Finite Group Databasebeta

← Group #13181101

Character table — Group #13181101

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222444444444448888888888888812121212121212121212121212121212121216161618181818242424242424242424363636363636363636365454727272108108108
order123444633336666121212361212121212121212121212122224666666121212121212121212121222246666666662444666661288121212888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1111
χ51111-1-11111111111-1-111111-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111111-1-1-111-1-11-1-1111-1-11-1-111-1
χ61111-1-11111111111-1-111111-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111111-1-1-1-1-1111-1-1-1-1111-111-1-11
χ71111-1-11111111111-1-111111-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111111-1-11-1-11-1-1-1-1-1-111111-1-11-1-1111111-1-1-1-11
χ81111-1-11111111111-1-111111-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111111-1-11-1-11-1-1-1-1-1-1111-1-1111-1-1-1-11-1-1-11111-1
χ9111-11-1111111111-11-111-1-1-1111-1-1-1-11-11-11-111-1-111-1-1-1-1-1-1-1-1-11-1-11-11111-1-1-11111-11-1-11-1111-1-1-11-11-11
χ10111-11-1111111111-11-111-1-1-1111-1-1-1-11-11-11-111-1-111-1-1-1-1-1-1-1-1-11-1-11-11111-1-1-1111-11-11-11-1-1-11111-11-11-1
χ11111-11-1111111111-11-111-1-1-1111-1-1-1-11-1-11-11-1-111-1-111111111-11-1-11-11-1-1-1111-1-1-11-11-1-11-111111-11-1-11-1
χ12111-11-1111111111-11-111-1-1-1111-1-1-1-11-1-11-11-1-111-1-111111111-11-1-11-11-1-1-1111-1-1-1-11-11-11-1-1-11-1-11-111-11
χ13111-1-11111111111-1-1111-1-1-1-1-1-1111-1-111-1-1111-1-1-1-111111111-1-11-1-111111-1-1-1-1-1-11-1-11-1-1111111-1-111-1-1
χ14111-1-11111111111-1-1111-1-1-1-1-1-1111-1-111-1-1111-1-1-1-111111111-1-11-1-111111-1-1-1-1-1-1-111-1-1-11-1-11-1-111-1-111
χ15111-1-11111111111-1-1111-1-1-1-1-1-1111-1-11-111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11111111-1-11-1-11111-1-1-1-11-111
χ16111-1-11111111111-1-1111-1-1-1-1-1-1111-1-11-111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1111111-111-1-1-11-1-111111-11-1-1
χ1722222222222222222222222222222222000000000000000000222-2-2-2-20000000000000-2-2-200-200000000
χ182222-2-22222222222-2-222222-2-2-2-2-2-22-2-20000000000000000002-2-2-222-20000000000000-22200-200000000
χ19222-22-2222222222-22-222-2-2-2222-2-2-2-22-2000000000000000000-22-22-22-200000000000002-2200-200000000
χ20222-2-22222222222-2-2222-2-2-2-2-2-2222-2-22000000000000000000-2-2222-2-2000000000000022-200-200000000
χ2122-1222-122-1-12-1-12-1-1-1-1-12-1-12-1-12-1-12220000−i3i3−i3i3−i3i3−i3i300−i3−i3i3i3-1-1-1-2-2-2-20−i3i30−i3i30−i3i3000011100100000000
χ2222-1222-122-1-12-1-12-1-1-1-1-12-1-12-1-12-1-12220000i3−i3i3−i3i3−i3i3−i300i3i3−i3−i3-1-1-1-2-2-2-20i3−i30i3−i30i3−i3000011100100000000
χ2322-1222-122-1-12-1-12-1-1-1-1-12-1-12-1-12-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-122222-1-12-1-12-1-10000-1-1-100-100000000
χ2422-1222-122-1-12-1-12-1-1-1-1-12-1-12-1-12-1-1222-2-2-2-211111111-2-21111-1-1-12222-211-211-2110000-1-1-100-100000000
χ2522-12-2-2-122-1-12-1-12-111-1-12-1-1-211-2112-2-20000−i3i3−i3i3i3−i3i3−i300i3i3−i3−i3-111-222-20−i3i30−i3i30i3−i300001-1-100100000000
χ2622-12-2-2-122-1-12-1-12-111-1-12-1-1-211-2112-2-20000i3−i3i3−i3−i3i3−i3i300−i3−i3i3i3-111-222-20i3−i30i3−i30−i3i300001-1-100100000000
χ2722-12-2-2-122-1-12-1-12-111-1-12-1-1-211-2112-2-222-2-2-1-1-1-11111-2-21111-1112-2-222-1-12-1-1-2110000-11100-100000000
χ2822-12-2-2-122-1-12-1-12-111-1-12-1-1-211-2112-2-2-2-2221111-1-1-1-122-1-1-1-1-1112-2-22-211-2112-1-10000-11100-100000000
χ2922-1-22-2-122-1-12-1-121-11-1-1-2112-1-1-211-22-20000−i3i3i3−i3−i3i3i3−i300i3i3−i3−i31-112-22-20−i3i30i3−i30−i3i30000-11-100100000000
χ3022-1-22-2-122-1-12-1-121-11-1-1-2112-1-1-211-22-20000i3−i3−i3i3i3−i3−i3i300−i3−i3i3i31-112-22-20i3−i30−i3i30i3−i30000-11-100100000000
