Finite Group Databasebeta

← Group #13181107

Character table — Group #13181107

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222224444444444466666688888888888888991212121212121212121212121212121616161818181818181824242424242424242436363636363636365454727272108108108
order123444633336666121212441212121236121212121212121212121212222226666661212121212121212124444466666666666222121212121244666444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1
χ4111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1111
χ51111-1-11111111111-1-111111111111-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111111-1-11-1-11111111-1-1-1-1-1-11-1-11-1-111111-1-11-1-1
χ61111-1-11111111111-1-111111111111-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111111-1-11-1-1-1-111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-111
χ71111-1-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-111-111-1-11111-1-1-1-1-1-11-1-11-1-11111-1-1-11111111-1-11-1-111-1-11-1-1-111
χ81111-1-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-111-111-1-11111-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1111111-1111-1-1-1-111-1111-1-1
χ9111-11-1111111111-11-111111111-1-1-1111-1-1-1-11-111-11-1-1-111-1-1111111-11-1-11-11111-1-1-1111-1-1-1-11-1-11-11111-11-1-11-1
χ10111-11-1111111111-11-111111111-1-1-1111-1-1-1-11-111-11-1-1-111-1-1111111-11-1-11-1-1-111-1-1-1111-1-1-11-11-11-1-1-1-1-11-111-11
χ11111-11-1111111111-11-1-1-1-1-1-1-111-1-1-1111-1-1-1-11-1111-1111-1-111-1-1-1-1-1-1-11-1-11-11111111-1-1-1111-11-1-11-111-1-1-11-11-11
χ12111-11-1111111111-11-1-1-1-1-1-1-111-1-1-1111-1-1-1-11-1111-1111-1-111-1-1-1-1-1-1-11-1-11-1-1-111111-1-1-11111-11-11-1-1-1111-11-11-1
χ13111-1-11111111111-1-1111111111-1-1-1-1-1-1111-1-1111-1-11-1-1-1-111111111-1-11-1-111111-1-1-1-1-1-1111-1-11-1-111111-1-11-1-11
χ14111-1-11111111111-1-1111111111-1-1-1-1-1-1111-1-1111-1-11-1-1-1-111111111-1-11-1-11-1-111-1-1-1-1-1-111111-1-1-11-1-1-1-111-111-1
χ15111-1-11111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1111-1-111111-11111-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-11-1-1111-1-1-1-1111-1
χ16111-1-11111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1111-1-111111-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-111-1-1-11-1-11111-1-1-11
χ1722222222222222222200000022222222222222-2-2000000000000000222-2-2-200-2-2000000000000-2-2-20000000000
χ182222-2-22222222222-2-200000022222-2-2-2-2-2-22-2-2-2-20000000000000002-2-2-22200-2-2000000000000-2220000000000
χ19222-22-2222222222-22-200000022-2-2-2222-2-2-2-22-2-2-2000000000000000-22-22-2200-2-20000000000002-220000000000
χ20222-2-22222222222-2-2200000022-2-2-2-2-2-2222-2-22-2-2000000000000000-2-2222-200-2-200000000000022-20000000000
χ2122-1222-12-1-122-1-12-1-1-100−i3−i3i3i3-1-12-1-12-1-12-1-1222-2-2000−i3i3−i3i3−i3i300−i3−i3i3i3-1-1-1-2-2-200110−i3i30−i3i30−i3i30001110000000000
χ2222-1222-12-1-122-1-12-1-1-100i3i3−i3−i3-1-12-1-12-1-12-1-1222-2-2000i3−i3i3−i3i3−i300i3i3−i3−i3-1-1-1-2-2-200110i3−i30i3−i30i3−i30001110000000000
χ2322-1222-12-1-122-1-12-1-1-122-1-1-1-1-1-12-1-12-1-12-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-122200-1-12-1-12-1-12-1-1000-1-1-10000000000
χ2422-1222-12-1-122-1-12-1-1-1-2-21111-1-12-1-12-1-12-1-122222-2-2-2111111-2-21111-1-1-122200-1-1-211-211-211000-1-1-10000000000
