Finite Group Databasebeta

← Group #13181097

Character table — Group #13181097

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222224444444444466666688888888888888991212121212121212121212121212121616161818181818181824242424242424242436363636363636365454727272108108108
order1222346333366666612441212121236666666661212121222244661212121212121212121266122222466666121212121212224666612446612444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-111-1-11-1-1-1-1-1-1-1-1
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
χ4111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1111
χ5111-11-1111111-11111-11111111111-1-1-11-11-1-1-1-111-11-1-1-111-1-11111111-1-11-111-111-1-1-1111-1-1-11-1-11-111-1111-1-1-11-1
χ6111-11-1111111-11111-11111111111-1-1-11-11-1-1-1-111-11-1-1-111-1-11111111-1-11-1-1-1-111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1111-11
χ7111-11-1111111-11111-1-1-1-1-1-1-11111-1-1-11-11-1-1-1-1111-1111-1-111-1-1-1-1-1-11-1-11-111-111111-1-1-11111-1-11-111-1-1-11-1-11-11
χ8111-11-1111111-11111-1-1-1-1-1-1-11111-1-1-11-11-1-1-1-1111-1111-1-111-1-1-1-1-1-11-1-11-1-1-1-111111-1-1-1111-1111-1-1-1-111-111-11-1
χ911-111-111111-111111-11111111-1-1-1111-111-1-1-1-111-1-11-1-1-1-111111111-11-1-1111-111-1-1-1-1-1-1111-11-1-1111-111-11-1-1-11
χ1011-111-111111-111111-11111111-1-1-1111-111-1-1-1-111-1-11-1-1-1-111111111-11-1-11-1-1-111-1-1-1-1-1-11111-11-11-1-1-1-1-11-1111-1
χ1111-111-111111-111111-1-1-1-1-1-1-11-1-1-1111-111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-11-1-1111-111111111-1-1-1-11-1-1111-1-1-1-11-111-1
χ1211-111-111111-111111-1-1-1-1-1-1-11-1-1-1111-111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-11-1-11-1-1-111111111-1-1-11-11-11-1-1-1111-11-1-11
χ1311-1-11111111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-11-1-111111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-1
χ1411-1-11111111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111
χ1511-1-11111111-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-11-1-111111-1-1-1111111-1-11-1-1111-1-1-1-11-111
χ1611-1-11111111-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-111111111-1-1-1-1-111111-11-1-1
χ1722222222222222222200000022222222222222-2-2000000000000000222-2-200-2-2-2000000000000-2-200-200000000
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χ192222-12-12-1-12-1-12-1-12-100i3i3−i3−i3-12-1-12-1-122-122-1-1-2-2000i3−i3i3−i3i3−i300i3i3−i3−i3-1-1-1-2-200-2110i3−i30i3−i30i3−i30001100100000000
χ202222-12-12-1-12-1-12-1-12-122-1-1-1-1-12-1-12-1-122-122-1-122222-1-1-1-1-1-122-1-1-1-1-1-1-122002-1-12-1-12-1-12-1-1000-1-100-100000000
χ212222-12-12-1-12-1-12-1-12-1-2-21111-12-1-12-1-122-122-1-122-2-2-2111111-2-21111-1-1-122002-1-1-211-211-211000-1-100-100000000
χ22222-22-2222222-22222-20000002222-2-2-22-22-2-2-2-2-2-20000000000000002-2-2-22002-2-2000000000000-2200200000000
χ23222-2-1-2-12-1-12-112-1-12100−i3−i3i3i3-12-1-1-2112-2-1-2-211-2-2000i3−i3−i3i3i3−i300−i3−i3i3i3-111-22002110i3−i30−i3i30i3−i30001-100-100000000
χ24222-2-1-2-12-1-12-112-1-12100i3i3−i3−i3-12-1-1-2112-2-1-2-211-2-2000−i3i3i3−i3−i3i300i3i3−i3−i3-111-22002110−i3i30i3−i30−i3i30001-100-100000000
