Finite Group Databasebeta

← Group #13181106

Character table — Group #13181106

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222224444444444466666688888888888888991212121212121212121212121212121616161818181818181824242424242424242436363636363636365454727272108108108
order12344463333666612121222666636121212121212121212121212224446666661212121212121212124444466121212121212121212222121212121244666444
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
χ51111-1-11111111111-1-1111111111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-11-1-11-1-11111111-1-1-1-1-1-11-1-11-1-111111-1-11-1-1
χ61111-1-11111111111-1-1111111111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-11-1-11-1-1-1-111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-111
χ71111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-11111111-1-11-1-111-1-11-1-1-111
χ81111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111111-1-11-1-1-1-111-1-1-1111111-1111-1-1-1-111-1111-1-1
χ9111-11-1111111111-11-111111111-1-1-1-11111-1-1-1-111-11-1111111-1-111-1-1-11-1-11-11111-1-1-1111-1-1-1-11-1-11-11111-11-1-11-1
χ10111-11-1111111111-11-111111111-1-1-1-11111-1-1-1-111-11-1111111-1-111-1-1-11-1-11-1-1-111-1-1-1111-1-1-11-11-11-1-1-1-1-11-111-11
χ11111-11-1111111111-11-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111-11-1-1-1-1-1-111-1-111-11-1-11-11111111-1-1-1111-11-1-11-111-1-1-11-11-11
χ12111-11-1111111111-11-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111-11-1-1-1-1-1-111-1-111-11-1-11-1-1-111111-1-1-11111-11-11-1-1-1111-11-11-1
χ13111-1-11111111111-1-1111111111-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1111-1-11-1-111111-1-11-1-11
χ14111-1-11111111111-1-1111111111-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-111-1-11-1-11-1-111-1-1-1-1-1-111111-1-1-11-1-1-1-111-111-1
χ15111-1-11111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-11-1-111111111111-1-1-1-1-11-1-1111-1-1-1-1111-1
χ16111-1-11111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-111111111-1-1-111-1-1-11-1-11111-1-1-11
χ1722222222222222222200000022222222222222-2-2000000000000000222-2-2-200-2-2000000000000-2-2-20000000000
χ182222-2-22222222222-2-2000000222222-2-2-2-2-2-2-2-2-2-20000000000000002-2-2-22200-2-2000000000000-2220000000000
χ19222-22-2222222222-22-200000022-2-2-2-22222-2-2-2-2-2-2000000000000000-22-22-2200-2-20000000000002-220000000000
χ20222-2-22222222222-2-2200000022-2-2-2-2-2-2-2-22222-2-2000000000000000-2-2222-200-2-200000000000022-20000000000
χ2122-1222-12-1-122-1-12-1-1-100−i3−i3i3i3-1-122-1-122-1-122-1-1-2-200000−i3−i3i3i3−i3i3−i3i3−i3i3-1-1-1-2-2-200110−i3i30−i3i30−i3i30001110000000000
χ2222-1222-12-1-122-1-12-1-1-100i3i3−i3−i3-1-122-1-122-1-122-1-1-2-200000i3i3−i3−i3i3−i3i3−i3i3−i3-1-1-1-2-2-200110i3−i30i3−i30i3−i30001110000000000
χ2322-1222-12-1-122-1-12-1-1-122-1-1-1-1-1-122-1-122-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-122200-1-12-1-12-1-12-1-1000-1-1-10000000000
χ2422-1222-12-1-122-1-12-1-1-1-2-21111-1-122-1-122-1-122-1-122-2-2-2-2-21111111111-1-1-122200-1-1-211-211-211000-1-1-10000000000
χ2522-12-2-2-12-1-122-1-12-11100−i3−i3i3i3-1-122-1-1-2-211-2-211-2-200000−i3−i3i3i3−i3i3i3−i3i3−i3-111-22200110−i3i30i3−i30i3−i30001-1-10000000000
χ2622-12-2-2-12-1-122-1-12-11100i3i3−i3−i3-1-122-1-1-2-211-2-211-2-200000i3i3−i3−i3i3−i3−i3i3−i3i3-111-22200110i3−i30−i3i30−i3i30001-1-10000000000
χ2722-12-2-2-12-1-122-1-12-11122-1-1-1-1-1-122-1-1-2-211-2-211222-2-222-1-1-1-1-1-11111-1112-2-200-1-12-1-1-211-211000-1110000000000
χ2822-12-2-2-12-1-122-1-12-111-2-21111-1-122-1-1-2-211-2-21122-222-2-2111111-1-1-1-1-1112-2-200-1-1-2112-1-12-1-1000-1110000000000
χ2922-1-22-2-12-1-122-1-121-1100−i3−i3i3i3-1-1-2-21122-1-1-2-211-2-200000−i3−i3i3i3i3−i3−i3i3i3−i31-112-2200110i3−i30−i3i30i3−i3000-11-10000000000
