Finite Group Databasebeta

← Group #13166542

Character table — Group #13166542

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112224444444488888899121216161616161616161818181818181818181818242424243636363636363636363636364848108108108108108108
order1234623366661233661212444866666612122888812122424242424242424468812122424242424241212244888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1111-1-11-1-1
χ3111111111111111111111-1-11111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111-111
χ51111111111111111111-1-11111111111-1ii−i−i-1-1ii−i−i1111-1-1i−i-1-1iii−i−i−i11-1i−i-1i−i
χ61111111111111111111-1-11111111111-1−i−iii-1-1−i−iii1111-1-1−ii-1-1−i−i−iiii11-1−ii-1−ii
χ71111111111111111111-1-1-1-111111111-1ii−i−i-1-1ii−i−i-1-1-1-1-1-1i−i-1-1iii−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−ii-1-1−i−i−iiii-1-11i−i1i−i
χ911111-111-1-1111111111111-1-1-1-1-1-1-11111111111111-1-1-1-1-11-1-1-1-11-1-11-1-1111-1-1-111
χ1011111-111-1-1111111111111-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-111-11111111-1-1-1
χ1111111-111-1-111111111111-11-1-1-1-1-1-111111111111111111-11-1-1-1-11-1-11-1-1-1-1-1111-1-1
χ1211111-111-1-111111111111-11-1-1-1-1-1-1111-1-1-1-111-1-1-1-11111-1111-1-1-111-111-1-1-1-1-1111
χ1311111-111-1-1111111111-1-11-1-1-1-1-1-1-111-1ii−i−i-1-1ii−i−i-1-1-1-11-1−ii11i−i−i−iii11-1−ii1i−i
χ1411111-111-1-1111111111-1-11-1-1-1-1-1-1-111-1−i−iii-1-1−i−iii-1-1-1-11-1i−i11−iiii−i−i11-1i−i1−ii
χ1511111-111-1-1111111111-1-1-11-1-1-1-1-1-111-1ii−i−i-1-1ii−i−i11111-1−ii11i−i−i−iii-1-11i−i-1−ii
χ1611111-111-1-1111111111-1-1-11-1-1-1-1-1-111-1−i−iii-1-1−i−iii11111-1i−i11−iiii−i−i-1-11−ii-1i−i
χ17222-220220022-22222-2-22200000000-2-2-22-22-222222200000-20000-200-20000000000
χ18222-220220022-22222-2-22200000000-2-2-2-22-2222-2-2-2-200000-2000020020000000000
χ19222-220220022-22222-2-2-2-200000000-2-222i−2i−2i2i-2-22i2i−2i−2i0000020000−2i002i0000000000
χ20222-220220022-22222-2-2-2-200000000-2-22−2i2i2i−2i-2-2−2i−2i2i2i00000200002i00−2i0000000000
χ2122-12-1222-1-122-1-1-1-1-122220022-1-1-1-1-1-122222-1-1-1-1-1-100002-122-1-1-1-1-1-1-1-100000000
χ2222-12-1222-1-122-1-1-1-1-122220022-1-1-1-1-1-12-2-2-2-2-1-1111100002-1-2-2-1-111111100000000
χ2322-12-1222-1-122-1-1-1-1-122-2-20022-1-1-1-1-1-1-22i2i−2i−2i11−i−iii0000-212i−2i11−i−i−iiii00000000
χ2422-12-1222-1-122-1-1-1-1-122-2-20022-1-1-1-1-1-1-2−2i−2i2i2i11ii−i−i0000-21−2i2i11iii−i−i−i00000000
χ2522-12-1-2221122-1-1-1-1-1222200-2-21111-1-122222-1-1-1-1-1-10000-2-1-2-211-111-11100000000
χ2622-12-1-2221122-1-1-1-1-1222200-2-21111-1-12-2-2-2-2-1-111110000-2-122111-1-11-1-100000000
χ2722-12-1-2221122-1-1-1-1-122-2-200-2-21111-1-1-22i2i−2i−2i11−i−iii000021−2i2i-1-1−iiii−i−i00000000
χ2822-12-1-2221122-1-1-1-1-122-2-200-2-21111-1-1-2−2i−2i2i2i11ii−i−i0000212i−2i-1-1i−i−i−iii00000000
χ2922-1-2-1022−i3i3221-1-1-1-1-2-2220000−i3−i3i3i311-22-22-2-1-1-1-1-1-100000100−i3i31−i3i31−i3i300000000
χ3022-1-2-1022−i3i3221-1-1-1-1-2-2220000−i3−i3i3i311-2-22-22-1-1111100000100−i3i3-1i3−i3-1i3−i300000000
χ3122-1-2-1022−i3i3221-1-1-1-1-2-2-2-20000−i3−i3i3i31122i−2i−2i2i11−i−iii00000-100i3−i3i3−3−i−3300000000
