Finite Group Databasebeta

← Group #11787051

Character table — Group #11787051

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111224444444444666688888888999912121212121212121212121212121616181824242424242424242424242436363636363648487272
order12442433668812121212888866121224242424224422448888882424242424242466881212242424242424444488242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ51111111111-1-1111111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ61111111111-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111
χ81111111111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ911-1-1-111111i−i-1-1-1-1ii−i−i-1-111ii−i−i11-1-111-1-1i−i11-1-1ii−i−ii−i-1111i−i-1-1i−i11-1-1ii−i−ii−ii−i1-1
χ1011-1-1-111111i−i-1-1-1-1ii−i−i-1-111ii−i−i11-1-111-1-1i−i-1-111ii−i−ii−i-1111−ii-1-1i−i-1-111−i−iiii−i−ii-11
χ1111-1-1-111111i−i-1-1-1-1−i−iii-1-111ii−i−i11-1-1-1-111−ii11-1-1−i−iiii−i-11-1-1i−i11−ii11-1-1−i−iiii−ii−i-11
χ1211-1-1-111111i−i-1-1-1-1−i−iii-1-111ii−i−i11-1-1-1-111−ii-1-111−i−iiii−i-11-1-1−ii11−ii-1-111ii−i−ii−i−ii1-1
χ1311-1-1-111111−ii-1-1-1-1ii−i−i-1-111−i−iii11-1-1-1-111i−i11-1-1ii−i−i−ii-11-1-1−ii11i−i11-1-1ii−i−i−ii−ii-11
χ1411-1-1-111111−ii-1-1-1-1ii−i−i-1-111−i−iii11-1-1-1-111i−i-1-111ii−i−i−ii-11-1-1i−i11i−i-1-111−i−iii−iii−i1-1
χ1511-1-1-111111−ii-1-1-1-1−i−iii-1-111−i−iii11-1-111-1-1−ii11-1-1−i−iii−ii-1111−ii-1-1−ii11-1-1−i−iii−ii−ii1-1
χ1611-1-1-111111−ii-1-1-1-1−i−iii-1-111−i−iii11-1-111-1-1−ii-1-111−i−iii−ii-1111i−i-1-1−ii-1-111ii−i−i−iii−i-11
χ172222222222222222000022222222-2-2-2-20000000000000022-2-20000000000000000-2-20000
χ182222222222-2-2222200002222-2-2-2-2-2-2-2-200000000000000-2-2-2-20000000000000000220000
χ192222-2-222220022220000-2-2-2-20000-2-2-2-22-22-2000000000000222-2002-20000000000000000
χ202222-2-222220022220000-2-2-2-20000-2-2-2-2-22-2200000000000022-2200-220000000000000000
χ212222-2-222220022222222-2-2-2-2000022220000-2-20000222200-2-2000000-2-200000000000000
χ222222-2-22222002222-2-2-2-2-2-2-2-2000022220000220000-2-2-2-200-2-20000002200000000000000
χ2322-2-22-2222200-2-2-2-2000022-2-20000-2-2222-2-22000000000000-222-200-220000000000000000
χ2422-2-22-2222200-2-2-2-2000022-2-20000-2-222-222-2000000000000-22-22002-20000000000000000
χ2522-2-22-2222200-2-2-2-22i2i−2i−2i22-2-2000022-2-20000−2i2i00002i2i−2i−2i002-2000000−2i2i00000000000000
χ2622-2-22-2222200-2-2-2-2−2i−2i2i2i22-2-2000022-2-200002i−2i0000−2i−2i2i2i002-20000002i−2i00000000000000
