111-24111111-2-2-2111-2-2-2-2111-2-2-2-2-2002222222222220000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ38444444444111-24111-24111111-2-2-2111-2-2-2-2111-2-2-2-2-200-2-2-2-2-2-2-2-2-2-2-2-2000000011111111111100000000000000
χ39444444444-2-2-214-2-2-214-2-2-2-2-2-2111-2-2-21111-2-2-211111000000000000000000000000000000000222200-1-1-1-10000
χ40444444444-2-2-214-2-2-214-2-2-2-2-2-2111-2-2-21111-2-2-211111000000000000000000000000000000000-2-2-2-20011110000
χ414444-4-44-4-4111-24111-2-4-1-1-1-1-1-122-2111-2-2-2-2-1-1-122222002-22-222-2-222-2-20000000-1-1-1111-1-1-111100000000000000
χ424444-4-44-4-4111-24111-2-4-1-1-1-1-1-122-2111-2-2-2-2-1-1-12222200-22-22-2-222-2-2220000000111-1-1-1111-1-1-100000000000000
χ434444-4-44-4-4-2-2-214-2-2-21-4222222-1-11-2-2-21111222-1-1-1-1-10000000000000000000000000000000002-22-200-11-110000
χ444444-4-44-4-4-2-2-214-2-2-21-4222222-1-11-2-2-21111222-1-1-1-1-1000000000000000000000000000000000-22-22001-11-10000
χ45444-244-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i32-2-211−1−3i32−1+3i32-21111−1−3i32−1+3i32-21111002222−1−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
χ46444-244-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-211−1−3i32−1−3i32−1+3i32−1+3i32-2-211−1−3i32−1+3i32-21111−1−3i32−1+3i32-2111100-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i300000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ47444-244-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i32-2-211−1+3i32−1−3i32-21111−1+3i32−1−3i32-21111002222−1+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
χ48444-244-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-211−1+3i32−1+3i32−1−3i32−1−3i32-2-211−1+3i32−1−3i32-21111−1+3i32−1−3i32-2111100-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i300000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ49444-2-4-4-2221−1−3i32−1+3i32-2-21−1−3i32−1+3i32-22-1-11+3i321+3i321−3i321−3i322211−1−3i32−1+3i32-2111-11+3i321−3i322-1-1-1-1002-22-2−1−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
χ50444-2-4-4-2221−1−3i32−1+3i32-2-21−1−3i32−1+3i32-22-1-11+3i321+3i321−3i321−3i322211−1−3i32−1+3i32-2111-11+3i321−3i322-1-1-1-100-22-221+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
χ51444-2-4-4-2221−1+3i32−1−3i32-2-21−1+3i32−1−3i32-22-1-11−3i321−3i321+3i321+3i322211−1+3i32−1−3i32-2111-11−3i321+3i322-1-1-1-1002-22-2−1+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
χ52444-2-4-4-2221−1+3i32−1−3i32-2-21−1+3i32−1−3i32-22-1-11−3i321−3i321+3i321+3i322211−1+3i32−1−3i32-2111-11−3i321+3i322-1-1-1-100-22-221−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
χ5344-444-4444111-2-4111-2-411111122-2-1-1-1222-2-1-1-1-2-2-222002-2-2222-2-2-2-2220000000-1-1-1111111-1-1-100000000000000
χ5444-444-4444111-2-4111-2-411111122-2-1-1-1222-2-1-1-1-2-2-22200-222-2-2-22222-2-20000000111-1-1-1-1-1-111100000000000000
χ5544-444-4444-2-2-21-4-2-2-21-4-2-2-2-2-2-2-1-11222-1-1-11222111-1-100000000000000000000000000000000022-2-200-1-1110000
χ5644-444-4444-2-2-21-4-2-2-21-4-2-2-2-2-2-2-1-11222-1-1-11222111-1-1000000000000000000000000000000000-2-2220011-1-10000
χ5744-44-444-4-4111-2-4111-24-1-1-1-1-1-1-2-2-2-1-1-1222-2111222-2-20022-2-22222-2-2-2-20000000-1-1-1-1-1-111111100000000000000
χ5844-44-444-4-4111-2-4111-24-1-1-1-1-1-1-2-2-2-1-1-1222-2111222-2-200-2-222-2-2-2-222220000000111111-1-1-1-1-1-100000000000000
χ5944-44-444-4-4-2-2-21-4-2-2-214222222111222-1-1-11-2-2-2-1-1-1110000000000000000000000000000000002-2-2200-111-10000
χ6044-44-444-4-4-2-2-21-4-2-2-214222222111222-1-1-11-2-2-2-1-1-111000000000000000000000000000000000-222-2001-1-110000
χ6144-4-24-4-2-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-2211−1−3i32−1−3i32−1+3i32−1+3i32221-11+3i321−3i322-1-11-11+3i321−3i32-211-1-1002-2-22−1−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
χ6244-4-24-4-2-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-2211−1−3i32−1−3i32−1+3i32−1+3i32221-11+3i321−3i322-1-11-11+3i321−3i32-211-1-100-222-21+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
