Finite Group Databasebeta

← Group #13180837

Character table — Group #13180837

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222334444466666666688888812121212121212161616161616161616161616161616181818181818363636363636363636363636484848484848108108108108
order1223366662236666224666666333666666666123336666666666662444444461212121212121212126661212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111-1-11111111111111-11111-1111111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111-1-11111111111111-11111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-111-1-111111-11-1-1-11-11-1-1111111111-1111-1-1-1111-1-1-1111-1-1-1-1-1-11-11111-1-11-111-1-111-1-1111-1-1-1-11-11
χ611-111-1-111111-11-1-1-11-11-1-1111111111-1111-1-1-1111-1-1-1111-1-1-1-1-1-11-1-1-1-1-1111-1-1-111-1-111111-1-1-11-11-1
χ711-111-1-111111-11-1-1-1-111-1-1111111111-1-111-1-11111-1-1-1111-1-1-1-1-1-1-111111-1-1-1111-1-111-1-1-1-1-11111-11-1
χ811-111-1-111111-11-1-1-1-111-1-1111111111-1-111-1-11111-1-1-1111-1-1-1-1-1-1-11-1-1-1-111-11-1-111-1-111-1-1-1111-11-11
χ92222222222222222222222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000002200000000-1-1-1-1-1-10000
χ1022222222222222222-2-2222222-1-1-1-1-1-12-22222-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000-2-2000000001111110000
χ112222-122-1222-1-1-1-1-1222222-1-122-1-12-1-1-1-1-1-1-1-1-12-1-12-1-12-1-122-1-1-1-122000000-1-1000000002-1-12-1-10000
χ122222-122-1222-1-1-1-1-1222222-1-12-12-1-12-1-1-1-1-1-1-1-1-12-1-12-1-12-1-1-122-1-122000000-1-100000000-12-1-12-10000
χ132222-122-1222-1-1-1-1-1222222-1-12-1-12-1-12-1-1-1-1-1-1-1-1-12-1-12-1-12-1-1-1-12222000000-1-100000000-1-12-1-120000
χ142222-122-1222-1-1-1-1-12-2-2222-1-122-1-12-1-1-11-1-1-1-112-1-12-1-12-1-122-1-1-1-1-2-20000001100000000-211-2110000
χ152222-122-1222-1-1-1-1-12-2-2222-1-12-12-1-12-1-11-1-1-1-11-12-1-12-1-12-1-1-122-1-1-2-200000011000000001-211-210000
χ162222-122-1222-1-1-1-1-12-2-2222-1-12-1-12-1-12-11-1-1-1-11-1-12-1-12-1-12-1-1-1-122-2-2000000110000000011-211-20000
χ17222-12-1-12-122-12-1-1-1200-1-1-122-122222220-1-1-1-10-1-1-1222-1-1-1-1-1-1-1-1-10022222200-1-1-1-1-1-1-1-10000000000
χ18222-12-1-12-122-12-1-1-1200-1-1-122-122222220-1-1-1-10-1-1-1222-1-1-1-1-1-1-1-1-100-2-2-2-2-2-200111111110000000000
χ1922-222-2-222222-22-2-2-22-22-2-2222-1-1-1-1-1-1-2222-2-2-2-1-1-1111-1-1-11111112-20000002-200000000-1-1-11110000
χ2022-222-2-222222-22-2-2-2-222-2-2222-1-1-1-1-1-1-2-222-2-22-1-1-1111-1-1-1111111-22000000-2200000000111-1-1-10000
χ2122-22-1-2-2-1222-11-111-22-22-2-2-1-122-1-12-1-11-1-1-11112-1-1-2112-1-1-2-211112-2000000-11000000002-1-1-2110000
χ2222-22-1-2-2-1222-11-111-22-22-2-2-1-12-12-1-12-11-1-1-1111-12-11-21-12-111-2-2112-2000000-1100000000-12-11-210000
χ2322-22-1-2-2-1222-11-111-22-22-2-2-1-12-1-12-1-121-1-1-1111-1-1211-2-1-121111-2-22-2000000-1100000000-1-1211-20000
χ2422-22-1-2-2-1222-11-111-2-222-2-2-1-122-1-12-1-111-1-111-12-1-1-2112-1-1-2-21111-220000001-100000000-2112-1-10000
χ2522-22-1-2-2-1222-11-111-2-222-2-2-1-12-12-1-12-111-1-111-1-12-11-21-12-111-2-211-220000001-1000000001-21-12-10000
χ2622-22-1-2-2-1222-11-111-2-222-2-2-1-12-1-12-1-1211-1-111-1-1-1211-2-1-121111-2-2-220000001-10000000011-2-1-120000