χ25222-2-1-2-12-1-12-112-1-12122-1-1-1-1-12-1-1-2112-2-1-2-21122-22-211-1-11122-1-1-1-1-1112-200-2-1-1-2112-1-1-211000-1100100000000
χ26222-2-1-2-12-1-12-112-1-121-2-21111-12-1-1-2112-2-1-2-211222-22-1-111-1-1-2-21111-1112-200-2-1-12-1-1-2112-1-1000-1100100000000
χ2722-222-222222-222222-20000002-2-2-2222-222-2-2-2-2-2-2000000000000000-22-22-2002-2-20000000000002-200200000000
χ2822-22-1-2-12-1-121-12-1-12100−i3−i3i3i3-1-2112-1-1-22-1-2-211-2-2000i3−i3i3−i3−i3i300−i3−i3i3i31-112-2002110i3−i30i3−i30−i3i3000-1100-100000000
χ2922-22-1-2-12-1-121-12-1-12100i3i3−i3−i3-1-2112-1-1-22-1-2-211-2-2000−i3i3−i3i3i3−i300i3i3−i3−i31-112-2002110−i3i30−i3i30i3−i3000-1100-100000000
χ3022-22-1-2-12-1-121-12-1-12122-1-1-1-1-1-2112-1-1-22-1-2-21122-2-221111-1-122-1-1-1-11-11-2200-2-1-1-211-2112-1-10001-100100000000
χ3122-22-1-2-12-1-121-12-1-121-2-21111-1-2112-1-1-22-1-2-2112222-2-1-1-1-111-2-211111-11-2200-2-1-12-1-12-1-1-2110001-100100000000
χ3222-2-22222222-2-2222220000002-2-2-2-2-2-2-2-222222-2-2000000000000000-2-222200-2-2-20000000000002200-200000000
χ3322-2-2-12-12-1-12112-1-12-100−i3−i3i3i3-1-211-211-2-2-122-1-1-2-2000−i3i3i3−i3i3−i300−i3−i3i3i311-12200-2110−i3i30i3−i30i3−i3000-1-100100000000
χ3422-2-2-12-12-1-12112-1-12-100i3i3−i3−i3-1-211-211-2-2-122-1-1-2-2000i3−i3−i3i3−i3i300i3i3−i3−i311-12200-2110i3−i30−i3i30−i3i3000-1-100100000000
χ3522-2-2-12-12-1-12112-1-12-122-1-1-1-1-1-211-211-2-2-122-1-1222-2-2-1-1111122-1-1-1-111-1-2-2002-1-12-1-1-211-2110001100-100000000
χ3622-2-2-12-12-1-12112-1-12-1-2-21111-1-211-211-2-2-122-1-122-22211-1-1-1-1-2-2111111-1-2-2002-1-1-2112-1-12-1-10001100-100000000
χ372-20020-2222200-2-2-2-202i−2i2i−2i2i−2i200000000-200002-20000000002i−2i2i−2i2i−2i000002-202-2000000000000002-202i−2i000000
χ382-20020-2222200-2-2-2-202i−2i2i−2i2i−2i200000000-200002-20000000002i−2i2i−2i2i−2i00000-2202-200000000000000-220−2i2i000000
χ392-20020-2222200-2-2-2-20−2i2i−2i2i−2i2i200000000-200002-2000000000−2i2i−2i2i−2i2i000002-202-2000000000000002-20−2i2i000000
χ402-20020-2222200-2-2-2-20−2i2i−2i2i−2i2i200000000-200002-2000000000−2i2i−2i2i−2i2i00000-2202-200000000000000-2202i−2i000000
χ414444444111-244111-24222222-2111111-2-2-21-21100222222222-1-1-1-1-1-1-2-2-20000000-1-1-1-1-1-1-1-1-10000000000000000
χ424444444111-244111-24-2-2-2-2-2-2-2111111-2-2-21-21100-2-2-2-2-2-2-2-2-2111111-2-2-200000001111111110000000000000000
χ434444444-2-2-2144-2-2-2140000001-2-2-2-2-2-2111-21-2-200000000000000000111002200000000000022200-1-1000-1-1-1000
χ444444444-2-2-2144-2-2-2140000001-2-2-2-2-2-2111-21-2-20000000000000000011100-2-2000000000000-2-2-20011000111000
χ454444-24-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-222−1−i3−1−i3−1+i3−1+i311−1−3i32−1+3i321−1−3i32−1+3i32-2-211-2−1−3i32−1+3i3200222−1−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
χ464444-24-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-2-2-21+i31+i31−i31−i311−1−3i32−1+3i321−1−3i32−1+3i32-2-211-2−1−3i32−1+3i3200-2-2-21+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