χ2722-2-2-2222222i−2i-2-2-2-20000-2-2222i2i−2i−2i-2-222000000000000002i−2i2-20000000000000000−2i2i0000
χ2822-2-2-222222−2i2i-2-2-2-20000-2-222−2i−2i2i2i-2-22200000000000000−2i2i2-200000000000000002i−2i0000
χ292-22i−2i0022-2-2002i−2i2i−2i2ζ−2ζ2ζ3−2ζ3000000002-22i−2i000000i2−i22−22ζ−2ζ2ζ3−2ζ3000000000000i2−i22−21−i−1+i1+i−1−i000000
χ302-22i−2i0022-2-2002i−2i2i−2i2ζ−2ζ2ζ3−2ζ3000000002-22i−2i000000−i2i2−222ζ−2ζ2ζ3−2ζ3000000000000−i2i2−22−1+i1−i−1−i1+i000000
χ312-22i−2i0022-2-2002i−2i2i−2i−2ζ2ζ−2ζ32ζ3000000002-22i−2i000000i2−i22−2−2ζ2ζ−2ζ32ζ3000000000000i2−i22−2−1+i1−i−1−i1+i000000
χ322-22i−2i0022-2-2002i−2i2i−2i−2ζ2ζ−2ζ32ζ3000000002-22i−2i000000−i2i2−22−2ζ2ζ−2ζ32ζ3000000000000−i2i2−221−i−1+i1+i−1−i000000
χ332-2−2i2i0022-2-200−2i2i−2i2i2ζ3−2ζ32ζ−2ζ000000002-2−2i2i000000i2−i2−222ζ3−2ζ32ζ−2ζ000000000000i2−i2−221+i−1−i1−i−1+i000000
χ342-2−2i2i0022-2-200−2i2i−2i2i2ζ3−2ζ32ζ−2ζ000000002-2−2i2i000000−i2i22−22ζ3−2ζ32ζ−2ζ000000000000−i2i22−2−1−i1+i−1+i1−i000000
χ352-2−2i2i0022-2-200−2i2i−2i2i−2ζ32ζ3−2ζ2ζ000000002-2−2i2i000000i2−i2−22−2ζ32ζ3−2ζ2ζ000000000000i2−i2−22−1−i1+i−1+i1−i000000
χ362-2−2i2i0022-2-200−2i2i−2i2i−2ζ32ζ3−2ζ2ζ000000002-2−2i2i000000−i2i22−2−2ζ32ζ3−2ζ2ζ000000000000−i2i22−21+i−1−i1−i−1+i000000
χ374444441-21-24411-2-200001-2-21-2-2-2-2000000000022220000110000220000-1-1-1-1000000-1-100
χ384444441-21-24411-2-200001-2-21-2-2-2-20000000000-2-2-2-20000110000-2-2000011110000001100
χ394444441-21-2-4-411-2-200001-2-212222000000000022220000-1-10000-2-20000-1-1-1-10000001100
χ404444441-21-2-4-411-2-200001-2-2122220000000000-2-2-2-20000-1-100002200001111000000-1-100
χ41444444-21-2144-2-2112222-211-2111100002222220000-1-1-1-1-2-200-1-100-1-1-1-100000000000000
χ42444444-21-2144-2-211-2-2-2-2-211-211110000-2-2-2-2-2-200001111-2-2001100111100000000000000
χ43444444-21-21-4-4-2-2112222-211-2-1-1-1-10000-2-2-2-2220000-1-1-1-12200110011-1-100000000000000
χ44444444-21-21-4-4-2-211-2-2-2-2-211-2-1-1-1-100002222-2-2000011112200-1-100-1-11100000000000000
χ454444-4-4-21-2100-2-21122222-1-123-33-300002-22-2-2-20000-1-1-1-10000-1100-111100000000000000
χ464444-4-4-21-2100-2-21122222-1-12-33-330000-22-22-2-20000-1-1-1-100001-1001-11100000000000000
χ474444-4-4-21-2100-2-211-2-2-2-22-1-123-33-30000-22-22220000111100001-1001-1-1-100000000000000
χ484444-4-4-21-2100-2-211-2-2-2-22-1-12-33-3300002-22-222000011110000-1100-11-1-100000000000000
χ4944-4-44-4-21-210022-1-12i2i−2i−2i-21-123i−3i−3i3i00002-2-22−2i2i0000−i−iii0000-11001-1i−i00000000000000
