Finite Group Databasebeta

← Group #11786661

Character table — Group #11786661

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122444444444488888888121212121212121212121212161618181818242424242424242424242424242436363636363648487272
order12442433668812121212661212242424242244888824242424242422446688881212242424242424888888242488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-111-1-1
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
χ51111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-1
χ61111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-111
χ71111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ81111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1
χ911-1-1-111111i−i-1-1-1-1-1-111ii−i−i11-1-1ii−i−iii−i−ii−i1-11-111i−i1-1-1-1i−i11-1-1i−iii−i−ii−i1-1
χ1011-1-1-111111i−i-1-1-1-1-1-111ii−i−i11-1-1ii−i−iii−i−ii−i1-11-111−ii-11-1-1i−i-1-111i−i−i−iii−ii-11
χ1111-1-1-111111i−i-1-1-1-1-1-111ii−i−i-1-111−i−iii−i−iiii−i1-11-1-1-1i−i1-111−ii11-1-1i−i−i−iiii−i-11
χ1211-1-1-111111i−i-1-1-1-1-1-111ii−i−i-1-111−i−iii−i−iiii−i1-11-1-1-1−ii-1111−ii-1-111i−iii−i−i−ii1-1
χ1311-1-1-111111−ii-1-1-1-1-1-111−i−iii11-1-1−i−iii−i−iii−ii1-11-111i−i-11-1-1−ii-1-111−iiii−i−ii−i-11
χ1411-1-1-111111−ii-1-1-1-1-1-111−i−iii11-1-1−i−iii−i−iii−ii1-11-111−ii1-1-1-1−ii11-1-1−ii−i−iii−ii1-1
χ1511-1-1-111111−ii-1-1-1-1-1-111−i−iii-1-111ii−i−iii−i−i−ii1-11-1-1-1i−i-1111i−i-1-111−ii−i−iiii−i1-1
χ1611-1-1-111111−ii-1-1-1-1-1-111−i−iii-1-111ii−i−iii−i−i−ii1-11-1-1-1−ii1-111i−i11-1-1−iiii−i−i−ii-11
χ1722222222222222222222222200000000000022-2-2-2-200000000000000-2-200000000
χ182222222222-2-222222222-2-2-2-2000000000000-2-2-2-2-2-2000000000000002200000000
χ192222-2-22222002222-2-2-2-2000000002-22-2222200-222-200000000-2-200000000000000
χ202222-2-22222002222-2-2-2-200000000-22-22-2-2-2-200-222-2000000002200000000000000
χ212222-2-22222002222-2-2-2-200002-22-200000000002-2-222-200002-20000000000000000
χ222222-2-22222002222-2-2-2-20000-22-2200000000002-2-22-220000-220000000000000000
χ2322-2-22-2222200-2-2-2-222-2-2000000002i−2i−2i2i2i2i−2i−2i00-2-22200000000−2i2i00000000000000
χ2422-2-22-2222200-2-2-2-222-2-200000000−2i2i2i−2i−2i−2i2i2i00-2-222000000002i−2i00000000000000
χ2522-2-22-2222200-2-2-2-222-2-200002-2-22000000000022-2-22-20000-220000000000000000
χ2622-2-22-2222200-2-2-2-222-2-20000-222-2000000000022-2-2-2200002-20000000000000000
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
χ294444441-21-24411-2-21-2-21-2-2-2-20000000000001100000022220000-1-1-1-1000000-1-100
χ304444441-21-24411-2-21-2-21-2-2-2-200000000000011000000-2-2-2-2000011110000001100
χ314444441-21-2-4-411-2-21-2-212222000000000000-1-100000022-2-200001111000000-1-100
χ324444441-21-2-4-411-2-21-2-212222000000000000-1-1000000-2-2220000-1-1-1-10000001100
χ33444444-21-2144-2-211-211-2111122222222-1-1-1-1-2-20000-1-10000-1-1-1-100000000000000
χ34444444-21-2144-2-211-211-21111-2-2-2-2-2-2-2-21111-2-20000110000111100000000000000
χ35444444-21-21-4-4-2-211-211-2-1-1-1-12222-2-2-2-21111220000-1-10000-1-11100000000000000
χ36444444-21-21-4-4-2-211-211-2-1-1-1-1-2-2-2-22222-1-1-1-122000011000011-1-100000000000000
χ374444-4-4-21-2100-2-2112-1-123-33-32-22-22-22-2-1-1-1-1000000-110000-111100000000000000
χ384444-4-4-21-2100-2-2112-1-123-33-3-22-22-22-2211110000001-100001-1-1-100000000000000
χ394444-4-4-21-2100-2-2112-1-12-33-332-22-2-22-221111000000-110000-11-1-100000000000000
χ404444-4-4-21-2100-2-2112-1-12-33-33-22-222-22-2-1-1-1-10000001-100001-11100000000000000
χ4144-4-44-4-21-210022-1-1-21-123i−3i−3i3i2-2-222i−2i−2i2i−i−iii000000-1100001-1i−i00000000000000
χ4244-4-44-4-21-210022-1-1-21-123i−3i−3i3i-222-2−2i2i2i−2iii−i−i0000001-10000-11−ii00000000000000
χ4344-4-44-4-21-210022-1-1-21-12−3i3i3i−3i2-2-22−2i2i2i−2iii−i−i000000-1100001-1−ii00000000000000
χ4444-4-44-4-21-210022-1-1-21-12−3i3i3i−3i-222-22i−2i−2i2i−i−iii0000001-10000-11i−i00000000000000
χ4544-4-4-441-21-24i−4i-1-122-12-21−2i−2i2i2i000000000000i−i0000002i−2i2-20000-1-111000000−ii00
χ4644-4-4-441-21-24i−4i-1-122-12-21−2i−2i2i2i000000000000i−i000000−2i2i-22000011-1-1000000i−i00
χ4744-4-4-441-21-2−4i4i-1-122-12-212i2i−2i−2i000000000000−ii0000002i−2i-22000011-1-1000000−ii00
χ4844-4-4-441-21-2−4i4i-1-122-12-212i2i−2i−2i000000000000−ii000000−2i2i2-20000-1-111000000i−i00
χ4944-4-4-44-21-214i−4i22-1-12-11-2ii−i−i22-2-22i2i−2i−2i−i−iii−2i2i0000-1-1000011−ii00000000000000
χ5044-4-4-44-21-214i−4i22-1-12-11-2ii−i−i-2-222−2i−2i2i2iii−i−i−2i2i0000110000-1-1i−i00000000000000
χ5144-4-4-44-21-21−4i4i22-1-12-11-2−i−iii22-2-2−2i−2i2i2iii−i−i2i−2i0000-1-1000011i−i00000000000000
χ5244-4-4-44-21-21−4i4i22-1-12-11-2−i−iii-2-2222i2i−2i−2i−i−iii2i−2i0000110000-1-1−ii00000000000000
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
χ578888-8-82-42-40022-4-4-244-20000000000000000000000000000000000000000000000
χ5888-8-88-82-42-400-2-2442-44-20000000000000000000000000000000000000000000000
χ598-88i−8i002-4-24002i−2i−4i4i000000000000000000000000000000000000i6−i66−60000000000
χ608-88i−8i002-4-24002i−2i−4i4i000000000000000000000000000000000000−i6i6−660000000000
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−4i000000000000000000000000000000000000i6−i6−660000000000
χ648-8−8i8i002-4-2400−2i2i4i−4i000000000000000000000000000000000000−i6i66−60000000000
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.