Finite Group Databasebeta

← Group #13166569

Character table — Group #13166569

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222444444668888888991216161616161616161818181818181824242424272727273636363636363636484854545454727272108108108
order12346334661288336612121244412121212121212122444412122424242488882688121212121212888862424288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-11-1-11-1-1
χ311111111111111111111-1-1111111111-1ii−i−i-1-11111ii−i−i-1-1i−iii−i−i11-1-1i−i-1i−i-1i−i
χ411111111111111111111-1-1111111111-1−i−iii-1-11111−i−iii-1-1−ii−i−iii11-1-1−ii-1−ii-1−ii
χ511111111111-1-1111111111-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1
χ611111111111-1-1111111111-1111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-111
χ711111111111-1-11111111-1-1-111111111-1ii−i−i-1-1-1-1-1-1−i−iii-1-1i−iii−i−i-1-111−ii-1i−i1−ii
χ811111111111-1-11111111-1-1-111111111-1−i−iii-1-1-1-1-1-1ii−i−i-1-1−ii−i−iii-1-111i−i-1−ii1i−i
χ91111111-1111111111-11111-1-1-111-1-1-1-1111111111111111-11-1-11111-1-11111-1-1-1-1-1-1
χ101111111-1111111111-11111-1-1-111-1-1-1-11-1-1-1-1111111-1-1-1-1-1111-1-1-1-1-1-111-1-1-111-111
χ111111111-1111111111-111-1-1-1-1-111-1-1-1-1-1ii−i−i-1-11111ii−i−i1-1−iiii−i−i-1-1-1-1i−i1−ii1−ii
χ121111111-1111111111-111-1-1-1-1-111-1-1-1-1-1−i−iii-1-11111−i−iii1-1i−i−i−iii-1-1-1-1−ii1i−i1i−i
χ131111111-1111-1-11111-111111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1111
χ141111111-1111-1-11111-111111-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-1111-1-1-1-111-1-111-1111-1-1
χ151111111-1111-1-11111-111-1-11-1-111-1-1-1-1-1ii−i−i-1-1-1-1-1-1−i−iii1-1−iiii−i−i1111−ii1−ii-1i−i
χ161111111-1111-1-11111-111-1-11-1-111-1-1-1-1-1−i−iii-1-1-1-1-1-1ii−i−i1-1i−i−i−iii1111i−i1i−i-1−ii
χ17222-2222022-20022220-2-222000-2-20000-2000022000022220-20000000000-2-2000000
χ18222-2222022-20022220-2-222000-2-20000-20000220000-2-2-2-20-2000000000022000000
χ19222-2222022-20022220-2-2-2-2000-2-2000020000-2-200002i2i−2i−2i020000000000−2i2i000000
χ20222-2222022-20022220-2-2-2-2000-2-2000020000-2-20000−2i−2i2i2i0200000000002i−2i000000
χ2122-12-122222-100-1-1-1-1-12222022-1-1-1-1-1-122222-1-1000000002-122-1-1-1-1000000-1-1-1000
χ2222-12-122222-100-1-1-1-1-12222022-1-1-1-1-1-12-2-2-2-2-1-1000000002-1-2-21111000000-111000
χ2322-12-122222-100-1-1-1-1-122-2-2022-1-1-1-1-1-1-22i2i−2i−2i1100000000-212i−2i−i−iii0000001−ii000
χ2422-12-122222-100-1-1-1-1-122-2-2022-1-1-1-1-1-1-2−2i−2i2i2i1100000000-21−2i2iii−i−i0000001i−i000
χ2522-12-122-222-100-1-1-1-1122220-2-2-1-1111122222-1-100000000-2-1-2-2-1-1-1-1000000111000
χ2622-12-122-222-100-1-1-1-1122220-2-2-1-111112-2-2-2-2-1-100000000-2-12211110000001-1-1000
χ2722-12-122-222-100-1-1-1-1122-2-20-2-2-1-11111-22i2i−2i−2i110000000021−2i2i−i−iii000000-1i−i000
χ2822-12-122-222-100-1-1-1-1122-2-20-2-2-1-11111-2−2i−2i2i2i1100000000212i−2iii−i−i000000-1−ii000
χ292-220-2220-2-202−222-2-20002i−2i00000000001+i−1−i1−i−1+i2i−2i22−2−22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300001+i−1−i1−i−1+i00−i2i200000000
χ302-220-2220-2-202−222-2-20002i−2i0000000000−1−i1+i−1+i1−i2i−2i22−2−2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−1−i1+i−1+i1−i00−i2i200000000
χ312-220-2220-2-202−222-2-2000−2i2i00000000001−i−1+i1+i−1−i−2i2i22−2−2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300001−i−1+i1+i−1−i00i2−i200000000
