Finite Group Databasebeta

← Group #11787790

Character table — Group #11787790

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122444444444488888888121212121212121212121212161618181818242424242424242424242424242436363636363648487272
order1244243366881212121266121224242424224488882424242424242244244466121212121212242444448861244
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
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
χ51111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-111-1-1
χ61111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ71111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ81111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-1
χ911-1-1-111111i−i-1-1-1-1-1-111ii−i−i11-1-1ii−i−iii−i−ii−i1-11-11-1i−i11-1-1ii−i−ii−i11-1-1i−i1-1i−i
χ1011-1-1-111111i−i-1-1-1-1-1-111ii−i−i11-1-1ii−i−iii−i−ii−i1-11-1-11−ii11-1-1−i−iiii−i-1-111i−i-11−ii
χ1111-1-1-111111i−i-1-1-1-1-1-111ii−i−i-1-111−i−iii−i−iiii−i1-11-11-1i−i-1-111ii−i−i−ii-1-111i−i1-1−ii
χ1211-1-1-111111i−i-1-1-1-1-1-111ii−i−i-1-111−i−iii−i−iiii−i1-11-1-11−ii-1-111−i−iii−ii11-1-1i−i-11i−i
χ1311-1-1-111111−ii-1-1-1-1-1-111−i−iii11-1-1−i−iii−i−iii−ii1-11-11-1−ii11-1-1−i−iii−ii11-1-1−ii1-1−ii
χ1411-1-1-111111−ii-1-1-1-1-1-111−i−iii11-1-1−i−iii−i−iii−ii1-11-1-11i−i11-1-1ii−i−i−ii-1-111−ii-11i−i
χ1511-1-1-111111−ii-1-1-1-1-1-111−i−iii-1-111ii−i−iii−i−i−ii1-11-11-1−ii-1-111−i−iiii−i-1-111−ii1-1i−i
χ1611-1-1-111111−ii-1-1-1-1-1-111−i−iii-1-111ii−i−iii−i−i−ii1-11-1-11i−i-1-111ii−i−ii−i11-1-1−ii-11−ii
χ1722222222222222222222222200000000000022-2-2-2-2000000000000000000-2-20000
χ182222222222-2-222222222-2-2-2-2000000000000-2-2-2-2-2-2000000000000000000220000
χ192222-2-22222002222-2-2-2-2000000002-22-2222200-222-2000000000000-2-20000000000
χ202222-2-22222002222-2-2-2-200000000-22-22-2-2-2-200-222-2000000000000220000000000
χ212222-2-22222002222-2-2-2-200002-22-200000000002-2-2200002-22-20000000000000000
χ222222-2-22222002222-2-2-2-20000-22-2200000000002-2-220000-22-220000000000000000
χ2322-2-22-2222200-2-2-2-222-2-2000000002i−2i−2i2i2i2i−2i−2i00-2-222000000000000−2i2i0000000000
χ2422-2-22-2222200-2-2-2-222-2-200000000−2i2i2i−2i−2i−2i2i2i00-2-2220000000000002i−2i0000000000
χ2522-2-22-2222200-2-2-2-222-2-200002-2-22000000000022-2-200002-2-220000000000000000
χ2622-2-22-2222200-2-2-2-222-2-20000-222-2000000000022-2-20000-222-20000000000000000
χ2722-2-2-2222222i−2i-2-2-2-2-2-2222i2i−2i−2i0000000000002i−2i-22-22000000000000000000−2i2i0000
χ2822-2-2-222222−2i2i-2-2-2-2-2-222−2i−2i2i2i000000000000−2i2i-22-220000000000000000002i−2i0000
χ294444441-21-24411-2-2-211-2-2-2-2-200000000000011000022220000-1-1-1-100000000-1-100
χ304444441-21-24411-2-2-211-2-2-2-2-2000000000000110000-2-2-2-200001111000000001100
χ314444441-21-2-4-411-2-2-211-22222000000000000-1-1000022-2-20000111100000000-1-100
χ324444441-21-2-4-411-2-2-211-22222000000000000-1-10000-2-2220000-1-1-1-1000000001100
χ33444444-21-2144-2-2111-2-21111122222222-1-1-1-1-2-200000000-1-1-1-10000-1-10000000000
