Finite Group Databasebeta

← Group #13166565

Character table — Group #13166565

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112224444444466888888999999121616161616161616181818181818181818242424243636363636363636363636364848545454545454108108108
order1234633466121212883366121244888841212121212121212288121224242424242424242666882424242424241212444488288
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-11111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1
χ3111111111111111111111-1-1ii−i−i111111111-1i−i-1-1ii−i−i1111-1-1-1-1i−iiii−i−i−i11ii−i−i-1-1-1i−i
χ4111111111111111111111-1-1−i−iii111111111-1−ii-1-1−i−iii1111-1-1-1-1−ii−i−i−iiii11−i−iii-1-1-1−ii
χ51111111111111-1-1111111111111-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111-1-111111111-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ71111111111111-1-1111111-1-1ii−i−i-111111111-1i−i-1-1ii−i−i-1-1-1-1-1-1-1-1i−iiii−i−i−i-1-1−i−iii111−ii
χ81111111111111-1-1111111-1-1−i−iii-111111111-1−ii-1-1−i−iii-1-1-1-1-1-1-1-1−ii−i−i−iiii-1-1ii−i−i111i−i
χ91111111-1111-1-111111111111111-1-1-111-1-1-1-11111111111111-11-1-1-1-11-1-11-1-1-1-1111111-1-1-1
χ101111111-1111-1-11111111111-1-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1-11111-11-1-111-111-111-1-1-1-1-1-111-111
χ111111111-1111-1-111111111-1-1ii−i−i-1-1-111-1-1-1-1-1i−i-1-1ii−i−i11111-111−iii−i−i−iii-1-1ii−i−i-1-11−ii
χ121111111-1111-1-111111111-1-1−i−iii-1-1-111-1-1-1-1-1−ii-1-1−i−iii11111-111i−i−iiii−i−i-1-1−i−iii-1-11i−i
χ131111111-1111-1-1-1-11111111111111-1-111-1-1-1-1111111111-1-1-1-1-11-1-1-1-11-1-11-1-111-1-1-1-1-1-1111
χ141111111-1111-1-1-1-111111111-1-1-1-11-1-111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-11-1-111-111-111111111-1-11-1-1
χ151111111-1111-1-1-1-1111111-1-1ii−i−i1-1-111-1-1-1-1-1i−i-1-1ii−i−i-1-1-1-11-111−iii−i−i−iii11−i−iii11-1i−i
χ161111111-1111-1-1-1-1111111-1-1−i−iii1-1-111-1-1-1-1-1−ii-1-1−i−iii-1-1-1-11-111i−i−iiii−i−i11ii−i−i11-1−ii
χ17222-2222022-200002222-2-2222222000-2-20000-2-2-222222200000-20000-200-20000000000000
χ18222-2222022-200002222-2-222-2-2-2-2000-2-20000-22222-2-2-2-200000-2000020020000000000000
χ19222-2222022-200002222-2-2-2-22i2i−2i−2i000-2-200002−2i2i-2-22i2i−2i−2i0000020000−2i002i0000000000000
χ20222-2222022-200002222-2-2-2-2−2i−2i2i2i000-2-2000022i−2i-2-2−2i−2i2i2i00000200002i00−2i0000000000000
χ2122-12-122222-1-1-100-1-1-1-122222222022-1-1-1-1-1-1222-1-1-1-1-1-100002-1-1-122-1-1-1-1-1-100000000000
χ2222-12-122222-1-1-100-1-1-1-12222-2-2-2-2022-1-1-1-1-1-12-2-2-1-1111100002-1-1-1-2-211111100000000000
χ2322-12-122222-1-1-100-1-1-1-122-2-22i2i−2i−2i022-1-1-1-1-1-1-22i−2i11−i−iii0000-21112i−2i−i−i−iiii00000000000
χ2422-12-122222-1-1-100-1-1-1-122-2-2−2i−2i2i2i022-1-1-1-1-1-1-2−2i2i11ii−i−i0000-2111−2i2iiii−i−i−i00000000000
χ2522-12-122-222-11100-1-1-1-1222222220-2-2-1-11111222-1-1-1-1-1-10000-2-111-2-2-111-11100000000000
χ2622-12-122-222-11100-1-1-1-12222-2-2-2-20-2-2-1-111112-2-2-1-111110000-2-111221-1-11-1-100000000000
χ2722-12-122-222-11100-1-1-1-122-2-22i2i−2i−2i0-2-2-1-11111-22i−2i11−i−iii000021-1-1−2i2i−iiii−i−i00000000000
χ2822-12-122-222-11100-1-1-1-122-2-2−2i−2i2i2i0-2-2-1-11111-2−2i2i11ii−i−i000021-1-12i−2ii−i−i−iii00000000000
χ2922-1-2-1220221−i3i300-1-1-1-1-2-222222200011−i3−i3i3i3-2-2-2-1-1-1-1-1-1000001−i3i3001−i3i31−i3i300000000000
χ3022-1-2-1220221−i3i300-1-1-1-1-2-222-2-2-2-200011−i3−i3i3i3-222-1-11111000001−i3i300-1i3−i3-1i3−i300000000000
χ3122-1-2-1220221−i3i300-1-1-1-1-2-2-2-22i2i−2i−2i00011−i3−i3i3i32−2i2i11−i−iii00000-1i3−i300i3−3−i−3300000000000
χ3222-1-2-1220221−i3i300-1-1-1-1-2-2-2-2−2i−2i2i2i00011−i3−i3i3i322i−2i11ii−i−i00000-1i3−i300−i−33i3−300000000000
χ3322-1-2-1220221i3−i300-1-1-1-1-2-222222200011i3i3−i3−i3-2-2-2-1-1-1-1-1-1000001i3−i3001i3−i31i3−i300000000000
χ3422-1-2-1220221i3−i300-1-1-1-1-2-222-2-2-2-200011i3i3−i3−i3-222-1-11111000001i3−i300-1−i3i3-1−i3i300000000000