χ3222-1-2-1022−i3i3221-1-1-1-1-2-2-2-20000−i3−i3i3i3112−2i2i2i−2i11ii−i−i00000-100i3−i3−i−33i3−300000000
χ3322-1-2-1022i3−i3221-1-1-1-1-2-2220000i3i3−i3−i311-22-22-2-1-1-1-1-1-100000100i3−i31i3−i31i3−i300000000
χ3422-1-2-1022i3−i3221-1-1-1-1-2-2220000i3i3−i3−i311-2-22-22-1-1111100000100i3−i3-1−i3i3-1−i3i300000000
χ3522-1-2-1022i3−i3221-1-1-1-1-2-2-2-20000i3i3−i3−i31122i−2i−2i2i11−i−iii00000-100−i3i3i−33−i3−300000000
χ3622-1-2-1022i3−i3221-1-1-1-1-2-2-2-20000i3i3−i3−i3112−2i2i2i−2i11ii−i−i00000-100−i3i3−i3−3i−3300000000
χ374444441-2441-241-21-21-200441-21-21-21-20000000000011-2-20000000000001-2000000
χ384444441-2441-241-21-21-200-4-41-21-21-21-200000000000-1-122000000000000-12000000
χ39444444-2144-214-21-21-210044-21-21-21-2100000000000-2-211000000000000-21000000
χ40444444-2144-214-21-21-2100-4-4-21-21-21-210000000000022-1-10000000000002-1000000
χ4144444-41-2-4-41-241-21-21-2004-4-12-12-121-200000000000-1-1220000000000001-2000000
χ4244444-41-2-4-41-241-21-21-200-44-12-12-121-20000000000011-2-2000000000000-12000000
χ4344444-4-21-4-4-214-21-21-21004-42-12-12-1-210000000000022-1-1000000000000-21000000
χ4444444-4-21-4-4-214-21-21-2100-442-12-12-1-2100000000000-2-2110000000000002-1000000
χ454-440-404400-4-4044-4-4004i−4i0000000000000004i−4i0000000000000000000000000000
χ464-440-404400-4-4044-4-400−4i4i000000000000000−4i4i0000000000000000000000000000
χ474-4-20204400-4-40-2-222004i−4i000000000000000−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000
χ484-4-20204400-4-40-2-222004i−4i000000000000000−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000
χ494-4-20204400-4-40-2-22200−4i4i0000000000000002i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000
χ504-4-20204400-4-40-2-22200−4i4i0000000000000002i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000
χ51888-8802-4002-4-82-42-4-240000000000-2400000000000000000000000000000000000
χ52888-880-4200-42-8-42-424-200000000004-200000000000000000000000000000000000
χ5388-48-482-4-4-42-4-4-12-122-400002-4-12-12-1200000000000000000000000000000000000
χ5488-48-48-42-4-4-42-42-12-1-420000-422-12-12-100000000000000000000000000000000000
χ5588-48-4-82-4442-4-4-12-122-40000-241-21-2-1200000000000000000000000000000000000
χ5688-48-4-8-4244-42-42-12-1-4200004-2-21-212-100000000000000000000000000000000000
χ5788-4-8-402-4−4i34i32-44-12-12-24000000−i32i3i3−2i31-200000000000000000000000000000000000
χ5888-4-8-402-44i3−4i32-44-12-12-24000000i3−2i3−i32i31-200000000000000000000000000000000000
χ5988-4-8-40-42−4i34i3-4242-12-14-20000002i3−i3−2i3i3-2100000000000000000000000000000000000
χ6088-4-8-40-424i3−4i3-4242-12-14-2000000−2i3i32i3−i3-2100000000000000000000000000000000000
χ618-880-802-400-2402-4-240000000000000000000000000−3i23i20000000000000000000000
χ628-880-802-400-2402-4-2400000000000000000000000003i2−3i20000000000000000000000
χ638-880-80-42004-20-424-2000000000000000000000000000−3i23i200000000000000000000
χ648-880-80-42004-20-424-20000000000000000000000000003i2−3i200000000000000000000
χ6516-16-80804-800-480-242-40000000000000000000000000000000000000000000000000
χ6616-16-8080-84008-404-2-420000000000000000000000000000000000000000000000000

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