χ6344-4-24-4-2-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-2211−1+3i32−1+3i32−1−3i32−1−3i32221-11−3i321+3i322-1-11-11−3i321+3i32-211-1-1002-2-22−1+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
χ6444-4-24-4-2-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-2211−1+3i32−1+3i32−1−3i32−1−3i32221-11−3i321+3i322-1-11-11−3i321+3i32-211-1-100-222-21−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
χ6544-4-2-44-2221−1−3i32−1+3i32-221−1−3i32−1+3i32-2-2-1-11+3i321+3i321−3i321−3i32-2-21-11+3i321−3i322-1-111−1−3i32−1+3i322-1-1110022-2-2−1−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
χ6644-4-2-44-2221−1−3i32−1+3i32-221−1−3i32−1+3i32-2-2-1-11+3i321+3i321−3i321−3i32-2-21-11+3i321−3i322-1-111−1−3i32−1+3i322-1-11100-2-2221+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
χ6744-4-2-44-2221−1+3i32−1−3i32-221−1+3i32−1−3i32-2-2-1-11−3i321−3i321+3i321+3i32-2-21-11−3i321+3i322-1-111−1+3i32−1−3i322-1-1110022-2-2−1+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
χ6844-4-2-44-2221−1+3i32−1−3i32-221−1+3i32−1−3i32-2-2-1-11−3i321−3i321+3i321+3i32-2-21-11−3i321+3i322-1-111−1+3i32−1−3i322-1-11100-2-2221−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
χ714-40-200223−234-2-240-422-400023−2323−2300-20000002000023−23004-4000000000000000-2223−2300000000000000000000000000
χ724-40-200223−234-2-240-422-400023−2323−2300-20000002000023−2300-440000000000000002-2−232300000000000000000000000000
χ734-40-2002−23234-2-240-422-4000−2323−232300-200000020000−2323004-4000000000000000-22−232300000000000000000000000000
χ744-40-2002−23234-2-240-422-4000−2323−232300-200000020000−232300-440000000000000002-223−2300000000000000000000000000
χ75888-488-4-4-4-4222-4-4222-4-4-4222222-1-4222-1-1-1-4222-1-1-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-444-4222-4-4222444-2-2-2-2-2-2-1-4222-1-1-14-2-2-2111100000000000000000000000000000000000000000000000
χ7788-8-48-8-4-4-4-42224-42224-4-42222-2-2-14-2-2-211-14-2-22-1-11100000000000000000000000000000000000000000000000
χ7888-8-4-88-444-42224-4222-444-2-2-2-222-14-2-2-211-1-422-211-1-100000000000000000000000000000000000000000000000
χ798-80800-800222-40-2-2-2406i−6i6i−6i−6i6i00-400000040000000000000000000000000000000000000000000000000000000
χ808-80800-800222-40-2-2-240−6i6i−6i6i6i−6i00-400000040000000000000000000000000000000000000000000000000000000
χ818-80800-800-4-4-420444-200000006i−6i2000000-20000006i−6i00000000000000000000000000000000000000000000000
χ828-80800-800-4-4-420444-20000000−6i6i2000000-2000000−6i6i00000000000000000000000000000000000000000000000
χ838-80-400443−432−1−3i3−1+3i3-40-21+3i31−3i3406i−6i2ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ11002000000-20000−23230000000000000000000000000000000000000000000000000
χ848-80-400443−432−1+3i3−1−3i3-40-21−3i31+3i340−6i6i−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ11002000000-20000−23230000000000000000000000000000000000000000000000000
χ858-80-400443−43-422204-2-2-2000−2323−23236i−6i-10000−3i33i3100003−3−3i3i00000000000000000000000000000000000000000000000
χ868-80-400443−43-422204-2-2-2000−2323−2323−6i6i-100003i3−3i3100003−33i−3i00000000000000000000000000000000000000000000000
χ878-80-4004−43432−1−3i3−1+3i3-40-21+3i31−3i340−6i6i−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ11002000000-2000023−230000000000000000000000000000000000000000000000000
χ888-80-4004−43432−1+3i3−1−3i3-40-21−3i31+3i3406i−6i4ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ11002000000-2000023−230000000000000000000000000000000000000000000000000
χ898-80-4004−4343-422204-2-2-200023−2323−236i−6i-100003i3−3i310000−33−3i3i00000000000000000000000000000000000000000000000
χ908-80-4004−4343-422204-2-2-200023−2323−23−6i6i-10000−3i33i310000−333i−3i00000000000000000000000000000000000000000000000

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