Finite Group Databasebeta

← Group #13151947

Character table — Group #13151947

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222224444466666688121212121212121212121212121818181818182424242424242424363636363636363636363636363636363636363636727272727272
order1223446246121233661212612366666121212121212122244886666121212122224446688812121212121224242424666122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-111111111-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111-1-1111111111-1-1111-1-1111-1-1111111111-11-1-1-11-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-111
χ61111111-1-1111111111-1-1111-1-1111-1-11111111-1-1-11-1-1-11-1-1111-1-1111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ71111111-1-1111111111-1-1111-1-1111-1-1111-1-1-1-111-11-1-1-11-1-1-11111-1-1-11-1-1-1-11111111111-1-1-1-1
χ81111111-1-1111111111-1-1111-1-1111-1-1111-1-1-1-1-1-1-11-1-1-11-1-11-1-1111-1-1-111-1-11111-1-1-1-1-1-11111
χ911-11-1111-1-1-111111-1-11-11-1-11111-1-1-1-1-111-11-1111-111-11-1-1-11-11-111-1-11-11-111-1-111-1-11-1-111-1
χ1011-11-1111-1-1-111111-1-11-11-1-11111-1-1-1-1-111-11-1-1-11-111-11-1-11-111-1-11-11-111-111-1-1-1-111-111-1-11
χ1111-11-1111-1-1-111111-1-11-11-1-11111-1-1-1-1-11-11-11111-111-11-1-1-1-11-111-11-1-11-11-1-11111-1-1-11-11-11
χ1211-11-1111-1-1-111111-1-11-11-1-11111-1-1-1-1-11-11-11-1-11-111-11-1-111-1-11-1-1111-1-11-1-111-1-1111-11-11-1
χ1311-11-111-11-1-111111-1-1-111-1-1-1-111-111-1-111-11-111-1-1-1-111111-11-11-11-1-11-11-1-1-11111-1-1-111-11-1
χ1411-11-111-11-1-111111-1-1-111-1-1-1-111-111-1-111-11-1-1-1-1-1-1-11111-11-1-1111-11-111-1-1-111-1-1111-1-11-11
χ1511-11-111-11-1-111111-1-1-111-1-1-1-111-111-1-11-11-1111-1-1-1-1111111-11-1-1-11-1-11-1111-1-111-1-11-11-1-11
χ1611-11-111-11-1-111111-1-1-111-1-1-1-111-111-1-11-11-11-1-1-1-1-1-11111-1-111-11-1111-1-1111-1-1-1-111-11-111-1
χ172222222222222-12-12222-12-1-1-1-1-1-1-1-1-1-122222002-1-1-12-1-1-1000220-1-1000-1-1-1-1-1-10000000000
χ182222222222222-12-12222-12-1-1-1-1-1-1-1-1-1-12-2-2-2-2002-1-1-12-1-1-1000-2-20110001111110000000000
χ19222222222222-12-12-1-122-1-1222-12222-1-1-1000022-1-1-1-1-1-1-1-120000200200000000-1-1-1-100-1-100
χ20222222222222-12-12-1-122-1-1222-12222-1-1-10000-2-2-1-1-1-1-1-1-1-1-20000-200-2000000001111001100
χ212222222-2-22222-12-122-2-2-12-111-1-1-111-1-12222200-2-111-2-111000-2-20-1-1000-1-111110000000000
χ222222222-2-22222-12-122-2-2-12-111-1-1-111-1-12-2-2-2-200-2-111-2-1110002201100011-1-1-1-10000000000
χ232222222-2-2222-12-12-1-1-2-2-1-12-2-2-122-2-2-1-1-10000221-1111-111-20000-200200000000-1-1-1-1001100
χ242222222-2-2222-12-12-1-1-2-2-1-12-2-2-122-2-2-1-1-10000-2-21-1111-11120000200-200000000111100-1-100
χ252222-2-22002-2-22222-2-200222002-2-200-2-2-22-2-220002000-2000000002-2000-2200000000000000
χ262222-2-22002-2-22222-2-200222002-2-200-2-2-2-222-20002000-200000000-220002-200000000000000
χ272222-2-22002-2-22-12-1-2-200-12-1−i3i3-111−i3i311-22-2-22000-1−i3i301−i3i3000000-110001-1−i3i3−i3i30000000000
χ282222-2-22002-2-22-12-1-2-200-12-1−i3i3-111−i3i311-2-222-2000-1−i3i301−i3i30000001-1000-11i3−i3i3−i30000000000
χ292222-2-22002-2-22-12-1-2-200-12-1i3−i3-111i3−i311-22-2-22000-1i3−i301i3−i3000000-110001-1i3−i3i3−i30000000000
χ302222-2-22002-2-22-12-1-2-200-12-1i3−i3-111i3−i311-2-222-2000-1i3−i301i3−i30000001-1000-11−i3i3−i3i30000000000
χ3122-222-2200-22-2222222002-2-2002-220022-222-2-2000-2000-20000000022000-2-200000000000000
χ3222-222-2200-22-2222222002-2-2002-220022-2-2-222000-2000-200000000-2-20002200000000000000
χ3322-222-2200-22-22-12-12200-1-21−i3i3-11-1i3−i3-1-1-222-2-20001−i3i301i3−i3000000-1-100011−i3i3i3−i30000000000
χ3422-222-2200-22-22-12-12200-1-21−i3i3-11-1i3−i3-1-1-2-2-2220001−i3i301i3−i300000011000-1-1i3−i3−i3i30000000000
χ3522-222-2200-22-22-12-12200-1-21i3−i3-11-1−i3i3-1-1-222-2-20001i3−i301−i3i3000000-1-100011i3−i3−i3i30000000000