χ3122-1-22-2-122-1-12-1-121-11-1-1-2112-1-1-211-22-22-22-2-1-111-1-111-2-211111-11-22-222-1-1-2112-1-100001-1100-100000000
χ3222-1-22-2-122-1-12-1-121-11-1-1-2112-1-1-211-22-2-22-2211-1-111-1-122-1-1-1-11-11-22-22-2112-1-1-21100001-1100-100000000
χ3322-1-2-22-122-1-12-1-1211-1-1-1-211-2112-1-1-2-220000−i3i3i3−i3i3−i3−i3i300−i3−i3i3i311-122-2-20−i3i30i3−i30i3−i30000-1-1100100000000
χ3422-1-2-22-122-1-12-1-1211-1-1-1-211-2112-1-1-2-220000i3−i3−i3i3−i3i3i3−i300i3i3−i3−i311-122-2-20i3−i30−i3i30−i3i30000-1-1100100000000
χ3522-1-2-22-122-1-12-1-1211-1-1-1-211-2112-1-1-2-222-2-22-1-11111-1-122-1-1-1-111-1-2-2222-1-1-211-211000011-100-100000000
χ3622-1-2-22-122-1-12-1-1211-1-1-1-211-2112-1-1-2-22-222-211-1-1-1-111-2-2111111-1-2-222-2112-1-12-1-1000011-100-100000000
χ3744444441-211111-2444-2-2111111111-2-2-2222222222222-1-1-1-1-1-1-2-2-20000-1-1-1-1-1-1-1-1-1000000000000000000
χ3844444441-211111-2444-2-2111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111-2-2-20000111111111000000000000000000
χ394444444-21-2-2-2-2-2144411-2-2-2-2-2-2-2-2-211100000000000000000011100000000000002222000-1-1000-1-1-1000
χ404444444-21-2-2-2-2-2144411-2-2-2-2-2-2-2-2-21110000000000000000001110000000000000-2-2-2-200011000111000
χ414444-4-441-211111-24-4-4-2-2111-1-1-1-1-1-1-22222-2-22222-2-2-2-2111111-2220000-1-1-1-1-1-1111000000000000000000
χ424444-4-441-211111-24-4-4-2-2111-1-1-1-1-1-1-222-2-222-2-2-2-22222-1-1-1-1-1-1-2220000111111-1-1-1000000000000000000
χ434444-4-44-21-2-2-2-2-214-4-411-2-2-22222221-1-10000000000000000001-1-1000000000000022-2-2000-1-1000-111000
χ444444-4-44-21-2-2-2-2-214-4-411-2-2-22222221-1-10000000000000000001-1-10000000000000-2-222000110001-1-1000
χ45444-44-441-211111-2-44-4-2-2-1-1-1111-1-1-12-222-22-222-2-222-2-21111112-220000-1-1-1111-1-1-1000000000000000000
χ46444-44-441-211111-2-44-4-2-2-1-1-1111-1-1-12-22-22-22-2-222-2-222-1-1-1-1-1-12-220000111-1-1-1111000000000000000000
χ47444-44-44-21-2-2-2-2-21-44-411222-2-2-2222-11-1000000000000000000-11-100000000000002-22-2000-1-10001-11000
χ48444-44-44-21-2-2-2-2-21-44-411222-2-2-2222-11-1000000000000000000-11-10000000000000-22-2200011000-11-1000
χ49444-4-4441-211111-2-4-44-2-2-1-1-1-1-1-111122-22-2-2222-2-2-2-222-1-1-1-1-1-122-20000-1-1-1111111000000000000000000
χ50444-4-4441-211111-2-4-44-2-2-1-1-1-1-1-111122-2-222-2-2-22222-2-211111122-20000111-1-1-1-1-1-1000000000000000000
χ51444-4-444-21-2-2-2-2-21-4-4411222222-2-2-2-1-11000000000000000000-1-1100000000000002-2-22000-1-100011-1000
χ52444-4-444-21-2-2-2-2-21-4-4411222222-2-2-2-1-11000000000000000000-1-110000000000000-222-200011000-1-11000
χ5344-2444-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i321110000-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ5444-2444-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211100001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ5544-2444-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i321110000-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ5644-2444-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211100001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ5744-24-4-4-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2-222111−1−3i32−1+3i32-11+3i321−3i32-11+3i321−3i32-22222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i321-1-10000-11+i321−i32-11+i321−i321−1−i32−1+i32000000000000000000
χ5844-24-4-4-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2-222111−1−3i32−1+3i32-11+3i321−3i32-11+3i321−3i32-222-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i321-1-100001−1−i32−1+i321−1−i32−1+i32-11+i321−i32000000000000000000
χ5944-24-4-4-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2-222111−1+3i32−1−3i32-11−3i321+3i32-11−3i321+3i32-22222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i321-1-10000-11−i321+i32-11−i321+i321−1+i32−1−i32000000000000000000