χ3022-1-22-2-12-1-122-1-121-1100i3i3−i3−i3-1-1-2-21122-1-1-2-211-2-200000i3i3−i3−i3−i3i3i3−i3−i3i31-112-2200110−i3i30i3−i30−i3i3000-11-10000000000
χ3122-1-22-2-12-1-122-1-121-1122-1-1-1-1-1-1-2-21122-1-1-2-21122-22-222-1-1-1-111-1-1111-11-22-200-1-1-2112-1-1-2110001-110000000000
χ3222-1-22-2-12-1-122-1-121-11-2-21111-1-1-2-21122-1-1-2-211222-22-2-21111-1-111-1-11-11-22-200-1-12-1-1-2112-1-10001-110000000000
χ3322-1-2-22-12-1-122-1-1211-100−i3−i3i3i3-1-1-2-211-2-21122-1-1-2-200000−i3−i3i3i3i3−i3i3−i3−i3i311-122-200110i3−i30i3−i30−i3i3000-1-110000000000
χ3422-1-2-22-12-1-122-1-1211-100i3i3−i3−i3-1-1-2-211-2-21122-1-1-2-200000i3i3−i3−i3−i3i3−i3i3i3−i311-122-200110−i3i30−i3i30i3−i3000-1-110000000000
χ3522-1-2-22-12-1-122-1-1211-122-1-1-1-1-1-1-2-211-2-21122-1-122-2-2222-1-1-1-11111-1-111-1-2-2200-1-1-211-2112-1-100011-10000000000
χ3622-1-2-22-12-1-122-1-1211-1-2-21111-1-1-2-211-2-21122-1-12222-2-2-21111-1-1-1-11111-1-2-2200-1-12-1-12-1-1-21100011-10000000000
χ372-22000-22222-2-2-2-20002-22-22-22-2000000000000-220002-22-22-20000000000002i−2i2-20000000000000002i−2i2i−2i000000
χ382-22000-22222-2-2-2-20002-22-22-22-2000000000000-220002-22-22-2000000000000−2i2i2-2000000000000000−2i2i−2i2i000000
χ392-22000-22222-2-2-2-2000-22-22-222-2000000000000-22000-22-22-220000000000002i−2i2-20000000000000002i−2i−2i2i000000
χ402-22000-22222-2-2-2-2000-22-22-222-2000000000000-22000-22-22-22000000000000−2i2i2-2000000000000000−2i2i2i−2i000000
χ414444444111-2111-2444222222-2-21-2111-2111-21100222-1-1-1-1-1-1222222-2-2-20000000-1-1-1-1-1-1-1-1-10000000000000000
χ424444444111-2111-2444-2-2-2-2-2-2-2-21-2111-2111-21100-2-2-2111111-2-2-2-2-2-2-2-2-200000001111111110000000000000000
χ434444444-2-2-21-2-2-2144400000011-21-2-2-21-2-2-21-2-2000000000000000001110002200000000000222000-1-100-1-1-1000
χ444444444-2-2-21-2-2-2144400000011-21-2-2-21-2-2-21-2-200000000000000000111000-2-200000000000-2-2-20001100111000
χ454444-4-44111-2111-24-4-4222222-2-21-211-12-1-1-12-1-1002-2-2-1-1-1-1-1-122-2-2-2-2-2220000000-1-1-11111110000000000000000
χ464444-4-44111-2111-24-4-4-2-2-2-2-2-2-2-21-211-12-1-1-12-1-100-222111111-2-22222-2220000000111-1-1-1-1-1-10000000000000000
χ474444-4-44-2-2-21-2-2-214-4-400000011-21-2-22-1222-122000000000000000001-1-100022000000000002-2-2000-1-100-111000
χ484444-4-44-2-2-21-2-2-214-4-400000011-21-2-22-1222-122000000000000000001-1-1000-2-200000000000-22200011001-1-1000
χ49444-44-44111-2111-2-44-4222222-2-2-12-1-11-211-12-1-100-22-2-1-1-1-1-1-1-2-222-2-22-220000000111-1-1-11110000000000000000
χ50444-44-44111-2111-2-44-4-2-2-2-2-2-2-2-2-12-1-11-211-12-1-1002-2211111122-2-2222-220000000-1-1-1111-1-1-10000000000000000
χ51444-44-44-2-2-21-2-2-21-44-4000000112-122-21-2-22-12200000000000000000-11-10002200000000000-22-2000-1-1001-11000
χ52444-44-44-2-2-21-2-2-21-44-4000000112-122-21-2-22-12200000000000000000-11-1000-2-2000000000002-220001100-11-1000
χ53444-4-444111-2111-2-4-44222222-2-2-12-1-1-12-1-11-21100-2-22-1-1-1-1-1-1-2-2-2-22222-20000000111111-1-1-10000000000000000
χ54444-4-444111-2111-2-4-44-2-2-2-2-2-2-2-2-12-1-1-12-1-11-2110022-21111112222-2-222-20000000-1-1-1-1-1-11110000000000000000
χ55444-4-444-2-2-21-2-2-21-4-44000000112-1222-122-21-2-200000000000000000-1-110002200000000000-2-22000-1-10011-1000
χ56444-4-444-2-2-21-2-2-21-4-44000000112-1222-122-21-2-200000000000000000-1-11000-2-20000000000022-20001100-1-11000