χ474444-24-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-222−1+i3−1+i3−1−i3−1−i311−1+3i32−1−3i321−1+3i32−1−3i32-2-211-2−1+3i32−1−3i3200222−1+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
χ484444-24-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-2-2-21−i31−i31+i31+i311−1+3i32−1−3i321−1+3i32−1−3i32-2-211-2−1+3i32−1−3i3200-2-2-21−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
χ49444-44-44111-24-4111-2-4222222-2111-1-1-1-22-2-12-1-100-22-2-2-222-2-2-1-1-1-1-1-1-2220000000111-1-1-11110000000000000000
χ50444-44-44111-24-4111-2-4-2-2-2-2-2-2-2111-1-1-1-22-2-12-1-1002-2222-2-222111111-2220000000-1-1-1111-1-1-10000000000000000
χ51444-44-44-2-2-214-4-2-2-21-40000001-2-2-22221-112-122000000000000000001-1-100220000000000002-2-200-1-1000-111000
χ52444-44-44-2-2-214-4-2-2-21-40000001-2-2-22221-112-122000000000000000001-1-100-2-2000000000000-22200110001-1-1000
χ53444-4-2-4-21−1−3i32−1+3i32-2-221−1−3i32−1+3i32-2222−1−i3−1−i3−1+i3−1+i311−1−3i32−1+3i32-11+3i321−3i32-221-121+3i321−3i3200-22-21+i31−i3−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i321-1-100000001−1−i32−1+i32-11+i321−i321−1−i32−1+i320000000000000000
χ54444-4-2-4-21−1−3i32−1+3i32-2-221−1−3i32−1+3i32-22-2-21+i31+i31−i31−i311−1−3i32−1+3i32-11+3i321−3i32-221-121+3i321−3i32002-22−1−i3−1+i31+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i321-1-10000000-11+i321−i321−1−i32−1+i32-11+i321−i320000000000000000
χ55444-4-2-4-21−1+3i32−1−3i32-2-221−1+3i32−1−3i32-2222−1+i3−1+i3−1−i3−1−i311−1+3i32−1−3i32-11−3i321+3i32-221-121−3i321+3i3200-22-21−i31+i3−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i321-1-100000001−1+i32−1−i32-11−i321+i321−1+i32−1−i320000000000000000
χ56444-4-2-4-21−1+3i32−1−3i32-2-221−1+3i32−1−3i32-22-2-21−i31−i31+i31+i311−1+3i32−1−3i32-11−3i321+3i32-221-121−3i321+3i32002-22−1+i3−1−i31−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i321-1-10000000-11−i321+i321−1+i32−1−i32-11−i321+i320000000000000000
χ5744-444-44111-2-44111-2-4222222-2-1-1-11112-2-2-12-1-100-2-22-2-2-2-222-1-1-1-1-1-12-220000000111111-1-1-10000000000000000
χ5844-444-44111-2-44111-2-4-2-2-2-2-2-2-2-1-1-11112-2-2-12-1-10022-22222-2-21111112-220000000-1-1-1-1-1-11110000000000000000
χ5944-444-44-2-2-21-44-2-2-21-40000001222-2-2-2-1112-12200000000000000000-11-10022000000000000-22-200-1-10001-11000
χ6044-444-44-2-2-21-44-2-2-21-40000001222-2-2-2-1112-12200000000000000000-11-100-2-20000000000002-220011000-11-1000
χ6144-44-2-4-21−1−3i32−1+3i32-22-21−1−3i32−1+3i32-2222−1−i3−1−i3−1+i3−1+i31-11+3i321−3i321−1−3i32−1+3i322-21-121+3i321−3i3200-2-221+i31−i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11-100000001−1−i32−1+i321−1−i32−1+i32-11+i321−i320000000000000000
χ6244-44-2-4-21−1−3i32−1+3i32-22-21−1−3i32−1+3i32-22-2-21+i31+i31−i31−i31-11+3i321−3i321−1−3i32−1+3i322-21-121+3i321−3i320022-2−1−i3−1+i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-11-10000000-11+i321−i32-11+i321−i321−1−i32−1+i320000000000000000
χ6344-44-2-4-21−1+3i32−1−3i32-22-21−1+3i32−1−3i32-2222−1+i3−1+i3−1−i3−1−i31-11−3i321+3i321−1+3i32−1−3i322-21-121−3i321+3i3200-2-221−i31+i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11-100000001−1+i32−1−i321−1+i32−1−i32-11−i321+i320000000000000000