χ2522-12-2-2-12-1-122-1-12-11100−i3−i3i3i3-1-12-1-1-211-2112-2-2-2-2000−i3i3i3−i3i3−i300−i3−i3i3i3-111-22200110−i3i30i3−i30i3−i30001-1-10000000000
χ2622-12-2-2-12-1-122-1-12-11100i3i3−i3−i3-1-12-1-1-211-2112-2-2-2-2000i3−i3−i3i3−i3i300i3i3−i3−i3-111-22200110i3−i30−i3i30−i3i30001-1-10000000000
χ2722-12-2-2-12-1-122-1-12-11122-1-1-1-1-1-12-1-1-211-2112-2-2222-2-2-1-1111122-1-1-1-1-1112-2-200-1-12-1-1-211-211000-1110000000000
χ2822-12-2-2-12-1-122-1-12-111-2-21111-1-12-1-1-211-2112-2-222-22211-1-1-1-1-2-21111-1112-2-200-1-1-2112-1-12-1-1000-1110000000000
χ2922-1-22-2-12-1-122-1-121-1100−i3−i3i3i3-1-1-2112-1-1-211-22-2-2-2000i3−i3−i3i3i3−i300−i3−i3i3i31-112-2200110i3−i30−i3i30i3−i3000-11-10000000000
χ3022-1-22-2-12-1-122-1-121-1100i3i3−i3−i3-1-1-2112-1-1-211-22-2-2-2000−i3i3i3−i3−i3i300i3i3−i3−i31-112-2200110−i3i30i3−i30−i3i3000-11-10000000000
χ3122-1-22-2-12-1-122-1-121-1122-1-1-1-1-1-1-2112-1-1-211-22-222-22-211-1-11122-1-1-1-11-11-22-200-1-1-2112-1-1-2110001-110000000000
χ3222-1-22-2-12-1-122-1-121-11-2-21111-1-1-2112-1-1-211-22-2222-22-1-111-1-1-2-211111-11-22-200-1-12-1-1-2112-1-10001-110000000000
χ3322-1-2-22-12-1-122-1-1211-100−i3−i3i3i3-1-1-211-2112-1-1-2-22-2-2000i3−i3i3−i3−i3i300−i3−i3i3i311-122-200110i3−i30i3−i30−i3i3000-1-110000000000
χ3422-1-2-22-12-1-122-1-1211-100i3i3−i3−i3-1-1-211-2112-1-1-2-22-2-2000−i3i3−i3i3i3−i300i3i3−i3−i311-122-200110−i3i30−i3i30i3−i3000-1-110000000000
χ3522-1-2-22-12-1-122-1-1211-122-1-1-1-1-1-1-211-2112-1-1-2-2222-2-221111-1-122-1-1-1-111-1-2-2200-1-1-211-2112-1-100011-10000000000
χ3622-1-2-22-12-1-122-1-1211-1-2-21111-1-1-211-2112-1-1-2-222222-2-1-1-1-111-2-2111111-1-2-2200-1-12-1-12-1-1-21100011-10000000000
χ372-22000-22222-2-2-2-20002i−2i2i−2i2i−2i2-20000000000002-20000000002i−2i2i−2i2i−2i0000002i−2i2-20000000000000002i−2i2-2000000
χ382-22000-22222-2-2-2-20002i−2i2i−2i2i−2i2-20000000000002-20000000002i−2i2i−2i2i−2i000000−2i2i2-2000000000000000−2i2i-22000000
χ392-22000-22222-2-2-2-2000−2i2i−2i2i−2i2i2-20000000000002-2000000000−2i2i−2i2i−2i2i0000002i−2i2-20000000000000002i−2i-22000000
χ402-22000-22222-2-2-2-2000−2i2i−2i2i−2i2i2-20000000000002-2000000000−2i2i−2i2i−2i2i000000−2i2i2-2000000000000000−2i2i2-2000000
χ414444444111-2111-2444222222-2-2111111111-2-2-200222222222-1-1-1-1-1-1-2-2-20000000-1-1-1-1-1-1-1-1-10000000000000000
χ424444444111-2111-2444-2-2-2-2-2-2-2-2111111111-2-2-200-2-2-2-2-2-2-2-2-2111111-2-2-200000001111111110000000000000000
χ434444444-2-2-21-2-2-2144400000011-2-2-2-2-2-2-2-2-2111000000000000000001110002200000000000222000-1-100-1-1-1000
χ444444444-2-2-21-2-2-2144400000011-2-2-2-2-2-2-2-2-211100000000000000000111000-2-200000000000-2-2-20001100111000
χ454444-4-44111-2111-24-4-4222222-2-2111-1-1-1-1-1-1-222002-2-222-2-2-2-2-1-1-1-1-1-1-2220000000-1-1-11111110000000000000000
χ464444-4-44111-2111-24-4-4-2-2-2-2-2-2-2-2111-1-1-1-1-1-1-22200-222-2-22222111111-2220000000111-1-1-1-1-1-10000000000000000
χ474444-4-44-2-2-21-2-2-214-4-400000011-2-2-22222221-1-1000000000000000001-1-100022000000000002-2-2000-1-100-111000
χ484444-4-44-2-2-21-2-2-214-4-400000011-2-2-22222221-1-1000000000000000001-1-1000-2-200000000000-22200011001-1-1000
χ49444-44-44111-2111-2-44-4222222-2-2-1-1-1111-1-1-12-2200-22-2-2-222-2-2-1-1-1-1-1-12-220000000111-1-1-11110000000000000000
χ50444-44-44111-2111-2-44-4-2-2-2-2-2-2-2-2-1-1-1111-1-1-12-22002-2222-2-2221111112-220000000-1-1-1111-1-1-10000000000000000
