Finite Group Databasebeta

← Group #10712002

Character table — Group #10712002

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222224444444444448888888888881212121212121212161616161616161616161616161624242424242424244848
order12442346121222244468888126668812121224242424444488884444121212121212121224242488888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ511111111111111111-1-1-1-11111-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111-1-1-1-11111-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111
χ711111111111111111-1-1-1-11111-1-1111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111-1-1-1-11111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-111-11-1-11-111-1-11ii−i−i-111-1i−i1-1-1ii−i−i11-1-1ii−i−ii−i1-1ii−i−i11-1-1i−i1-1ii−i−ii−i1-1
χ1011-1-111-11-1-11-111-1-11ii−i−i-111-1i−i1-1-1ii−i−i11-1-1ii−i−i−ii-11−i−iii-1-111i−i1-1−i−iiii−i-11
χ1111-1-111-11-1-11-111-1-11ii−i−i-111-1i−i1-1-1ii−i−i-1-111−i−iiii−i1-1ii−i−i11-1-1i−i-11−i−iii−ii-11
χ1211-1-111-11-1-11-111-1-11ii−i−i-111-1i−i1-1-1ii−i−i-1-111−i−iii−ii-11−i−iii-1-111i−i-11ii−i−i−ii1-1
χ1311-1-111-11-1-11-111-1-11−i−iii-111-1−ii1-1-1−i−iii11-1-1−i−iiii−i-11ii−i−i-1-111−ii1-1ii−i−i−ii-11
χ1411-1-111-11-1-11-111-1-11−i−iii-111-1−ii1-1-1−i−iii11-1-1−i−iii−ii1-1−i−iii11-1-1−ii1-1−i−iii−ii1-1
χ1511-1-111-11-1-11-111-1-11−i−iii-111-1−ii1-1-1−i−iii-1-111ii−i−ii−i-11ii−i−i-1-111−ii-11−i−iiii−i1-1
χ1611-1-111-11-1-11-111-1-11−i−iii-111-1−ii1-1-1−i−iii-1-111ii−i−i−ii1-1−i−iii11-1-1−ii-11ii−i−ii−i-11
χ1722222222222-2-2-22-2200002-22-200-22-200000000222200000000000000000000-2-200
χ1822222222222-2-2-22-2200002-22-200-22-200000000-2-2-2-2000000000000000000002200
χ192222222222-22-22-2-2200002-2-22002-2-200002222000000000000000000-2-200000000
χ202222222222-22-22-2-2200002-2-22002-2-20000-2-2-2-20000000000000000002200000000
χ212222222222-2-22-2-222222222-2-2-2-2-2-22222200000000000000000000-2-20000000000
χ222222222222-2-22-2-222-2-2-2-222-2-222-2-22-2-2-2-200000000000000000000220000000000
χ2322222-12-1-1-1222222-12222-1-1-1-122-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-10000000000
χ2422222-12-1-1-1222222-12222-1-1-1-122-1-1-1-1-1-1-100000000-2-2-2-211111111-1-10000000000
χ2522222-12-1-1-1222222-1-2-2-2-2-1-1-1-1-2-2-1-1-111110000000022-2-2-1-1-1-11111110000000000
χ2622222-12-1-1-1222222-1-2-2-2-2-1-1-1-1-2-2-1-1-1111100000000-2-2221111-1-1-1-1110000000000
χ2722222-12-1-1-1-2-22-2-22-12222-1-111-2-211-1-1-1-1-10000000000003−33−33−33−3110000000000
χ2822222-12-1-1-1-2-22-2-22-12222-1-111-2-211-1-1-1-1-1000000000000−33−33−33−33110000000000
χ2922222-12-1-1-1-2-22-2-22-1-2-2-2-2-1-1112211-111110000000000003−33−3−33−33-1-10000000000
χ3022222-12-1-1-1-2-22-2-22-1-2-2-2-2-1-1112211-11111000000000000−33−333−33−3-1-10000000000
χ3122-2-222-22-2-222-2-2-2220000-2-22200-2-22000000002i2i−2i−2i00000000000000000000−2i2i00
χ3222-2-222-22-2-222-2-2-2220000-2-22200-2-2200000000−2i−2i2i2i000000000000000000002i−2i00