χ6444-44-2-4-21−1+3i32−1−3i32-22-21−1+3i32−1−3i32-22-2-21−i31−i31+i31+i31-11−3i321+3i321−1+3i32−1−3i322-21-121−3i321+3i320022-2−1+i3−1−i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-11-10000000-11−i321+i32-11−i321+i321−1+i32−1−i320000000000000000
χ6544-4-4444111-2-4-4111-24222222-2-1-1-1-1-1-122-21-211002-2-222-2-2-2-2-1-1-1-1-1-122-20000000-1-1-11111110000000000000000
χ6644-4-4444111-2-4-4111-24-2-2-2-2-2-2-2-1-1-1-1-1-122-21-21100-222-2-2222211111122-20000000111-1-1-1-1-1-10000000000000000
χ6744-4-4444-2-2-21-4-4-2-2-2140000001222222-1-11-21-2-200000000000000000-1-110022000000000000-2-2200-1-100011-1000
χ6844-4-4444-2-2-21-4-4-2-2-2140000001222222-1-11-21-2-200000000000000000-1-1100-2-200000000000022-20011000-1-11000
χ6944-4-4-24-21−1−3i32−1+3i32-2221−1−3i32−1+3i32-2-222−1−i3−1−i3−1+i3−1+i31-11+3i321−3i32-11+3i321−3i322211-2−1−3i32−1+3i32002-2-2−1−i3−1+i31+i31−i31+i31−i3-1-11+i321+i321−i321−i32-1-110000000-11+i321−i321−1−i32−1+i321−1−i32−1+i320000000000000000
χ7044-4-4-24-21−1−3i32−1+3i32-2221−1−3i32−1+3i32-2-2-2-21+i31+i31−i31−i31-11+3i321−3i32-11+3i321−3i322211-2−1−3i32−1+3i3200-2221+i31−i3−1−i3−1+i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-1100000001−1−i32−1+i32-11+i321−i32-11+i321−i320000000000000000
χ7144-4-4-24-21−1+3i32−1−3i32-2221−1+3i32−1−3i32-2-222−1+i3−1+i3−1−i3−1−i31-11−3i321+3i32-11−3i321+3i322211-2−1+3i32−1−3i32002-2-2−1+i3−1−i31−i31+i31−i31+i3-1-11−i321−i321+i321+i32-1-110000000-11−i321+i321−1+i32−1−i321−1+i32−1−i320000000000000000
χ7244-4-4-24-21−1+3i32−1−3i32-2221−1+3i32−1−3i32-2-2-2-21−i31−i31+i31+i31-11−3i321+3i32-11−3i321+3i322211-2−1+3i32−1−3i3200-2221−i31+i3−1+i3−1−i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-1100000001−1+i32−1−i32-11−i321+i32-11−i321+i320000000000000000
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χ828-80080-8222-400-2-2-2404i−4i4i−4i4i−4i-4000000004000000000000000−2i2i−2i2i−2i2i00000000000000000000000000000000000
χ838-80080-8222-400-2-2-240−4i4i−4i4i−4i4i-40000000040000000000000002i−2i2i−2i2i−2i00000000000000000000000000000000000
χ848-80080-8-4-4-4200444-20000000200000000-2000000000000000000000000004-400000000000000000-22000000000
χ858-80080-8-4-4-4200444-20000000200000000-200000000000000000000000000-44000000000000000002-2000000000
χ868-800-4042−1−3i3−1+3i3-400-21+3i31−3i3404i−4i4ζ11−4ζ114ζ7−4ζ7200000000-2000000000000000−2i2i−2ζ112ζ11−2ζ72ζ700000000000000000000000000000000000
χ878-800-4042−1−3i3−1+3i3-400-21+3i31−3i340−4i4i−4ζ114ζ11−4ζ74ζ7200000000-20000000000000002i−2i2ζ11−2ζ112ζ7−2ζ700000000000000000000000000000000000
χ888-800-4042−1+3i3−1−3i3-400-21−3i31+3i3404i−4i4ζ7−4ζ74ζ11−4ζ11200000000-2000000000000000−2i2i−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000000000
χ898-800-4042−1+3i3−1−3i3-400-21−3i31+3i340−4i4i−4ζ74ζ7−4ζ114ζ11200000000-20000000000000002i−2i2ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000000000
χ9016-1600-808-8444008-4-4-40000000-200000000200000000000000000000000000000000000000000000000000000000

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