Finite Group Databasebeta

← Group #13180648

Character table — Group #13180648

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111133334444444488889999121212121212121216161616161616161616161616161616272727275454545454545454545454545454545472727272
order12442244336612121212361212224466661212121233336666121212121212121222448888888888888888661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1
χ411111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1
χ511-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ611-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ711-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ811-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ91-1i−i1-1i−i11-1-1ii−i−i1-1i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ131-1i−i
χ101-1i−i1-1i−i11-1-1ii−i−i1-1i−i1-1i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ131-1i−i
χ111-1i−i1-1i−i11-1-1ii−i−i1-1i−i-11−ii11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23-11−ii
χ121-1i−i1-1i−i11-1-1ii−i−i1-1i−i-11−ii11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11−iiζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23-11−ii
χ131-1−ii1-1−ii11-1-1−i−iii1-1−ii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ231-1−ii
χ141-1−ii1-1−ii11-1-1−i−iii1-1−ii1-1−ii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ231-1−ii
χ151-1−ii1-1−ii11-1-1−i−iii1-1−ii-11i−i11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11i−iζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13-11i−i
χ161-1−ii1-1−ii11-1-1−i−iii1-1−ii-11i−i11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11i−i−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13-11i−i
χ172222222222222222-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1
χ182222222222222222-1-1-1-1-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000001111
χ1922-2-222-2-22222-2-2-2-2-1-11122-2-22222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-20000000000000000-1-111
χ2022-2-222-2-22222-2-2-2-2-1-111-2-2222222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222000000000000000011-1-1
χ212-22i−2i2-22i−2i22-2-22i2i−2i−2i-11−ii2-22i−2i22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii2-22i−2i0000000000000000-11−ii
χ222-22i−2i2-22i−2i22-2-22i2i−2i−2i-11−ii-22−2i2i22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii-22−2i2i00000000000000001-1i−i
χ232-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i-11i−i2-2−2i2i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i2-2−2i2i0000000000000000-11i−i
χ242-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i-11i−i-222i−2i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i-222i−2i00000000000000001-1−ii
χ253333-1-1-1-13333333300003333-1-1-1-1-1-1-1-10000000000000000-1-1-1-111111111-1-1-1-1-1-1-1-10000
χ263333-1-1-1-13333333300003333-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1-1-1-1111111110000
χ273333-1-1-1-1333333330000-3-3-3-3-1-1-1-1-1-1-1-100000000000000001111iiii−i−i−i−i−i−i−i−iiiii0000
χ283333-1-1-1-1333333330000-3-3-3-3-1-1-1-1-1-1-1-100000000000000001111−i−i−i−iiiiiiiii−i−i−i−i0000
χ2933-3-3-1-1113333-3-3-3-3000033-3-3-1-1-1-111110000000000000000-1-111ii−i−iii−i−i−i−iii−i−iii0000
χ3033-3-3-1-1113333-3-3-3-3000033-3-3-1-1-1-111110000000000000000-1-111−i−iii−i−iiiii−i−iii−i−i0000
χ3133-3-3-1-1113333-3-3-3-30000-3-333-1-1-1-11111000000000000000011-1-111-1-1-1-111-1-11111-1-10000
χ3233-3-3-1-1113333-3-3-3-30000-3-333-1-1-1-11111000000000000000011-1-1-1-11111-1-111-1-1-1-1110000
χ333-33i−3i-11−ii33-3-33i3i−3i−3i00003-33i−3i-1-111−i−iii0000000000000000-11−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ343-33i−3i-11−ii33-3-33i3i−3i−3i00003-33i−3i-1-111−i−iii0000000000000000-11−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ353-33i−3i-11−ii33-3-33i3i−3i−3i0000-33−3i3i-1-111−i−iii00000000000000001-1i−i−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ230000
χ363-33i−3i-11−ii33-3-33i3i−3i−3i0000-33−3i3i-1-111−i−iii00000000000000001-1i−iζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ230000
χ373-3−3i3i-11i−i33-3-3−3i−3i3i3i00003-3−3i3i-1-111ii−i−i0000000000000000-11i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000
χ383-3−3i3i-11i−i33-3-3−3i−3i3i3i00003-3−3i3i-1-111ii−i−i0000000000000000-11i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000
