Finite Group Databasebeta

← Group #11787655

Character table — Group #11787655

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122444444444488888888121212121212121212121212161618181818242424242424242424242424242436363636363648487272
order124424336688121212126612122424242422446688881212242422442444612121212122424242488888861288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ51111111111-1-111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-111111111-1-1-1-1111111-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ71111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ81111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-111
χ911-1-1-111111i−i-1-1-1-1-1-111ii−i−i1-11-111ii−i−i-1-1i−i1-11-11-1i−i-11ii−i−iii−i−ii−iii−i−i1-11-1
χ1011-1-1-111111i−i-1-1-1-1-1-111ii−i−i1-11-111ii−i−i-1-1i−i1-11-1-11−ii-11−i−iiiii−i−ii−i−i−iii-11-11
χ1111-1-1-111111i−i-1-1-1-1-1-111ii−i−i-11-11-1-1−i−iii11i−i1-11-11-1i−i1-1ii−i−i−i−iiii−i−i−iii1-1-11
χ1211-1-1-111111i−i-1-1-1-1-1-111ii−i−i-11-11-1-1−i−iii11i−i1-11-1-11−ii1-1−i−iii−i−iiii−iii−i−i-111-1
χ1311-1-1-111111−ii-1-1-1-1-1-111−i−iii1-11-111−i−iii-1-1−ii1-11-11-1−ii-11−i−iii−i−iii−ii−i−iii1-11-1
χ1411-1-1-111111−ii-1-1-1-1-1-111−i−iii1-11-111−i−iii-1-1−ii1-11-1-11i−i-11ii−i−i−i−iii−iiii−i−i-11-11
χ1511-1-1-111111−ii-1-1-1-1-1-111−i−iii-11-11-1-1ii−i−i11−ii1-11-11-1−ii1-1−i−iiiii−i−i−iiii−i−i1-1-11
χ1611-1-1-111111−ii-1-1-1-1-1-111−i−iii-11-11-1-1ii−i−i11−ii1-11-1-11i−i1-1ii−i−iii−i−i−ii−i−iii-111-1
χ1722222222222222222222222200000000000022-2-2-2-200000000000000-2-200000000
χ182222222222-2-222222222-2-2-2-2000000000000-2-2-2-2-2-2000000000000002200000000
χ192222-2-22222002222-2-2-2-200000000002-22-200002-2-2200000000002-22-20000000000
χ202222-2-22222002222-2-2-2-20000000000-22-2200002-2-220000000000-22-220000000000
χ212222-2-22222002222-2-2-2-200002-2-222200002200-222-20000-2-2000000000000000000
χ222222-2-22222002222-2-2-2-20000-222-2-2-20000-2-200-222-2000022000000000000000000
χ2322-2-22-2222200-2-2-2-222-2-200000000002i−2i−2i2i000022-2-200000000002i−2i−2i2i0000000000
χ2422-2-22-2222200-2-2-2-222-2-20000000000−2i2i2i−2i000022-2-20000000000−2i2i2i−2i0000000000
χ2522-2-22-2222200-2-2-2-222-2-2000022-2-2220000-2-200-2-22200002-2000000000000000000
χ2622-2-22-2222200-2-2-2-222-2-20000-2-222-2-200002200-2-2220000-22000000000000000000
χ2722-2-2-2222222i−2i-2-2-2-2-2-2222i2i−2i−2i0000000000002i−2i-22-2200000000000000−2i2i00000000
χ2822-2-2-222222−2i2i-2-2-2-2-2-222−2i−2i2i2i000000000000−2i2i-22-22000000000000002i−2i00000000
χ294444441-21-24411-2-2-211-2-2-2-2-2000000000000110000222200-1-1-1-10000000000-1-100
χ304444441-21-24411-2-2-211-2-2-2-2-2000000000000110000-2-2-2-200111100000000001100
χ314444441-21-2-4-411-2-2-211-22222000000000000-1-1000022-2-20011110000000000-1-100
χ324444441-21-2-4-411-2-2-211-22222000000000000-1-10000-2-22200-1-1-1-100000000001100
χ33444444-21-2144-2-2111-2-2111112222-1-12222-1-1-2-200000000-1-10000-1-1-1-10000000000
χ34444444-21-2144-2-2111-2-211111-2-2-2-211-2-2-2-211-2-20000000011000011110000000000
