Finite Group Databasebeta

← Group #13166539

Character table — Group #13166539

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112224444444466888888999999121616161616161616181818181818181818242424243636363636363636363636364848545454545454108108108
order12346233666612883366121244888826666661212288121224242424242424244688121224242424242466444488488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1111-1-1
χ3111111111111111111111-1-1ii−i−i111111111-1i−i-1-1ii−i−i1111-1-1i−i-1-1iii−i−i−i11ii−i−i-1-1-1i−i
χ4111111111111111111111-1-1−i−iii111111111-1−ii-1-1−i−iii1111-1-1−ii-1-1−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
χ61111111111111-1-111111111-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-111
χ71111111111111-1-1111111-1-1ii−i−i-111111111-1i−i-1-1ii−i−i-1-1-1-1-1-1i−i-1-1iii−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−ii-1-1−i−i−iiii-1-1ii−i−i111i−i
χ911111-111-1-111111111111111111-1-1-1-1-1-1-1111111111111111-11-1-1-1-11-1-11-1-1-1-1111111-1-1-1
χ1011111-111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111-1111-1-1-111-111-1-1-1-1-1-111-111
χ1111111-111-1-111111111111-1-1ii−i−i-1-1-1-1-1-1-111-1i−i-1-1ii−i−i11111-1−ii11i−i−i−iii-1-1ii−i−i-1-11−ii
χ1211111-111-1-111111111111-1-1−i−iii-1-1-1-1-1-1-111-1−ii-1-1−i−iii11111-1i−i11−iiii−i−i-1-1−i−iii-1-11i−i
χ1311111-111-1-1111-1-11111111111111-1-1-1-1-1-111111111111-1-1-1-1-11-1-1-1-11-1-11-1-111-1-1-1-1-1-1111
χ1411111-111-1-1111-1-111111111-1-1-1-11-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1111-1-1-111-111111111-1-11-1-1
χ1511111-111-1-1111-1-1111111-1-1ii−i−i1-1-1-1-1-1-111-1i−i-1-1ii−i−i-1-1-1-11-1−ii11i−i−i−iii11−i−iii11-1i−i
χ1611111-111-1-1111-1-1111111-1-1−i−iii1-1-1-1-1-1-111-1−ii-1-1−i−iii-1-1-1-11-1i−i11−iiii−i−i11ii−i−i11-1−ii
χ17222-220220022-2002222-2-22222220000000-2-2-2-2-222222200000-20000-200-20000000000000
χ18222-220220022-2002222-2-222-2-2-2-20000000-2-2-22222-2-2-2-200000-2000020020000000000000
χ19222-220220022-2002222-2-2-2-22i2i−2i−2i0000000-2-22−2i2i-2-22i2i−2i−2i0000020000−2i002i0000000000000
χ20222-220220022-2002222-2-2-2-2−2i−2i2i2i0000000-2-222i−2i-2-2−2i−2i2i2i00000200002i00−2i0000000000000
χ2122-12-1222-1-122-100-1-1-1-122222222022-1-1-1-1-1-1222-1-1-1-1-1-100002-122-1-1-1-1-1-1-1-100000000000
χ2222-12-1222-1-122-100-1-1-1-12222-2-2-2-2022-1-1-1-1-1-12-2-2-1-1111100002-1-2-2-1-111111100000000000
χ2322-12-1222-1-122-100-1-1-1-122-2-22i2i−2i−2i022-1-1-1-1-1-1-22i−2i11−i−iii0000-212i−2i11−i−i−iiii00000000000
χ2422-12-1222-1-122-100-1-1-1-122-2-2−2i−2i2i2i022-1-1-1-1-1-1-2−2i2i11ii−i−i0000-21−2i2i11iii−i−i−i00000000000
χ2522-12-1-2221122-100-1-1-1-1222222220-2-21111-1-1222-1-1-1-1-1-10000-2-1-2-211-111-11100000000000
χ2622-12-1-2221122-100-1-1-1-12222-2-2-2-20-2-21111-1-12-2-2-1-111110000-2-122111-1-11-1-100000000000
χ2722-12-1-2221122-100-1-1-1-122-2-22i2i−2i−2i0-2-21111-1-1-22i−2i11−i−iii000021−2i2i-1-1−iiii−i−i00000000000
χ2822-12-1-2221122-100-1-1-1-122-2-2−2i−2i2i2i0-2-21111-1-1-2−2i2i11ii−i−i0000212i−2i-1-1i−i−i−iii00000000000
χ2922-1-2-1022−i3i322100-1-1-1-1-2-2222222000−i3−i3i3i311-2-2-2-1-1-1-1-1-100000100−i3i31−i3i31−i3i300000000000
χ3022-1-2-1022−i3i322100-1-1-1-1-2-222-2-2-2-2000−i3−i3i3i311-222-1-1111100000100−i3i3-1i3−i3-1i3−i300000000000
χ3122-1-2-1022−i3i322100-1-1-1-1-2-2-2-22i2i−2i−2i000−i3−i3i3i3112−2i2i11−i−iii00000-100i3−i3i3−3−i−3300000000000
χ3222-1-2-1022−i3i322100-1-1-1-1-2-2-2-2−2i−2i2i2i000−i3−i3i3i31122i−2i11ii−i−i00000-100i3−i3−i−33i3−300000000000
χ3322-1-2-1022i3−i322100-1-1-1-1-2-2222222000i3i3−i3−i311-2-2-2-1-1-1-1-1-100000100i3−i31i3−i31i3−i300000000000
χ3422-1-2-1022i3−i322100-1-1-1-1-2-222-2-2-2-2000i3i3−i3−i311-222-1-1111100000100i3−i3-1−i3i3-1−i3i300000000000
χ3522-1-2-1022i3−i322100-1-1-1-1-2-2-2-22i2i−2i−2i000i3i3−i3−i3112−2i2i11−i−iii00000-100−i3i3i−33−i3−300000000000