χ51444-44-44-2-2-21-2-2-21-44-400000011222-2-2-2222-11-100000000000000000-11-10002200000000000-22-2000-1-1001-11000
χ52444-44-44-2-2-21-2-2-21-44-400000011222-2-2-2222-11-100000000000000000-11-1000-2-2000000000002-220001100-11-1000
χ53444-4-444111-2111-2-4-44222222-2-2-1-1-1-1-1-111122-200-2-22-2-2-2-222-1-1-1-1-1-122-20000000111111-1-1-10000000000000000
χ54444-4-444111-2111-2-4-44-2-2-2-2-2-2-2-2-1-1-1-1-1-111122-20022-22222-2-211111122-20000000-1-1-1-1-1-11110000000000000000
χ55444-4-444-2-2-21-2-2-21-4-4400000011222222-2-2-2-1-1100000000000000000-1-110002200000000000-2-22000-1-10011-1000
χ56444-4-444-2-2-21-2-2-21-4-4400000011222222-2-2-2-1-1100000000000000000-1-11000-2-20000000000022-20001100-1-11000
χ5744-2444-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-222−1−i3−1−i3−1+i3−1+i3111−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-200222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i321110000000-11+i321−i32-11+i321−i32-11+i321−i320000000000000000
χ5844-2444-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2-2-21+i31+i31−i31−i3111−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-200-2-2-21+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211100000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i320000000000000000
χ5944-2444-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-222−1+i3−1+i3−1−i3−1−i3111−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-200222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i321110000000-11−i321+i32-11−i321+i32-11−i321+i320000000000000000
χ6044-2444-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2-2-21−i31−i31+i31+i3111−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-200-2-2-21−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211100000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i320000000000000000
χ6144-24-4-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-22222−1−i3−1−i3−1+i3−1+i3111−1−3i32−1+3i32-11+3i321−3i32-11+3i321−3i32-222002-2-2−1−i3−1+i31+i31−i31+i31−i3-1-11+i321+i321−i321−i321-1-10000000-11+i321−i321−1−i32−1+i321−1−i32−1+i320000000000000000
χ6244-24-4-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-222-2-21+i31+i31−i31−i3111−1−3i32−1+3i32-11+3i321−3i32-11+3i321−3i32-22200-2221+i31−i3−1−i3−1+i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i321-1-100000001−1−i32−1+i32-11+i321−i32-11+i321−i320000000000000000
χ6344-24-4-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-22222−1+i3−1+i3−1−i3−1−i3111−1+3i32−1−3i32-11−3i321+3i32-11−3i321+3i32-222002-2-2−1+i3−1−i31−i31+i31−i31+i3-1-11−i321−i321+i321+i321-1-10000000-11−i321+i321−1+i32−1−i321−1+i32−1−i320000000000000000
χ6444-24-4-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-222-2-21−i31−i31+i31+i3111−1+3i32−1−3i32-11−3i321+3i32-11−3i321+3i32-22200-2221−i31+i3−1+i3−1−i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i321-1-100000001−1+i32−1−i32-11−i321+i32-11−i321+i320000000000000000
χ6544-2-44-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-22-2222−1−i3−1−i3−1+i3−1+i311-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-2200-22-21+i31−i3−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i32-11-100000001−1−i32−1+i32-11+i321−i321−1−i32−1+i320000000000000000