χ35444444-21-21-4-4-2-2111-2-21-1-1-1-12222-1-1-2-2-2-2-1-12200000000-1-1000011110000000000
χ36444444-21-21-4-4-2-2111-2-21-1-1-1-1-2-2-2-2112222112200000000110000-1-1-1-10000000000
χ374444-4-4-21-2100-2-211-122-13-33-32-2-22-1-12-22-2-1-10000000000110000-11-110000000000
χ384444-4-4-21-2100-2-211-122-13-33-3-222-211-22-22110000000000-1-100001-11-10000000000
χ394444-4-4-21-2100-2-211-122-1-33-332-2-22-1-1-22-22-1-100000000001100001-11-10000000000
χ404444-4-4-21-2100-2-211-122-1-33-33-222-2112-22-2110000000000-1-10000-11-110000000000
χ4144-4-44-4-21-210022-1-11-22-13i−3i−3i3i22-2-2-1-12i−2i−2i2i110000000000-110000−iii−i0000000000
χ4244-4-44-4-21-210022-1-11-22-13i−3i−3i3i-2-22211−2i2i2i−2i-1-100000000001-10000i−i−ii0000000000
χ4344-4-44-4-21-210022-1-11-22-1−3i3i3i−3i22-2-2-1-1−2i2i2i−2i110000000000-110000i−i−ii0000000000
χ4444-4-44-4-21-210022-1-11-22-1−3i3i3i−3i-2-222112i−2i−2i2i-1-100000000001-10000−iii−i0000000000
χ4544-4-4-441-21-24i−4i-1-1222-11-2−2i−2i2i2i000000000000i−i00002-22i−2i00−i−iii0000000000-1100
χ4644-4-4-441-21-24i−4i-1-1222-11-2−2i−2i2i2i000000000000i−i0000-22−2i2i00ii−i−i00000000001-100
χ4744-4-4-441-21-2−4i4i-1-1222-11-22i2i−2i−2i000000000000−ii00002-2−2i2i00ii−i−i0000000000-1100
χ4844-4-4-441-21-2−4i4i-1-1222-11-22i2i−2i−2i000000000000−ii0000-222i−2i00−i−iii00000000001-100
χ4944-4-4-44-21-214i−4i22-1-1-12-21ii−i−i2-22-2-1-12i2i−2i−2i11−2i2i000000001-10000−i−iii0000000000
χ5044-4-4-44-21-214i−4i22-1-1-12-21ii−i−i-22-2211−2i−2i2i2i-1-1−2i2i00000000-110000ii−i−i0000000000
χ5144-4-4-44-21-21−4i4i22-1-1-12-21−i−iii2-22-2-1-1−2i−2i2i2i112i−2i000000001-10000ii−i−i0000000000
χ5244-4-4-44-21-21−4i4i22-1-1-12-21−i−iii-22-22112i2i−2i−2i-1-12i−2i00000000-110000−i−iii0000000000
χ534-44i−4i0044-4-4004i−4i4i−4i0000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ544-44i−4i0044-4-4004i−4i4i−4i000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ554-4−4i4i0044-4-400−4i4i−4i4i000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ564-4−4i4i0044-4-400−4i4i−4i4i0000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ578888-8-82-42-40022-4-44-2-240000000000000000000000000000000000000000000000
χ5888-8-88-82-42-400-2-244-42-240000000000000000000000000000000000000000000000
χ598-88i−8i002-4-24002i−2i−4i4i00000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000
χ608-88i−8i002-4-24002i−2i−4i4i00000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000
χ618-88i−8i00-424-200−4i4i2i−2i000000000000−2i32i3000023−23000000000000000000000000000000
χ628-88i−8i00-424-200−4i4i2i−2i0000000000002i3−2i30000−2323000000000000000000000000000000
χ638-8−8i8i002-4-2400−2i2i4i−4i00000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000
χ648-8−8i8i002-4-2400−2i2i4i−4i00000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000
χ658-8−8i8i00-424-2004i−4i−2i2i000000000000−2i32i30000−2323000000000000000000000000000000
χ668-8−8i8i00-424-2004i−4i−2i2i0000000000002i3−2i3000023−23000000000000000000000000000000

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