Finite Group Databasebeta

← Group #13166100

Character table — Group #13166100

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222224444668888999912121212161616161616161616161616161616161818181818181818242436363636363636363636363654547272727272727272
order1244336612121212361212243612128888661212333366661212121212121212444488886122488121212122424242488612242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ31111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ511-1-11111-1-1-1-111-1-1-1111-1-1ii−i−i-1-11111111111-1-1-1-1-1-1-1-1ii−i−i11-1-1-111-1i−iii−i−i11-1-1i−i1-1i−iii−i−i
χ611-1-11111-1-1-1-111-1-1-1111-1-1ii−i−i-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-111-11-11−ii−i−iii-1-111i−i-11−iiii−i−i
χ711-1-11111-1-1-1-111-1-1-1111-1-1−i−iii-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-111-11-11i−iii−i−i-1-111−ii-11i−i−i−iii
χ811-1-11111-1-1-1-111-1-1-1111-1-1−i−iii-1-11111111111-1-1-1-1-1-1-1-1−i−iii11-1-1-111-1−ii−i−iii11-1-1−ii1-1−ii−i−iii
χ9222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022000000000000220000-1-1-1-1
χ10222222222222222222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022000000000000-2-200001111
χ1122222-12-1-1-122-1-1-1-12222220000-122-12-1-1-12-1-1-122-1-1-1-1-1-100002222-1-122000000-1-1-1-100-1-1000000
χ1222222-12-1-1-122-1-1-1-12222220000-122-12-1-1-12-1-1-122-1-1-1-1-1-10000-2-2-2-2-1-1-2-200000011110011000000
χ132222-12-1222-1-1-1-1-1-122222200002-1-12-12-1-1-12-1-1-1-122-1-1-1-122220000-1-10022-1-1-1-100000000-1-10000
χ142222-12-1222-1-1-1-1-1-122222200002-1-12-12-1-1-12-1-1-1-122-1-1-1-1-2-2-2-20000-1-100-2-2111100000000110000
χ1522-2-22222-2-2-2-222-2-2-22-1-1112i2i−2i−2i-2-222-1-1-1-1-1-1-1-11111111100000000-220000000000002i−2i0000−i−iii
χ1622-2-22222-2-2-2-222-2-2-22-1-111−2i−2i2i2i-2-222-1-1-1-1-1-1-1-11111111100000000-22000000000000−2i2i0000ii−i−i
χ1722-2-22-12-111-2-2-1-111-2222-2-200001-22-12-1-1-12-1-1-1-2-2111111000022-2-21-12-2000000-1-11100-11000000
χ1822-2-22-12-111-2-2-1-111-2222-2-200001-22-12-1-1-12-1-1-1-2-21111110000-2-2221-1-2200000011-1-1001-1000000
χ1922-2-2-12-12-2-211-1-111-2222-2-20000-21-12-12-1-1-12-1-111-2-211112i2i−2i−2i00001-1002i−2i−i−iii00000000−ii0000
χ2022-2-2-12-12-2-211-1-111-2222-2-20000-21-12-12-1-1-12-1-111-2-21111−2i−2i2i2i00001-100−2i2iii−i−i00000000i−i0000
χ212-22i−2i22-2-22i−2i2i−2i2-22i−2i00-11i−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000-1-1-1-11111i−ii−iii−i−i1−i−1+i1+i−1−i−i2i22−20000001−i−1+i1+i−1−i−i2i22−2000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ222-22i−2i22-2-22i−2i2i−2i2-22i−2i00-11i−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000-1-1-1-11111i−ii−iii−i−i−1+i1−i−1−i1+ii2−i2−22000000−1+i1−i−1−i1+ii2−i2−22000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ232-22i−2i22-2-22i−2i2i−2i2-22i−2i00-11i−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000-1-1-1-11111i−ii−iii−i−i1−i−1+i1+i−1−ii2−i2−220000001−i−1+i1+i−1−ii2−i2−22000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ242-22i−2i22-2-22i−2i2i−2i2-22i−2i00-11i−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000-1-1-1-11111i−ii−iii−i−i−1+i1−i−1−i1+i−i2i22−2000000−1+i1−i−1−i1+i−i2i22−2000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ252-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i00-11−ii−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000-1-1-1-11111−ii−ii−i−iii1+i−1−i1−i−1+ii2−i22−20000001+i−1−i1−i−1+ii2−i22−2000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ262-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i00-11−ii−