χ3322-2-222-22-2-2-222-22-222i2i−2i−2i-22-22−2i2i-22-22i2i−2i−2i00000000000000000000−2i2i0000000000
χ3422-2-222-22-2-2-222-22-22−2i−2i2i2i-22-222i−2i-22-2−2i−2i2i2i000000000000000000002i−2i0000000000
χ3522-2-222-22-2-2-2-2-222220000-2-2-2-200222000022-2-2000000000000000000-2200000000
χ3622-2-222-22-2-2-2-2-222220000-2-2-2-2002220000-2-2220000000000000000002-200000000
χ3722-2-22-1-2-1112-222-2-2-12i2i−2i−2i1-1-112i−2i-111−i−iii000000002i−2i2-2−i−iii-1-111−ii0000000000
χ3822-2-22-1-2-1112-222-2-2-12i2i−2i−2i1-1-112i−2i-111−i−iii00000000−2i2i-22ii−i−i11-1-1−ii0000000000
χ3922-2-22-1-2-1112-222-2-2-1−2i−2i2i2i1-1-11−2i2i-111ii−i−i000000002i−2i-22−i−iii11-1-1i−i0000000000
χ4022-2-22-1-2-1112-222-2-2-1−2i−2i2i2i1-1-11−2i2i-111ii−i−i00000000−2i2i2-2ii−i−i-1-111i−i0000000000
χ4122-2-22-1-2-111-222-22-2-12i2i−2i−2i1-11-1−2i2i1-11−i−iii000000000000−i3i3i3−i3−333−3i−i0000000000
χ4222-2-22-1-2-111-222-22-2-12i2i−2i−2i1-11-1−2i2i1-11−i−iii000000000000i3−i3−i3i33−3−33i−i0000000000
χ4322-2-22-1-2-111-222-22-2-1−2i−2i2i2i1-11-12i−2i1-11ii−i−i000000000000−i3i3i3−i33−3−33−ii0000000000
χ4422-2-22-1-2-111-222-22-2-1−2i−2i2i2i1-11-12i−2i1-11ii−i−i000000000000i3−i3−i3i3−333−3−ii0000000000
χ4544444-24-2-2-24-4-4-44-4-20000-22-22002-22000000000000000000000000000000000000
χ4644444-24-2-2-2-44-44-4-4-20000-222-200-222000000000000000000000000000000000000
χ474444-44-4444000000-40000-40000000000000000000000000000000000002-22-20000
χ484444-44-4444000000-40000-4000000000000000000000000000000000000-22-220000
χ4944-4-44-2-4-22244-4-4-44-2000022-2-20022-2000000000000000000000000000000000000
χ5044-4-44-2-4-222-4-4-4444-20000222200-2-2-2000000000000000000000000000000000000
χ5144-4-4-4444-4-4000000-4000040000000000000000000000000000000000002i−2i−2i2i0000
χ5244-4-4-4444-4-4000000-400004000000000000000000000000000000000000−2i2i2i−2i0000
χ534-44i−4i040-44i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ544-44i−4i040-44i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ554-44i−4i040-44i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ564-44i−4i040-44i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ574-4−4i4i040-4−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ584-4−4i4i040-4−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ594-4−4i4i040-4−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ604-4−4i4i040-4−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ618888-8-4-8-4-4-400000040000400000000000000000000000000000000000000000000
χ6288-8-8-8-48-44400000040000-400000000000000000000000000000000000000000000
χ638-88i−8i0-404−4i4i00000004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ648-88i−8i0-404−4i4i0000000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ658-8−8i8i0-4044i−4i0000000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ668-8−8i8i0-4044i−4i00000004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000

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