Finite Group Databasebeta

← Group #13166564

Character table — Group #13166564

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112224444444488888899121216161616161616161818181818181818181818242424243636363636363636363636364848108108108108108108
order12346334661212123366121244281212121212121212288881212242424242424242426668824242424242466444888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1
χ3111111111111111111111-1-11111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-111
χ51111111111111111111-1-11111111111-1ii−i−i-1-1ii−i−i1111-1-1-1-1i−iiii−i−i−i11-1i−i-1i−i
χ61111111111111111111-1-11111111111-1−i−iii-1-1−i−iii1111-1-1-1-1−ii−i−i−iiii11-1−ii-1−ii
χ71111111111111111111-1-1-1-111111111-1ii−i−i-1-1ii−i−i-1-1-1-1-1-1-1-1i−iiii−i−i−i-1-11−ii1−ii
χ81111111111111111111-1-1-1-111111111-1−i−iii-1-1−i−iii-1-1-1-1-1-1-1-1−ii−i−i−iiii-1-11i−i1i−i
χ91111111-1111-1-1111111111-1-1-111-1-1-1-111111111111-1-1-1-1-11-1-1-1-11-1-11-1-1111-1-1-111
χ101111111-1111-1-1111111111-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11-1-111-111-11111111-1-1-1
χ111111111-1111-1-111111111-11-1-111-1-1-1-1111111111111111-11-1-1-1-11-1-11-1-1-1-1-1111-1-1
χ121111111-1111-1-111111111-11-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-11-1-111-111-111-1-1-1-1-1111
χ131111111-1111-1-1111111-1-11-1-1-111-1-1-1-1-1ii−i−i-1-1ii−i−i-1-1-1-11-111−iii−i−i−iii11-1−ii1i−i
χ141111111-1111-1-1111111-1-11-1-1-111-1-1-1-1-1−i−iii-1-1−i−iii-1-1-1-11-111i−i−iiii−i−i11-1i−i1−ii
χ151111111-1111-1-1111111-1-1-11-1-111-1-1-1-1-1ii−i−i-1-1ii−i−i11111-111−iii−i−i−iii-1-11i−i-1−ii
χ161111111-1111-1-1111111-1-1-11-1-111-1-1-1-1-1−i−iii-1-1−i−iii11111-111i−i−iiii−i−i-1-11−ii-1i−i
χ17222-2222022-2002222-2-2220000-2-20000-22-22-222222200000-20000-200-20000000000
χ18222-2222022-2002222-2-2220000-2-20000-2-22-2222-2-2-2-200000-2000020020000000000
χ19222-2222022-2002222-2-2-2-20000-2-2000022i−2i−2i2i-2-22i2i−2i−2i0000020000−2i002i0000000000
χ20222-2222022-2002222-2-2-2-20000-2-200002−2i2i2i−2i-2-2−2i−2i2i2i00000200002i00−2i0000000000
χ2122-12-122222-1-1-1-1-1-1-122220022-1-1-1-1-1-122222-1-1-1-1-1-100002-1-1-122-1-1-1-1-1-100000000
χ2222-12-122222-1-1-1-1-1-1-122220022-1-1-1-1-1-12-2-2-2-2-1-1111100002-1-1-1-2-211111100000000
χ2322-12-122222-1-1-1-1-1-1-122-2-20022-1-1-1-1-1-1-22i2i−2i−2i11−i−iii0000-21112i−2i−i−i−iiii00000000
χ2422-12-122222-1-1-1-1-1-1-122-2-20022-1-1-1-1-1-1-2−2i−2i2i2i11ii−i−i0000-2111−2i2iiii−i−i−i00000000
χ2522-12-122-222-111-1-1-1-1222200-2-2-1-1111122222-1-1-1-1-1-10000-2-111-2-2-111-11100000000
χ2622-12-122-222-111-1-1-1-1222200-2-2-1-111112-2-2-2-2-1-111110000-2-111221-1-11-1-100000000
χ2722-12-122-222-111-1-1-1-122-2-200-2-2-1-11111-22i2i−2i−2i11−i−iii000021-1-1−2i2i−iiii−i−i00000000
χ2822-12-122-222-111-1-1-1-122-2-200-2-2-1-11111-2−2i−2i2i2i11ii−i−i000021-1-12i−2ii−i−i−iii00000000
χ2922-1-2-1220221−i3i3-1-1-1-1-2-222000011−i3−i3i3i3-22-22-2-1-1-1-1-1-1000001−i3i3001−i3i31−i3i300000000
χ3022-1-2-1220221−i3i3-1-1-1-1-2-222000011−i3−i3i3i3-2-22-22-1-11111000001−i3i300-1i3−i3-1i3−i300000000