χ3622-222-2200-22-22-12-12200-1-21i3−i3-11-1−i3i3-1-1-2-2-2220001i3−i301−i3i300000011000-1-1−i3i3i3−i30000000000
χ3722-22-2222-2-2-222-12-1-2-22-2-1-21-1-1-1-11111122-22-20021-1-1-2-1110002-20-11000-11-1-1110000000000
χ3822-22-2222-2-2-222-12-1-2-22-2-1-21-1-1-1-1111112-22-220021-1-1-2-111000-2201-10001-111-1-10000000000
χ3922-22-2222-2-2-22-12-12112-2-11-222-12-2-2-211-1000022-11-1-11-111-20000200-200000000-1-111001-100
χ4022-22-2222-2-2-22-12-12112-2-11-222-12-2-2-211-10000-2-2-11-1-11-11120000-20020000000011-1-100-1100
χ4122-22-222-22-2-222-12-1-2-2-22-1-2111-1-11-1-11122-22-200-21112-1-1-1000-220-11000-1111-1-10000000000
χ4222-22-222-22-2-222-12-1-2-2-22-1-2111-1-11-1-1112-22-2200-21112-1-1-10002-201-10001-1-1-1110000000000
χ4322-22-222-22-2-22-12-1211-22-11-2-2-2-12-22211-10000221111-1-1-1-120000-200-200000000-1-11100-1100
χ4422-22-222-22-2-22-12-1211-22-11-2-2-2-12-22211-10000-2-21111-1-1-1-1-2000020020000000011-1-1001-100
χ45444444444444-2-2-2-2-2-2441-2-2-2-21-2-2-2-211-2000000-2111-2111000000000000000000000000000
χ464444444-4-4444-2-2-2-2-2-2-4-41-2-2221-2-22211-200000021-1-121-1-1000000000000000000000000000
χ474444-4-44004-4-4-24-242200-2-2400-2-4-4002220000000-2000200000000000000000000000000000
χ484444-4-44004-4-4-2-2-2-222001-2-2−2i32i3122−2i32i3-1-1200000001i3−i30-1i3−i3000000000000000000000000000
χ494444-4-44004-4-4-2-2-2-222001-2-22i3−2i31222i3−2i3-1-1200000001−i3i30-1−i3i3000000000000000000000000000
χ5044-444-4400-44-4-24-24-2-200-22-400-2-4400-2-2200000002000200000000000000000000000000000
χ5144-444-4400-44-4-2-2-2-2-2-200122−2i32i312-22i3−2i31120000000-1i3−i30-1−i3i3000000000000000000000000000
χ5244-444-4400-44-4-2-2-2-2-2-2001222i3−2i312-2−2i32i31120000000-1−i3i30-1i3−i3000000000000000000000000000
χ5344-44-4444-4-4-44-2-2-2-2224-4122-2-21-2222-1-1-2000000-2-11121-1-1000000000000000000000000000
χ5444-44-444-44-4-44-2-2-2-222-44122221-22-2-2-1-1-20000002-1-1-1-2111000000000000000000000000000
χ554-40400-40000044-4-4000040000-400000000000−2i22i20000000000000000000000000−2i22i200000000
χ564-40400-40000044-4-4000040000-4000000000002i2−2i200000000000000000000000002i2−2i200000000
χ574-40400-400000-242-423−2300-200002000023−2300000−2i22i20000000000000000000000000i2−i2i6−i6000000
χ584-40400-400000-242-423−2300-200002000023−23000002i2−2i20000000000000000000000000−i2i2−i6i6000000
χ594-40400-400000-242-4−232300-2000020000−232300000−2i22i20000000000000000000000000i2−i2−i6i6000000
χ604-40400-400000-242-4−232300-2000020000−2323000002i2−2i20000000000000000000000000−i2i2i6−i6000000
χ61666-366-366-3-3-3000000-3-3000000000000000000000000000022000000220000000000-1-100-1-1
χ62666-366-366-3-3-3000000-3-30000000000000000000000000000-2-2000000-2-20000000000110011
χ63666-366-3-6-6-3-3-300000033000000000000000000000000000022000000-2-20000000000-1-10011
χ64666-366-3-6-6-3-3-3000000330000000000000000000000000000-2-20000002200000000001100-1-1
χ6566-6-3-66-36-633-3000000-3300000000000000000000000000002-20000002-20000000000-1100-11
χ6666-6-3-66-36-633-3000000-330000000000000000000000000000-22000000-2200000000001-1001-1
χ6766-6-3-66-3-6633-30000003-300000000000000000000000000002-2000000-220000000000-11001-1
χ6866-6-3-66-3-6633-30000003-30000000000000000000000000000-220000002-200000000001-100-11
χ698-80800-8000008-4-840000-400004000000000000000000000000000000000000000000000000
χ708-80800-800000-4-44443−430020000-20000−2323000000000000000000000000000000000000000000
χ718-80800-800000-4-444−43430020000-2000023−23000000000000000000000000000000000000000000
χ72121212-6-12-12-600-66600000000000000000000000000000000000000000000000000000000000000
χ731212-12-612-12-6006-6600000000000000000000000000000000000000000000000000000000000000
χ7424-240-1200120000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).