χ2722-2-12112-122-1-2-111-200-11122-1222222-20-1-1110-1-1-1-2-2-2-1-1-1111111002222-2-200-1-111-1-1110000000000
χ2822-2-12112-122-1-2-111-200-11122-1222222-20-1-1110-1-1-1-2-2-2-1-1-111111100-2-2-2-2220011-1-111-1-10000000000
χ292-202200-2-22-220-2000002002-2-2222-2-2-2002-2000222000-2-2-2000000002i−2i2i−2i00002i−2i002i−2i000000000000
χ302-202200-2-22-220-2000002002-2-2222-2-2-2002-2000222000-2-2-200000000−2i2i−2i2i0000−2i2i00−2i2i000000000000
χ312-20-12−i3i3-212-2-101−i3i3000-1−i3i32-21222-2-2-200-11−i3i30-1-1-1000111−i3i3−i3i3−i3i3002i−2i2i−2i0000−ii3−3−ii3−30000000000
χ322-20-12−i3i3-212-2-101−i3i3000-1−i3i32-21222-2-2-200-11−i3i30-1-1-1000111−i3i3−i3i3−i3i300−2i2i−2i2i0000i−i−33i−i−330000000000
χ332-20-12i3−i3-212-2-101i3−i3000-1i3−i32-21222-2-2-200-11i3−i30-1-1-1000111i3−i3i3−i3i3−i3002i−2i2i−2i0000−ii−33−ii−330000000000
χ342-20-12i3−i3-212-2-101i3−i3000-1i3−i32-21222-2-2-200-11i3−i30-1-1-1000111i3−i3i3−i3i3−i300−2i2i−2i2i0000i−i3−3i−i3−30000000000
χ35333333333-1-133333-133-1-1-1-1-1-1000000-13-1-1-1-13000000000000000-1-111-1-11-1-1-11111-1-1-1-100000011-1-1
χ36333333333-1-133333-133-1-1-1-1-1-1000000-13-1-1-1-13000000000000000-1-1-1-111-11-1-1-1-1-1-11111000000-1-111
χ37333333333-1-133333-1-3-3-1-1-1-1-1-1000000-1-3-1-1-1-1-30000000000000001111-1-11-1111111-1-1-1-1000000-1-111
χ38333333333-1-133333-1-3-3-1-1-1-1-1-1000000-1-3-1-1-1-1-300000000000000011-1-111-1111-1-1-1-1111100000011-1-1
χ3933-333-3-333-1-13-33-3-313-3-111-1-1-100000013-1-111-3000000000000000-1111-1-1-11-1111-1-1-1-111000000-111-1
χ4033-333-3-333-1-13-33-3-313-3-111-1-1-100000013-1-111-3000000000000000-11-1-1111-1-11-1-11111-1-10000001-1-11
χ4133-333-3-333-1-13-33-3-31-33-111-1-1-10000001-3-1-11130000000000000001-111-1-1-111-111-1-1-1-1110000001-1-11
χ4233-333-3-333-1-13-33-3-31-33-111-1-1-10000001-3-1-11130000000000000001-1-1-1111-11-1-1-11111-1-1000000-111-1
χ43444-24-2-24-244-24-2-2-2400-2-2-244-2-2-2-2-2-2-240-2-2-2-20111-2-2-21111111110000000000000000000000000000
χ44444-2-2-2-2-2-2441-2111400-2-2-2-2-2-24-2-24-2-2-2011110-2114-2-2-211-2-211110000000000000000000000000000
χ45444-2-2-2-2-2-2441-2111400-2-2-2-2-2-2-24-2-24-2-20111101-21-24-21-2111-2-2110000000000000000000000000000
χ46444-2-2-2-2-2-2441-2111400-2-2-2-2-2-2-2-24-2-24-201111011-2-2-2411-21111-2-20000000000000000000000000000
χ4744-4-24224-244-2-4-222-400-22244-2-2-2-2-2-2-2-40-2-2220111222111-1-1-1-1-1-10000000000000000000000000000
χ4844-4-2-222-2-244121-1-1-400-222-2-2-24-2-24-2-22011-1-10-211-422-21122-1-1-1-10000000000000000000000000000
χ4944-4-2-222-2-244121-1-1-400-222-2-2-2-24-2-24-22011-1-101-212-421-21-1-122-1-10000000000000000000000000000
χ5044-4-2-222-2-244121-1-1-400-222-2-2-2-2-24-2-242011-1-1011-222-411-2-1-1-1-1220000000000000000000000000000
χ514-404400-4-44-440-4000004004-4-4-2-2-2222004-4000-2-2-20002220000000000000000000000000000000000
χ524-404-2002-44-4-20200000400-22-44-2-2-42200-220004-2-2000-4220000000000000000000000000000000000
χ534-404-2002-44-4-20200000400-22-4-24-22-4200-22000-24-20002-420000000000000000000000000000000000
χ544-404-2002-44-4-20200000400-22-4-2-2422-400-22000-2-2400022-40000000000000000000000000000000000