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000-1-1-1-11111−ii−ii−i−iii−1−i1+i−1+i1−i−i2i2−22000000−1−i1+i−1+i1−i−i2i2−22000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ272-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i00-11−ii2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000-1-1-1-11111−ii−ii−i−iii1+i−1−i1−i−1+i−i2i2−220000001+i−1−i1−i−1+i−i2i2−22000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ282-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i00-11−ii2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000-1-1-1-11111−ii−ii−i−iii−1−i1+i−1+i1−ii2−i22−2000000−1−i1+i−1+i1−ii2−i22−2000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ293333333333333333-1-100003333-1-1-1-1000000000000000011111111-1-1-1-1-1-111111111-1-1-1-1-1-10000
χ303333333333333333-1-100003333-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111110000
χ313333333333333333-1-10000-3-3-3-3-1-1-1-100000000000000001111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-10000
χ323333333333333333-1-10000-3-3-3-3-1-1-1-10000000000000000-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1110000
χ3333-3-33333-3-3-3-333-3-31-100003i3i−3i−3i11-1-10000000000000000ii−i−i11-1-11-1-11−iiii−i−i11-1-1−ii-11−ii0000
χ3433-3-33333-3-3-3-333-3-31-100003i3i−3i−3i11-1-10000000000000000−i−iii-1-1111-11-1i−i−i−iii-1-111−ii1-1i−i0000
χ3533-3-33333-3-3-3-333-3-31-10000−3i−3i3i3i11-1-10000000000000000ii−i−i-1-1111-11-1−iiii−i−i-1-111i−i1-1−ii0000
χ3633-3-33333-3-3-3-333-3-31-10000−3i−3i3i3i11-1-10000000000000000−i−iii11-1-11-1-11i−i−i−iii11-1-1i−i-11i−i0000
χ3744444-24-2-2-244-2-2-2-244-2-2-2-20000-244-2-2111-2111-2-211111100000000-2-20000000000000000000000
χ384444-24-2444-2-2-2-2-2-244-2-2-2-200004-2-241-2111-21111-2-2111100000000-2-20000000000000000000000
χ394444-2-2-2-2-2-2-2-211114444440000-2-2-2-2-2-211-2-211-2-2-2-2111100000000110000000000000000000000
χ404444-2-2-2-2-2-2-2-2111144-2-2-2-20000-2-2-2-211−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1+3i32−1−3i32−1+3i3200000000110000000000000000000000
χ414444-2-2-2-2-2-2-2-2111144-2-2-2-20000-2-2-2-211−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1−3i32−1+3i32−1−3i3200000000110000000000000000000000
χ4244-4-44-24-222-4-4-2-222-44-2-22200002-44-2-2111-211122-1-1-1-1-1-1000000002-20000000000000000000000
χ4344-4-4-24-24-4-422-2-222-44-2-2220000-42-241-2111-211-1-122-1-1-1-1000000002-20000000000000000000000
χ4444-4-4-2-2-2-2222211-1-1-4444-4-4000022-2-2-2-211-2-2112222-1-1-1-100000000-110000000000000000000000
χ4544-4-4-2-2-2-2222211-1-1-44-2-222000022-2-211−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321−3i321+3i321−3i3200000000-110000000000000000000000
χ4644-4-4-2-2-2-2222211-1-1-44-2-222000022-2-211−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321+3i321−3i321+3i3200000000-110000000000000000000000
χ474-44i−4i44-4-44i−4i4i−4i4-44i−4i001-1−ii4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300001111-1-1-1-1−ii−ii−i−iii0000000000000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ484-44i−4i44-4-44i−4i4i−4i4-44i−4i001-1−ii−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300001111-1-1-1-1−ii−ii−i−iii0000000000000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ494-44i−4i4-2-42−2i2i4i−4i-22−2i2i00-222i−2i00000000-21112-1-1-12i−2i−ii−i−iii0000−2i22i222−220000000000i2−i2−220000000000
χ504-44i−4i4-2-42−2i2i4i−4i-22−2i2i00-222i−2i00000000-21112-1-1-12i−2i−ii−i−iii00002i2−2i2−22220000000000−i2i22−20000000000
χ514-44i−4i-242-44i−4i−2i2i-22−2i2i00-222i−2i000000001-211-12-1-1−ii2i−2i−i−iii2−2i−2+2i2+2i−2−2i0000000000−1+i1−i−1−i1+i00000000000000