χ322-220-2220-2-202−222-2-2000−2i2i0000000000−1+i1−i−1−i1+i−2i2i22−2−22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−1+i1−i−1−i1+i00i2−i200000000
χ332-220-2220-2-20−2222-2-20002i−2i00000000001+i−1−i1−i−1+i2i−2i−2−222−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300001+i−1−i1−i−1+i00i2−i200000000
χ342-220-2220-2-20−2222-2-20002i−2i0000000000−1−i1+i−1+i1−i2i−2i−2−2222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−1−i1+i−1+i1−i00i2−i200000000
χ352-220-2220-2-20−2222-2-2000−2i2i00000000001−i−1+i1+i−1−i−2i2i−2−2222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300001−i−1+i1+i−1−i00−i2i200000000
χ362-220-2220-2-20−2222-2-2000−2i2i0000000000−1+i1−i−1−i1+i−2i2i−2−222−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−1+i1−i−1−i1+i00−i2i200000000
χ37444441-241-24441-21-241-20041-21-211-2-200000001-21-20000000000001-20000000000
χ38444441-241-24-4-41-21-241-200-41-21-211-2-20000000-12-12000000000000-120000000000
χ39444441-2-41-24441-21-2-41-200-4-121-2-1-12200000001-21-2000000000000-120000000000
χ40444441-2-41-24-4-41-21-2-41-2004-121-2-1-1220000000-12-120000000000001-20000000000
χ4144444-214-21444-21-214-21004-21-21-2-2110000000-21-21000000000000-210000000000
χ4244444-214-214-4-4-21-214-2100-4-21-21-2-21100000002-12-10000000000002-10000000000
χ4344444-21-4-21444-21-21-4-2100-42-1-2122-1-10000000-21-210000000000002-10000000000
χ4444444-21-4-214-4-4-21-21-4-210042-1-2122-1-100000002-12-1000000000000-210000000000
χ4544-2-4-244044200-2-2-2-20-4-444000220000-40000-2-20000000002000000000000000000
χ4644-2-4-244044200-2-2-2-20-4-4-4-40002200004000022000000000-2000000000000000000
χ474-4-202440-4-4000-2-2220004i−4i00000000002+2i−2−2i2−2i−2+2i−2i2i000000000000−1−i1+i−1+i1−i000000000000
χ484-4-202440-4-4000-2-2220004i−4i0000000000−2−2i2+2i−2+2i2−2i−2i2i0000000000001+i−1−i1−i−1+i000000000000
χ494-4-202440-4-4000-2-222000−4i4i00000000002−2i−2+2i2+2i−2−2i2i−2i000000000000−1+i1−i−1−i1+i000000000000
χ504-4-202440-4-4000-2-222000−4i4i0000000000−2+2i2−2i−2−2i2+2i2i−2i0000000000001−i−1+i1+i−1−i000000000000
χ51888-882-402-4-8002-42-40-2400000-24000000000000000000000000000000000000000
χ52888-88-420-42-800-42-4204-2000004-2000000000000000000000000000000000000000
χ5388-48-42-482-4-400-12-12-42-40002-4-12-1-12200000000000000000000000000000000000
χ5488-48-42-4-82-4-400-12-1242-4000-24-1211-2-200000000000000000000000000000000000
χ5588-48-4-428-42-4002-12-1-4-42000-422-122-1-100000000000000000000000000000000000
χ5688-48-4-42-8-42-4002-12-14-420004-22-1-2-21100000000000000000000000000000000000
χ5788-4-8-42-402-4400-12-120-24000001-2−3i33i30000000000000000000000000000000000000
χ5888-4-8-42-402-4400-12-120-24000001-23i3−3i30000000000000000000000000000000000000
χ5988-4-8-4-420-424002-12-104-200000-2100−3i33i300000000000000000000000000000000000
χ6088-4-8-4-420-424002-12-104-200000-21003i3−3i300000000000000000000000000000000000
χ618-880-82-40-24042−422-4-240000000000000000000002−22−222000000000000000000000000
χ628-880-82-40-240−42422-4-24000000000000000000000−2222−22000000000000000000000000
χ638-880-8-4204-2042−42-424-2000000000000000000000−22222−2000000000000000000000000
χ648-880-8-4204-20−4242-424-200000000000000000000022−2−222000000000000000000000000
χ6516-16-8084-80-48000-242-40000000000000000000000000000000000000000000000000
χ6616-16-808-8408-40004-2-420000000000000000000000000000000000000000000000000

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