χ554-40-24−2i32i3-424-4-202−2i32i3000-2−2i32i34-42-2-2-222200-22−2i32i30111000-1-1-1i3−i3i3−i3i3−i30000000000000000000000000000
χ564-40-242i3−2i3-424-4-2022i3−2i3000-22i3−2i34-42-2-2-222200-222i3−2i30111000-1-1-1−i3i3−i3i3−i3i30000000000000000000000000000
χ574-40-2-2−2i32i3224-410-1i3−i3000-2−2i32i3-2224-2-2-422001-1i3−i30-2110002-1-1−2i32i3i3−i3i3−i30000000000000000000000000000
χ584-40-2-2−2i32i3224-410-1i3−i3000-2−2i32i3-222-24-22-42001-1i3−i301-21000-12-1i3−i3−2i32i3i3−i30000000000000000000000000000
χ594-40-2-2−2i32i3224-410-1i3−i3000-2−2i32i3-222-2-2422-4001-1i3−i3011-2000-1-12i3−i3i3−i3−2i32i30000000000000000000000000000
χ604-40-2-22i3−2i3224-410-1−i3i3000-22i3−2i3-2224-2-2-422001-1−i3i30-2110002-1-12i3−2i3−i3i3−i3i30000000000000000000000000000
χ614-40-2-22i3−2i3224-410-1−i3i3000-22i3−2i3-222-24-22-42001-1−i3i301-21000-12-1−i3i32i3−2i3−i3i30000000000000000000000000000
χ624-40-2-22i3−2i3224-410-1−i3i3000-22i3−2i3-222-2-2422-4001-1−i3i3011-2000-1-12−i3i3−i3i32i3−2i30000000000000000000000000000
χ636666-366-36-2-2-3-3-3-3-3-266-2-2-211-20000001-31111-3000000000000000-2-200000011000000000000000000
χ646666-366-36-2-2-3-3-3-3-3-2-6-6-2-2-211-2000000131111300000000000000022000000-1-1000000000000000000
χ65666-36-3-36-3-2-2-36-3-3-3-200111-2-21000000-20111100000000000000000022-2-22-200-1-1-1-111110000000000
χ66666-36-3-36-3-2-2-36-3-3-3-200111-2-21000000-201111000000000000000000-2-222-22001111-1-1-1-10000000000
χ6766-66-3-6-6-36-2-2-33-33326-6-22211-2000000-1-311-1-13000000000000000-220000001-1000000000000000000
χ6866-66-3-6-6-36-2-2-33-3332-66-22211-2000000-1311-1-1-30000000000000002-2000000-11000000000000000000
χ6966-6-36336-3-2-2-3-6-3332001-1-1-2-210000002011-1-100000000000000000022-2-2-2200-1-11111-1-10000000000
χ7066-6-36336-3-2-2-3-6-3332001-1-1-2-210000002011-1-1000000000000000000-2-2222-20011-1-1-1-1110000000000
χ716-606600-6-6-2260-600000-200-22200000000-22000000000000000000002i−2i−2i2i00002i−2i00−2i2i000000000000
χ726-606600-6-6-2260-600000-200-22200000000-2200000000000000000000−2i2i2i−2i0000−2i2i002i−2i000000000000
χ736-60-36−3i33i3-63-22-303−3i33i30001i3−i3-22-1000000001-1i3−i30000000000000000002i−2i−2i2i0000−ii3−3i−i−330000000000
χ746-60-36−3i33i3-63-22-303−3i33i30001i3−i3-22-1000000001-1i3−i3000000000000000000−2i2i2i−2i0000i−i−33−ii3−30000000000
χ756-60-363i3−3i3-63-22-3033i3−3i30001−i3i3-22-1000000001-1−i3i30000000000000000002i−2i−2i2i0000−ii−33i−i3−30000000000
χ766-60-363i3−3i3-63-22-3033i3−3i30001−i3i3-22-1000000001-1−i3i3000000000000000000−2i2i2i−2i0000i−i3−3−ii−330000000000
χ77121212-6-6-6-6-6-6-4-43-6333-40022222200000020-1-1-1-100000000000000000000000000000000000000000000
χ781212-12-6-666-6-6-4-4363-3-34002-2-2222000000-20-1-11100000000000000000000000000000000000000000000
χ7912-12012-6006-12-44-60600000-4002-24000000002-20000000000000000000000000000000000000000000000
χ8012-120-6-6−6i36i366-4430-33i3−3i300022i3−2i32-2-200000000-11−i3i300000000000000000000000000000000000000000000
χ8112-120-6-66i3−6i366-4430-3−3i33i30002−2i32i32-2-200000000-11i3−i300000000000000000000000000000000000000000000

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