χ3122-1-2-1220221−i3i3-1-1-1-1-2-2-2-2000011−i3−i3i3i322i−2i−2i2i11−i−iii00000-1i3−i300i3−3−i−3300000000
χ3222-1-2-1220221−i3i3-1-1-1-1-2-2-2-2000011−i3−i3i3i32−2i2i2i−2i11ii−i−i00000-1i3−i300−i−33i3−300000000
χ3322-1-2-1220221i3−i3-1-1-1-1-2-222000011i3i3−i3−i3-22-22-2-1-1-1-1-1-1000001i3−i3001i3−i31i3−i300000000
χ3422-1-2-1220221i3−i3-1-1-1-1-2-222000011i3i3−i3−i3-2-22-22-1-11111000001i3−i300-1−i3i3-1−i3i300000000
χ3522-1-2-1220221i3−i3-1-1-1-1-2-2-2-2000011i3i3−i3−i322i−2i−2i2i11−i−iii00000-1−i3i300i−33−i3−300000000
χ3622-1-2-1220221i3−i3-1-1-1-1-2-2-2-2000011i3i3−i3−i32−2i2i2i−2i11ii−i−i00000-1−i3i300−i3−3i−3300000000
χ37444441-241-24441-21-21-200441-21-21-21-20000000000011-2-20000000000001-2000000
χ38444441-241-24441-21-21-200-4-41-21-21-21-200000000000-1-122000000000000-12000000
χ39444441-2-41-24-4-41-21-21-2004-4-121-2-12-1200000000000-1-1220000000000001-2000000
χ40444441-2-41-24-4-41-21-21-200-44-121-2-12-120000000000011-2-2000000000000-12000000
χ4144444-214-21444-21-21-210044-21-21-21-2100000000000-2-211000000000000-21000000
χ4244444-214-21444-21-21-2100-4-4-21-21-21-210000000000022-1-10000000000002-1000000
χ4344444-21-4-214-4-4-21-21-21004-42-1-212-12-10000000000022-1-1000000000000-21000000
χ4444444-21-4-214-4-4-21-21-2100-442-1-212-12-100000000000-2-2110000000000002-1000000
χ454-440-4440-4-400044-4-4004i−4i0000000000000004i−4i0000000000000000000000000000
χ464-440-4440-4-400044-4-400−4i4i000000000000000−4i4i0000000000000000000000000000
χ474-4-202440-4-4000-2-222004i−4i000000000000000−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000
χ484-4-202440-4-4000-2-222004i−4i000000000000000−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000
χ494-4-202440-4-4000-2-22200−4i4i0000000000000002i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000
χ504-4-202440-4-4000-2-22200−4i4i0000000000000002i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000
χ51888-882-402-4-8002-42-4-24000000-24000000000000000000000000000000000000000
χ52888-88-420-42-800-42-424-20000004-2000000000000000000000000000000000000000
χ5388-48-42-482-4-4-4-4-12-122-400002-4-12-12-1200000000000000000000000000000000000
χ5488-48-42-4-82-4-444-12-122-40000-24-121-21-200000000000000000000000000000000000
χ5588-48-4-428-42-4-4-42-12-1-420000-422-12-12-100000000000000000000000000000000000
χ5688-48-4-42-8-42-4442-12-1-4200004-22-1-21-2100000000000000000000000000000000000
χ5788-4-8-42-402-44−4i34i3-12-12-240000001-2−i32i3i3−2i300000000000000000000000000000000000
χ5888-4-8-42-402-444i3−4i3-12-12-240000001-2i3−2i3−i32i300000000000000000000000000000000000
χ5988-4-8-4-420-424−4i34i32-12-14-2000000-212i3−i3−2i3i300000000000000000000000000000000000
χ6088-4-8-4-420-4244i3−4i32-12-14-2000000-21−2i3i32i3−i300000000000000000000000000000000000
χ618-880-82-40-240002-4-240000000000000000000000000−3i23i20000000000000000000000
χ628-880-82-40-240002-4-2400000000000000000000000003i2−3i20000000000000000000000
χ638-880-8-4204-2000-424-2000000000000000000000000000−3i23i200000000000000000000
χ648-880-8-4204-2000-424-20000000000000000000000000003i2−3i200000000000000000000
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.