χ393-3−3i3i-11i−i33-3-3−3i−3i3i3i0000-333i−3i-1-111ii−i−i00000000000000001-1−iiζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ130000
χ403-3−3i3i-11i−i33-3-3−3i−3i3i3i0000-333i−3i-1-111ii−i−i00000000000000001-1−ii−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ130000
χ41444444441-21-21-21-2444400001-21-21-21-211-2-211-2-211-2-211-2-2000000000000000000000000
χ42444444441-21-21-21-2-2-2-2-200001-21-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000000
χ43444444441-21-21-21-2-2-2-2-200001-21-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000000
χ4444444444-21-21-21-2144440000-21-21-21-21-2-211-2-211-2-211-2-211000000000000000000000000
χ4544444444-21-21-21-21-2-2-2-20000-21-21-21-2111−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000000000000
χ4644444444-21-21-21-21-2-2-2-20000-21-21-21-2111−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i32000000000000000000000000
χ4744-4-444-4-41-21-2-12-1244-4-400001-21-2-12-1211-2-211-2-2-1-122-1-122000000000000000000000000
χ4844-4-444-4-41-21-2-12-12-2-22200001-21-2-12-12−1−3i32−1+3i3211−1−3i32−1+3i32111+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000
χ4944-4-444-4-41-21-2-12-12-2-22200001-21-2-12-12−1+3i32−1−3i3211−1+3i32−1−3i32111−3i321+3i32-1-11−3i321+3i32-1-1000000000000000000000000
χ5044-4-444-4-4-21-212-12-144-4-40000-21-212-12-1-2-211-2-21122-1-122-1-1000000000000000000000000
χ5144-4-444-4-4-21-212-12-1-2-2220000-21-212-12-111−1−3i32−1+3i3211−1−3i32−1+3i32-1-11+3i321−3i32-1-11+3i321−3i32000000000000000000000000
χ5244-4-444-4-4-21-212-12-1-2-2220000-21-212-12-111−1+3i32−1−3i3211−1+3i32−1−3i32-1-11−3i321+3i32-1-11−3i321+3i32000000000000000000000000
χ534-44i−4i4-44i−4i1-2-12i−2i−i2i4-44i−4i00001-2-12i−2i−i2i11-2-2-1-122ii−2i−2i−i−i2i2i000000000000000000000000
χ544-44i−4i4-44i−4i1-2-12i−2i−i2i-22−2i2i00001-2-12i−2i−i2i−1−3i32−1+3i32111+3i321−3i32-1-1−ζ14+2ζ222ζ14−ζ22iiζ14−2ζ22−2ζ14+ζ22−i−i000000000000000000000000
χ554-44i−4i4-44i−4i1-2-12i−2i−i2i-22−2i2i00001-2-12i−2i−i2i−1+3i32−1−3i32111−3i321+3i32-1-12ζ14−ζ22−ζ14+2ζ22ii−2ζ14+ζ22ζ14−2ζ22−i−i000000000000000000000000
χ564-44i−4i4-44i−4i-212-1−2ii2i−i4-44i−4i0000-212-1−2ii2i−i-2-21122-1-1−2i−2iii2i2i−i−i000000000000000000000000
χ574-44i−4i4-44i−4i-212-1−2ii2i−i-22−2i2i0000-212-1−2ii2i−i11−1−3i32−1+3i32-1-11+3i321−3i32ii−ζ14+2ζ222ζ14−ζ22−i−iζ14−2ζ22−2ζ14+ζ22000000000000000000000000
χ584-44i−4i4-44i−4i-212-1−2ii2i−i-22−2i2i0000-212-1−2ii2i−i11−1+3i32−1−3i32-1-11−3i321+3i32ii2ζ14−ζ22−ζ14+2ζ22−i−i−2ζ14+ζ22ζ14−2ζ22000000000000000000000000
χ594-4−4i4i4-4−4i4i1-2-12−i2ii−2i4-4−4i4i00001-2-12−i2ii−2i11-2-2-1-122−i−i2i2iii−2i−2i000000000000000000000000
χ604-4−4i4i4-4−4i4i1-2-12−i2ii−2i-222i−2i00001-2-12−i2ii−2i−1−3i32−1+3i32111+3i321−3i32-1-1ζ14−2ζ22−2ζ14+ζ22−i−i−ζ14+2ζ222ζ14−ζ22ii000000000000000000000000
χ614-4−4i4i4-4−4i4i1-2-12−i2ii−2i-222i−2i00001-2-12−i2ii−2i−1+3i32−1−3i32111−3i321+3i32-1-1−2ζ14+ζ22ζ14−2ζ22−i−i2ζ14−ζ22−ζ14+2ζ22ii000000000000000000000000
χ624-4−4i4i4-4−4i4i-212-12i−i−2ii4-4−4i4i0000-212-12i−i−2ii-2-21122-1-12i2i−i−i−2i−2iii000000000000000000000000
χ634-4−4i4i4-4−4i4i-212-12i−i−2ii-222i−2i0000-212-12i−i−2ii11−1−3i32−1+3i32-1-11+3i321−3i32−i−iζ14−2ζ22−2ζ14+ζ22ii−ζ14+2ζ222ζ14−ζ22000000000000000000000000
χ644-4−4i4i4-4−4i4i-212-12i−i−2ii-222i−2i0000-212-12i−i−2ii11−1+3i32−1−3i32-1-11−3i321+3i32−i−i−2ζ14+ζ22ζ14−2ζ22ii2ζ14−ζ22−ζ14+2ζ22000000000000000000000000
χ6512121212-4-4-4-43-63-63-63-600000000-12-12-12-120000000000000000000000000000000000000000
χ6612121212-4-4-4-4-63-63-63-63000000002-12-12-12-10000000000000000000000000000000000000000
χ671212-12-12-4-4443-63-6-36-3600000000-12-121-21-20000000000000000000000000000000000000000
χ681212-12-12-4-444-63-636-36-3000000002-12-1-21-210000000000000000000000000000000000000000
χ6912-1212i−12i-44−4i4i3-6-363i−6i−3i6i00000000-121-2−i2ii−2i0000000000000000000000000000000000000000
χ7012-1212i−12i-44−4i4i-636-3−6i3i6i−3i000000002-1-212i−i−2ii0000000000000000000000000000000000000000
χ7112-12−12i12i-444i−4i3-6-36−3i6i3i−6i00000000-121-2i−2i−i2i0000000000000000000000000000000000000000
χ7212-12−12i12i-444i−4i-636-36i−3i−6i3i000000002-1-21−2ii2i−i0000000000000000000000000000000000000000

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