χ6044-24-4-4-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2-222111−1+3i32−1−3i32-11−3i321+3i32-11−3i321+3i32-222-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i321-1-100001−1+i32−1−i321−1+i32−1−i32-11−i321+i32000000000000000000
χ6144-2-44-4-21-2−1−3i32−1+3i321−1−3i32−1+3i32-22-2211-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-222-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-11-10000-11+i321−i321−1−i32−1+i32-11+i321−i32000000000000000000
χ6244-2-44-4-21-2−1−3i32−1+3i321−1−3i32−1+3i32-22-2211-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-22-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11-100001−1−i32−1+i32-11+i321−i321−1−i32−1+i32000000000000000000
χ6344-2-44-4-21-2−1+3i32−1−3i321−1+3i32−1−3i32-22-2211-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-222-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-11-10000-11−i321+i321−1+i32−1−i32-11−i321+i32000000000000000000
χ6444-2-44-4-21-2−1+3i32−1−3i321−1+3i32−1−3i32-22-2211-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-22-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11-100001−1+i32−1−i32-11−i321+i321−1+i32−1−i32000000000000000000
χ6544-2-4-44-21-2−1−3i32−1+3i321−1−3i32−1+3i32-222-211-11+3i321−3i32-11+3i321−3i321−1−3i32−1+3i3222-22-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-110000-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ6644-2-4-44-21-2−1−3i32−1+3i321−1−3i32−1+3i32-222-211-11+3i321−3i32-11+3i321−3i321−1−3i32−1+3i3222-2-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-1100001−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ6744-2-4-44-21-2−1+3i32−1−3i321−1+3i32−1−3i32-222-211-11−3i321+3i32-11−3i321+3i321−1+3i32−1−3i3222-22-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-110000-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ6844-2-4-44-21-2−1+3i32−1−3i321−1+3i32−1−3i32-222-211-11−3i321+3i32-11−3i321+3i321−1+3i32−1−3i3222-2-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-1100001−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ694-44000-44444-4-4-4-40004-400000000000000000000000000000000000000000000000000000000−2i22i2000000
χ704-44000-44444-4-4-4-40004-4000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ7188-4888-4-4222-4222-4-4-4-1-1-422-422-422222000000000000000000-1-1-10000000000000000000000000000000
χ7288-48-8-8-4-4222-4222-444-1-1-4224-2-24-2-22-2-2000000000000000000-1110000000000000000000000000000000
χ7388-4-88-8-4-4222-42224-44-1-14-2-2-4224-2-2-22-20000000000000000001-110000000000000000000000000000000
χ7488-4-8-88-4-4222-422244-4-1-14-2-24-2-2-422-2-2200000000000000000011-10000000000000000000000000000000
χ758-88000-82-422-2-2-24000-4400000000000000000000000023−2323−2323−230000000000000000000000000000000000
χ768-88000-82-422-2-2-24000-44000000000000000000000000−2323−2323−23230000000000000000000000000000000000
χ778-88000-8-42-4-4444-20002-200000000000000000000000000000000000000000000000000000−2i32i3000000000
χ788-88000-8-42-4-4444-20002-2000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ798-8-400042-4−1−3i3−1+3i3-21+3i31−3i340002-200000000000000000000000023−234ζ14+2ζ22−4ζ14−2ζ22−2ζ14−4ζ222ζ14+4ζ220000000000000000000000000000000000
χ808-8-400042-4−1−3i3−1+3i3-21+3i31−3i340002-2000000000000000000000000−2323−4ζ14−2ζ224ζ14+2ζ222ζ14+4ζ22−2ζ14−4ζ220000000000000000000000000000000000
χ818-8-400042-4−1+3i3−1−3i3-21−3i31+3i340002-200000000000000000000000023−23−2ζ14−4ζ222ζ14+4ζ224ζ14+2ζ22−4ζ14−2ζ220000000000000000000000000000000000
χ828-8-400042-4−1+3i3−1−3i3-21−3i31+3i340002-2000000000000000000000000−23232ζ14+4ζ22−2ζ14−4ζ22−4ζ14−2ζ224ζ14+2ζ220000000000000000000000000000000000
χ838-8-4000488-4-4-844-8000-440000000000000000000000000000000000000000000000000000000000000000
χ8416-16-80008-84448-4-4-4000-220000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.