χ524-44i−4i-242-44i−4i−2i2i-22−2i2i00-222i−2i000000001-211-12-1-1−ii2i−2i−i−iii−2+2i2−2i−2−2i2+2i00000000001−i−1+i1+i−1−i00000000000000
χ534-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i001-1i−i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300001111-1-1-1-1i−ii−iii−i−i0000000000000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ544-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i001-1i−i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300001111-1-1-1-1i−ii−iii−i−i0000000000000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ554-4−4i4i4-2-422i−2i−4i4i-222i−2i00-22−2i2i00000000-21112-1-1-1−2i2ii−iii−i−i0000−2i22i2−22220000000000i2−i22−20000000000
χ564-4−4i4i4-2-422i−2i−4i4i-222i−2i00-22−2i2i00000000-21112-1-1-1−2i2ii−iii−i−i00002i2−2i222−220000000000−i2i2−220000000000
χ574-4−4i4i-242-4−4i4i2i−2i-222i−2i00-22−2i2i000000001-211-12-1-1i−i−2i2iii−i−i2+2i−2−2i2−2i−2+2i0000000000−1−i1+i−1+i1−i00000000000000
χ584-4−4i4i-242-4−4i4i2i−2i-222i−2i00-22−2i2i000000001-211-12-1-1i−i−2i2iii−i−i−2−2i2+2i−2+2i2−2i00000000001+i−1−i1−i−1+i00000000000000
χ5966666-36-3-3-366-3-3-3-3-2-2000000001-2-2100000000000000000000222211-2-2000000-1-1-1-10011000000
χ6066666-36-3-3-366-3-3-3-3-2-2000000001-2-2100000000000000000000-2-2-2-21122000000111100-1-1000000
χ616666-36-3666-3-3-3-3-3-3-2-200000000-211-20000000000000000222200001100-2-2-1-1-1-100000000110000
χ626666-36-3666-3-3-3-3-3-3-2-200000000-211-20000000000000000-2-2-2-20000110022111100000000-1-10000
χ6366-6-66-36-333-6-6-3-3332-200000000-12-210000000000000000000022-2-2-11-22000000-1-111001-1000000
χ6466-6-66-36-333-6-6-3-3332-200000000-12-2100000000000000000000-2-222-112-200000011-1-100-11000000
χ6566-6-6-36-36-6-633-3-3332-2000000002-11-200000000000000002i2i−2i−2i0000-1100−2i2i−i−iii00000000i−i0000
χ6666-6-6-36-36-6-633-3-3332-2000000002-11-20000000000000000−2i−2i2i2i0000-11002i−2iii−i−i00000000−ii0000
χ678-88i−8i8-4-84−4i4i8i−8i-44−4i4i002-2−2i2i000000002-1-1-1-2111−2i2ii−iii−i−i00000000000000000000000000000000
χ688-88i−8i-484-88i−8i−4i4i-44−4i4i002-2−2i2i00000000-12-1-11-211i−i−2i2iii−i−i00000000000000000000000000000000
χ698-88i−8i-4-444−4i4i−4i4i2-22i−2i002-2−2i2i00000000-1-11−3i321+3i3211−1+3i32−1−3i32i−ii−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ2200000000000000000000000000000000
χ708-88i−8i-4-444−4i4i−4i4i2-22i−2i002-2−2i2i00000000-1-11+3i321−3i3211−1−3i32−1+3i32i−ii−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ2200000000000000000000000000000000
χ718-88i−8i-4-444−4i4i−4i4i2-22i−2i00-444i−4i0000000022-1-1-2-211−2i2i−2i2iii−i−i00000000000000000000000000000000
χ728-8−8i8i8-4-844i−4i−8i8i-444i−4i002-22i−2i000000002-1-1-1-21112i−2i−ii−i−iii00000000000000000000000000000000
χ738-8−8i8i-484-8−8i8i4i−4i-444i−4i002-22i−2i00000000-12-1-11-211−ii2i−2i−i−iii00000000000000000000000000000000
χ748-8−8i8i-4-4444i−4i4i−4i2-2−2i2i002-22i−2i00000000-1-11−3i321+3i3211−1+3i32−1−3i32−ii−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ2200000000000000000000000000000000
χ758-8−8i8i-4-4444i−4i4i−4i2-2−2i2i002-22i−2i00000000-1-11+3i321−3i3211−1−3i32−1+3i32−ii−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ2200000000000000000000000000000000
χ768-8−8i8i-4-4444i−4i4i−4i2-2−2i2i00-44−4i4i0000000022-1-1-2-2112i−2i2i−2i−i−iii00000000000000000000000000000000
χ7712121212-6-6-6-6-6-6-6-63333-4-4000000002222000000000000000000000000-1-10000000000000000000000
χ781212-12-12-6-6-6-6666633-3-34-400000000-2-2220000000000000000000000001-10000000000000000000000

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