χ34444444-21-2144-2-2111-2-211111-2-2-2-2-2-2-2-21111-2-20000000011110000110000000000
χ35444444-21-21-4-4-2-2111-2-21-1-1-1-12222-2-2-2-211112200000000-1-1-1-10000110000000000
χ36444444-21-21-4-4-2-2111-2-21-1-1-1-1-2-2-2-22222-1-1-1-1220000000011110000-1-10000000000
χ374444-4-4-21-2100-2-211-122-13-33-32-22-22-22-2-1-1-1-10000000000-11-110000110000000000
χ384444-4-4-21-2100-2-211-122-13-33-3-22-22-22-22111100000000001-11-10000-1-10000000000
χ394444-4-4-21-2100-2-211-122-1-33-332-22-2-22-2211110000000000-11-110000-1-10000000000
χ404444-4-4-21-2100-2-211-122-1-33-33-22-222-22-2-1-1-1-100000000001-11-10000110000000000
χ4144-4-44-4-21-210022-1-11-22-13i−3i−3i3i2-2-222i−2i−2i2i−i−iii0000000000-111-10000i−i0000000000
χ4244-4-44-4-21-210022-1-11-22-13i−3i−3i3i-222-2−2i2i2i−2iii−i−i00000000001-1-110000−ii0000000000
χ4344-4-44-4-21-210022-1-11-22-1−3i3i3i−3i2-2-22−2i2i2i−2iii−i−i0000000000-111-10000−ii0000000000
χ4444-4-44-4-21-210022-1-11-22-1−3i3i3i−3i-222-22i−2i−2i2i−i−iii00000000001-1-110000i−i0000000000
χ4544-4-4-441-21-24i−4i-1-1222-11-2−2i−2i2i2i000000000000i−i00002-22i−2i0000−i−iii00000000-1100
χ4644-4-4-441-21-24i−4i-1-1222-11-2−2i−2i2i2i000000000000i−i0000-22−2i2i0000ii−i−i000000001-100
χ4744-4-4-441-21-2−4i4i-1-1222-11-22i2i−2i−2i000000000000−ii00002-2−2i2i0000ii−i−i00000000-1100
χ4844-4-4-441-21-2−4i4i-1-1222-11-22i2i−2i−2i000000000000−ii0000-222i−2i0000−i−iii000000001-100
χ4944-4-4-44-21-214i−4i22-1-1-12-21ii−i−i22-2-22i2i−2i−2i−i−iii−2i2i00000000-1-1110000−ii0000000000
χ5044-4-4-44-21-214i−4i22-1-1-12-21ii−i−i-2-222−2i−2i2i2iii−i−i−2i2i0000000011-1-10000i−i0000000000
χ5144-4-4-44-21-21−4i4i22-1-1-12-21−i−iii22-2-2−2i−2i2i2iii−i−i2i−2i00000000-1-1110000i−i0000000000
χ5244-4-4-44-21-21−4i4i22-1-1-12-21−i−iii-2-2222i2i−2i−2i−i−iii2i−2i0000000011-1-10000−ii0000000000
χ534-44i−4i0044-4-4004i−4i4i−4i00000000000000000000000000000000000000002-22i−2i000000
χ544-44i−4i0044-4-4004i−4i4i−4i0000000000000000000000000000000000000000-22−2i2i000000
χ554-4−4i4i0044-4-400−4i4i−4i4i00000000000000000000000000000000000000002-2−2i2i000000
χ564-4−4i4i0044-4-400−4i4i−4i4i0000000000000000000000000000000000000000-222i−2i000000
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−4i4i0000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000
χ608-88i−8i002-4-24002i−2i−4i4i0000000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000
χ618-88i−8i00-424-200−4i4i2i−2i0000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000
χ628-88i−8i00-424-200−4i4i2i−2i00000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000
χ638-8−8i8i002-4-2400−2i2i4i−4i0000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000
χ648-8−8i8i002-4-2400−2i2i4i−4i0000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000
χ658-8−8i8i00-424-2004i−4i−2i2i00000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000
χ668-8−8i8i00-424-2004i−4i−2i2i0000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000

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