χ6644-2-44-4-21−1−3i32−1+3i32-21−1−3i32−1+3i32-22-22-2-21+i31+i31−i31−i311-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-22002-22−1−i3−1+i31+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-11-10000000-11+i321−i321−1−i32−1+i32-11+i321−i320000000000000000
χ6744-2-44-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-22-2222−1+i3−1+i3−1−i3−1−i311-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-2200-22-21−i31+i3−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i32-11-100000001−1+i32−1−i32-11−i321+i321−1+i32−1−i320000000000000000
χ6844-2-44-4-21−1+3i32−1−3i32-21−1+3i32−1−3i32-22-22-2-21−i31−i31+i31+i311-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-22002-22−1+i3−1−i31−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-11-10000000-11−i321+i321−1+i32−1−i32-11−i321+i320000000000000000
χ6944-2-4-44-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222-222−1−i3−1−i3−1+i3−1+i311-11+3i321−3i32-11+3i321−3i321−1−3i32−1+3i3222-200-2-221+i31−i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-1100000001−1−i32−1+i321−1−i32−1+i32-11+i321−i320000000000000000
χ7044-2-4-44-21−1−3i32−1+3i32-21−1−3i32−1+3i32-222-2-2-21+i31+i31−i31−i311-11+3i321−3i32-11+3i321−3i321−1−3i32−1+3i3222-20022-2−1−i3−1+i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-110000000-11+i321−i32-11+i321−i321−1−i32−1+i320000000000000000
χ7144-2-4-44-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222-222−1+i3−1+i3−1−i3−1−i311-11−3i321+3i32-11−3i321+3i321−1+3i32−1−3i3222-200-2-221−i31+i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-1100000001−1+i32−1−i321−1+i32−1−i32-11−i321+i320000000000000000
χ7244-2-4-44-21−1+3i32−1−3i32-21−1+3i32−1−3i32-222-2-2-21−i31−i31+i31+i311-11−3i321+3i32-11−3i321+3i321−1+3i32−1−3i3222-20022-2−1+i3−1−i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-110000000-11−i321+i32-11−i321+i321−1+i32−1−i320000000000000000
χ734-44000-44444-4-4-4-40000000004-4000000000000-4400000000000000000000000-440000000000000000000000000
χ744-4-200024-2-24-422-40000023−23−2323-22000000000000-440000000000023−23−2323000000002-20000000000000000000000000
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χ8188-4-8-88-4-4222-422244-4000000-1-14-2-24-2-2-422-2-220000000000000000011-100000000000000000000000000000000
χ828-88000-8222-4-2-2-240004i−4i4i−4i4i−4i-4400000000000000000000000−2i2i−2i2i−2i2i00000000000000000000000000000000000
χ838-88000-8222-4-2-2-24000−4i4i−4i4i−4i4i-44000000000000000000000002i−2i2i−2i2i−2i00000000000000000000000000000000000
χ848-88000-8-4-4-42444-20000000002-2000000000000000000000000000000000004i−4i00000000000000000−2i2i00000000
χ858-88000-8-4-4-42444-20000000002-200000000000000000000000000000000000−4i4i000000000000000002i−2i00000000
χ868-8-400042−1−3i3−1+3i3-4-21+3i31−3i340004i−4i4ζ11−4ζ114ζ7−4ζ72-200000000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ700000000000000000000000000000000000
χ878-8-400042−1−3i3−1+3i3-4-21+3i31−3i34000−4i4i−4ζ114ζ11−4ζ74ζ72-2000000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ700000000000000000000000000000000000
χ888-8-400042−1+3i3−1−3i3-4-21−3i31+3i340004i−4i4ζ7−4ζ74ζ11−4ζ112-200000000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000000000
χ898-8-400042−1+3i3−1−3i3-4-21−3i31+3i34000−4i4i−4ζ74ζ7−4ζ114ζ112-2000000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000000000
χ9016-16-80008-84448-4-4-4000000000-220000000000000000000000000000000000000000000000000000000000000000

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