χ3522-1-2-1220221i3−i300-1-1-1-1-2-2-2-22i2i−2i−2i00011i3i3−i3−i32−2i2i11−i−iii00000-1−i3i300i−33−i3−300000000000
χ3622-1-2-1220221i3−i300-1-1-1-1-2-2-2-2−2i−2i2i2i00011i3i3−i3−i322i−2i11ii−i−i00000-1−i3i300−i3−3i−3300000000000
χ372-220-2220-2-20002−222-2-2002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322−2−2000000000000001+i−1−i1−i−1+i−i2i2000
χ382-220-2220-2-20002−222-2-2002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322−2−200000000000000−1−i1+i−1+i1−i−i2i2000
χ392-220-2220-2-20002−222-2-200−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322−2−2000000000000001−i−1+i1+i−1−ii2−i2000
χ402-220-2220-2-20002−222-2-200−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322−2−200000000000000−1+i1−i−1−i1+ii2−i2000
χ412-220-2220-2-2000−2222-2-2002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2−22200000000000000−1−i1+i−1+i1−ii2−i2000
χ422-220-2220-2-2000−2222-2-2002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2−222000000000000001+i−1−i1−i−1+ii2−i2000
χ432-220-2220-2-2000−2222-2-200−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2−22200000000000000−1+i1−i−1−i1+i−i2i2000
χ442-220-2220-2-2000−2222-2-200−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2−222000000000000001−i−1+i1+i−1−i−i2i2000
χ45444441-241-2444441-21-21-200000041-21-21-21-20000000001-21-20000000000001-2000000000
χ46444441-241-2444-4-41-21-21-2000000-41-21-21-21-2000000000-12-12000000000000-12000000000
χ47444441-2-41-24-4-4441-21-21-2000000-4-121-2-12-120000000001-21-2000000000000-12000000000
χ48444441-2-41-24-4-4-4-41-21-21-20000004-121-2-12-12000000000-12-120000000000001-2000000000
χ4944444-214-2144444-21-21-210000004-21-21-21-21000000000-21-21000000000000-21000000000
χ5044444-214-21444-4-4-21-21-21000000-4-21-21-21-210000000002-12-10000000000002-1000000000
χ5144444-21-4-214-4-444-21-21-21000000-42-1-212-12-1000000000-21-210000000000002-1000000000
χ5244444-21-4-214-4-4-4-4-21-21-2100000042-1-212-12-10000000002-12-1000000000000-21000000000
χ534-4-202440-4-400000-2-222004i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000000000−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000
χ544-4-202440-4-400000-2-222004i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13000000000000−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000
χ554-4-202440-4-400000-2-22200−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000
χ564-4-202440-4-400000-2-22200−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000
χ57888-882-402-4-800002-42-4-24000000000-240000000000000000000000000000000000000000
χ58888-88-420-42-80000-42-424-20000000004-20000000000000000000000000000000000000000
χ5988-48-42-482-4-4-4-400-12-122-400000002-4-12-12-12000000000000000000000000000000000000
χ6088-48-42-4-82-4-44400-12-122-40000000-24-121-21-2000000000000000000000000000000000000
χ6188-48-4-428-42-4-4-4002-12-1-420000000-422-12-12-1000000000000000000000000000000000000
χ6288-48-4-42-8-42-444002-12-1-4200000004-22-1-21-21000000000000000000000000000000000000
χ6388-4-8-42-402-44−4i34i300-12-12-240000000001-2−i32i3i3−2i3000000000000000000000000000000000000
χ6488-4-8-42-402-444i3−4i300-12-12-240000000001-2i3−2i3−i32i3000000000000000000000000000000000000
χ6588-4-8-4-420-424−4i34i3002-12-14-2000000000-212i3−i3−2i3i3000000000000000000000000000000000000
χ6688-4-8-4-420-4244i3−4i3002-12-14-2000000000-21−2i3i32i3−i3000000000000000000000000000000000000
χ678-880-82-40-2400042−422-4-24000000000000000000000000002−22−22200000000000000000000000
χ688-880-82-40-24000−42422-4-2400000000000000000000000000−2222−2200000000000000000000000
χ698-880-8-4204-200042−42-424-200000000000000000000000000−22222−200000000000000000000000
χ708-880-8-4204-2000−4242-424-20000000000000000000000000022−2−22200000000000000000000000
χ7116-16-8084-80-4800000-242-400000000000000000000000000000000000000000000000000000
χ7216-16-808-8408-4000004-2-4200000000000000000000000000000000000000000000000000000

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