χ5044-4-44-4-21-210022-1-12i2i−2i−2i-21-12−3i3i3i−3i0000-222-2−2i2i0000−i−iii00001-100-11i−i00000000000000
χ5144-4-44-4-21-210022-1-1−2i−2i2i2i-21-123i−3i−3i3i0000-222-22i−2i0000ii−i−i00001-100-11−ii00000000000000
χ5244-4-44-4-21-210022-1-1−2i−2i2i2i-21-12−3i3i3i−3i00002-2-222i−2i0000ii−i−i0000-11001-1−ii00000000000000
χ5344-4-4-441-21-24i−4i-1-1220000-12-21−2i−2i2i2i000000000022-2-20000i−i00002i−2i0000-1-111000000−ii00
χ5444-4-4-441-21-24i−4i-1-1220000-12-21−2i−2i2i2i0000000000-2-2220000i−i0000−2i2i000011-1-1000000i−i00
χ5544-4-4-441-21-2−4i4i-1-1220000-12-212i2i−2i−2i000000000022-2-20000−ii0000−2i2i0000-1-111000000i−i00
χ5644-4-4-441-21-2−4i4i-1-1220000-12-212i2i−2i−2i0000000000-2-2220000−ii00002i−2i000011-1-1000000−ii00
χ5744-4-4-44-21-214i−4i22-1-12i2i−2i−2i2-11-2ii−i−i000022-2-22i−2i0000−i−iii−2i2i00-1-10011−ii00000000000000
χ5844-4-4-44-21-214i−4i22-1-1−2i−2i2i2i2-11-2ii−i−i0000-2-222−2i2i0000ii−i−i−2i2i001100-1-1i−i00000000000000
χ5944-4-4-44-21-21−4i4i22-1-12i2i−2i−2i2-11-2−i−iii0000-2-2222i−2i0000−i−iii2i−2i001100-1-1−ii00000000000000
χ6044-4-4-44-21-21−4i4i22-1-1−2i−2i2i2i2-11-2−i−iii000022-2-2−2i2i0000ii−i−i2i−2i00-1-10011i−i00000000000000
χ614-44i−4i0044-4-4004i−4i4i−4i000000000000-44−4i4i0000000000000000000000000000000000000000
χ624-4−4i4i0044-4-400−4i4i−4i4i000000000000-444i−4i0000000000000000000000000000000000000000
χ638888-8-82-42-40022-4-40000-244-2000000000000000000000000000000000000000000000000
χ6488-8-88-82-42-400-2-24400002-44-2000000000000000000000000000000000000000000000000
χ658-88i−8i002-4-24002i−2i−4i4i00000000000000000000002i2−2i222−220000000000000000−i2i2−220000000000
χ668-88i−8i002-4-24002i−2i−4i4i0000000000000000000000−2i22i2−22220000000000000000i2−i22−20000000000
χ678-88i−8i00-424-200−4i4i2i−2i4ζ−4ζ4ζ3−4ζ30000000000000000000000−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ688-88i−8i00-424-200−4i4i2i−2i−4ζ4ζ−4ζ34ζ300000000000000000000002ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ698-8−8i8i002-4-2400−2i2i4i−4i00000000000000000000002i2−2i2−22220000000000000000−i2i22−20000000000
χ708-8−8i8i002-4-2400−2i2i4i−4i0000000000000000000000−2i22i222−220000000000000000i2−i2−220000000000
χ718-8−8i8i00-424-2004i−4i−2i2i4ζ3−4ζ34ζ−4ζ0000000000000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ728-8−8i8i00-424-2004i−4i−2i2i−4ζ34ζ3−4ζ4ζ00000000000000000000002ζ3−2ζ32ζ−2ζ00000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.