χ5744-2444-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-222−1−i3−1−i3−1+i3−1+i3111-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i3200222-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31110000000-11+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−i3111-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i3200-2-2-211−1−i32−1−i32−1+i32−1+i321+i31−i31+i31−i31+i31−i311100000001−1−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−i3111-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i3200222-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31110000000-11−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+i3111-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i3200-2-2-211−1+i32−1+i32−1−i32−1−i321−i31+i31−i31+i31−i31+i311100000001−1+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+i3111-2−1−3i32−1+3i32-121+3i321−3i32-121+3i321−3i32002-2-2-1-11+i321+i321−i321−i32−1−i3−1+i31+i31−i31+i31−i31-1-10000000-11+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−i3111-2−1−3i32−1+3i32-121+3i321−3i32-121+3i321−3i3200-22211−1−i32−1−i32−1+i32−1+i321+i31−i3−1−i3−1+i3−1−i3−1+i31-1-100000001−1−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−i3111-2−1+3i32−1−3i32-121−3i321+3i32-121−3i321+3i32002-2-2-1-11−i321−i321+i321+i32−1+i3−1−i31−i31+i31−i31+i31-1-10000000-11−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+i3111-2−1+3i32−1−3i32-121−3i321+3i32-121−3i321+3i3200-22211−1+i32−1+i32−1−i32−1−i321−i31+i3−1+i3−1−i3−1+i3−1−i31-1-100000001−1+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+i311-121+3i321−3i321-2−1−3i32−1+3i32-121+3i321−3i3200-22-2-1-11+i321+i321−i321−i321+i31−i3−1−i3−1+i31+i31−i3-11-100000001−1−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−i311-121+3i321−3i321-2−1−3i32−1+3i32-121+3i321−3i32002-2211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i31−i3−1−i3−1+i3-11-10000000-11+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−i311-121−3i321+3i321-2−1+3i32−1−3i32-121−3i321+3i3200-22-2-1-11−i321−i321+i321+i321−i31+i3−1+i3−1−i31−i31+i3-11-100000001−1+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+i311-121−3i321+3i321-2−1+3i32−1−3i32-121−3i321+3i32002-2211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31−i31+i3−1+i3−1−i3-11-10000000-11−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+i311-121+3i321−3i32-121+3i321−3i321-2−1−3i32−1+3i3200-2-22-1-11+i321+i321−i321−i321+i31−i31+i31−i3−1−i3−1+i3-1-1100000001−1−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−i311-121+3i321−3i32-121+3i321−3i321-2−1−3i32−1+3i320022-211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i3−1+i31+i31−i3-1-110000000-11+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−i311-121−3i321+3i32-121−3i321+3i321-2−1+3i32−1−3i3200-2-22-1-11−i321−i321+i321+i321−i31+i31−i31+i3−1+i3−1−i3-1-1100000001−1+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+i311-121−3i321+3i32-121−3i321+3i321-2−1+3i32−1−3i320022-211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3−1+i3−1−i31−i31+i3-1-110000000-11−i321+i32-11−i321+i321−1+i32−1−i320000000000000000
χ734-44000-44444-4-4-4-40000000004-40000000000004-400000000000000000000000-440000000000000000000000000
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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+3i31−3i340004-4−2−2i32+2i3−2+2i32−2i32-200000000000000000-221+i3−1−i31−i3−1+i300000000000000000000000000000000000000000
χ878-8-400042−1−3i3−1+3i3-4-21+3i31−3i34000-442+2i3−2−2i32−2i3−2+2i32-2000000000000000002-2−1−i31+i3−1+i31−i300000000000000000000000000000000000000000
χ888-8-400042−1+3i3−1−3i3-4-21−3i31+3i340004-4−2+2i32−2i3−2−2i32+2i32-200000000000000000-221−i3−1+i31+i3−1−i300000000000000000000000000000000000000000
χ898-8-400042−1+3i3−1−3i3-4-21−3i31+3i34000-442−2i3−2+2i32+2i3−2−2i32-2000000000000000002-2−1+i31−i3−1−i31+i300000000000000000000000000000000000000000
χ9016-16-80008-84448-4-4-4000000000-220000000000000000000000000000000000000000000000000000000000000000

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