χ3622-1-2-1022i3−i322100-1-1-1-1-2-2-2-2−2i−2i2i2i000i3i3−i3−i31122i−2i11ii−i−i00000-100−i3i3−i3−3i−3300000000000
χ372-220-202200-2-202−222-2-2002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322−2−2000000000000001+i−1−i1−i−1+i−i2i2000
χ382-220-202200-2-202−222-2-2002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322−2−200000000000000−1−i1+i−1+i1−i−i2i2000
χ392-220-202200-2-202−222-2-200−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322−2−2000000000000001−i−1+i1+i−1−ii2−i2000
χ402-220-202200-2-202−222-2-200−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322−2−200000000000000−1+i1−i−1−i1+ii2−i2000
χ412-220-202200-2-20−2222-2-2002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2−22200000000000000−1−i1+i−1+i1−ii2−i2000
χ422-220-202200-2-20−2222-2-2002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2−222000000000000001+i−1−i1−i−1+ii2−i2000
χ432-220-202200-2-20−2222-2-200−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2−22200000000000000−1+i1−i−1−i1+i−i2i2000
χ442-220-202200-2-20−2222-2-200−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2−222000000000000001−i−1+i1+i−1−i−i2i2000
χ454444441-2441-24441-21-21-200000041-21-21-21-20000000001-21-20000000000001-2000000000
χ464444441-2441-24-4-41-21-21-2000000-41-21-21-21-2000000000-12-12000000000000-12000000000
χ47444444-2144-21444-21-21-210000004-21-21-21-21000000000-21-21000000000000-21000000000
χ48444444-2144-214-4-4-21-21-21000000-4-21-21-21-210000000002-12-10000000000002-1000000000
χ4944444-41-2-4-41-24441-21-21-2000000-4-12-12-121-20000000001-21-2000000000000-12000000000
χ5044444-41-2-4-41-24-4-41-21-21-20000004-12-12-121-2000000000-12-120000000000001-2000000000
χ5144444-4-21-4-4-21444-21-21-21000000-42-12-12-1-21000000000-21-210000000000002-1000000000
χ5244444-4-21-4-4-214-4-4-21-21-2100000042-12-12-1-210000000002-12-1000000000000-21000000000
χ534-4-20204400-4-4000-2-222004i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000000000−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000
χ544-4-20204400-4-4000-2-222004i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13000000000000−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000
χ554-4-20204400-4-4000-2-22200−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000
χ564-4-20204400-4-4000-2-22200−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000
χ57888-8802-4002-4-8002-42-4-240000000000000-24000000000000000000000000000000000000
χ58888-880-4200-42-800-42-424-200000000000004-2000000000000000000000000000000000000
χ5988-48-482-4-4-42-4-400-12-122-400000002-4-12-12-12000000000000000000000000000000000000
χ6088-48-48-42-4-4-42-4002-12-1-420000000-422-12-12-1000000000000000000000000000000000000
χ6188-48-4-82-4442-4-400-12-122-40000000-241-21-2-12000000000000000000000000000000000000
χ6288-48-4-8-4244-42-4002-12-1-4200000004-2-21-212-1000000000000000000000000000000000000
χ6388-4-8-402-4−4i34i32-4400-12-12-24000000000−i32i3i3−2i31-2000000000000000000000000000000000000
χ6488-4-8-402-44i3−4i32-4400-12-12-24000000000i3−2i3−i32i31-2000000000000000000000000000000000000
χ6588-4-8-40-42−4i34i3-424002-12-14-20000000002i3−i3−2i3i3-21000000000000000000000000000000000000
χ6688-4-8-40-424i3−4i3-424002-12-14-2000000000−2i3i32i3−i3-21000000000000000000000000000000000000
χ678-880-802-400-24042−422-4-24000000000000000000000000002−22−22200000000000000000000000
χ688-880-802-400-240−42422-4-2400000000000000000000000000−2222−2200000000000000000000000
χ698-880-80-42004-2042−42-424-200000000000000000000000000−22222−200000000000000000000000
χ708-880-80-42004-20−4242-424-20000000000000000000000000022−2−22200000000000000000000000
χ7116-16-80804-800-48000-242-400000000000000000000000000000000000000000000000000000
χ7216-16-8080-84008-40004-2-4200000000000000000000000000000000000000000000000000000

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