Finite Group Databasebeta

← Group #13180793

Character table — Group #13180793

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222334444466666666688888812121212121212161616161616161616161616161616181818181818363636363636363636363636484848484848108108108108
order12334661212223612121244466661212333666661212121212333666121212121212121212444444246612121212121212121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ311111111111111111-1-1111111111111111-1-111111111111111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111-1-1111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-111-1-11111-1-1-1-11-11111-1-111111111-11-1-1-1111111-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-111-1-1111-1-1-11-11-1
χ61111-111-1-11111-1-1-1-11-11111-1-111111111-11-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-11-1-1-111111-1-1-1-11-11
χ71111-111-1-11111-1-1-1-1-111111-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1111-1-1-1-1-1111-11-11
χ81111-111-1-11111-1-1-1-1-111111-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-11-1-111-1-1-11111-11-1
χ92222222222222222222222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000000000220000-1-1-1-1-1-10000
χ1022222222222222222-2-2222222-1-1-1-1-1-1222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000000-2-200001111110000
χ112222-222-2-22222-2-2-2-22-22222-2-2-1-1-1-1-1-122-22-2-2-2-1-1-1-1-1-11111111112-200000000002-20000-1-1-11110000
χ122222-222-2-22222-2-2-2-2-222222-2-2-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1111111111-220000000000-220000111-1-1-10000
χ13222-12-12-1-122-1-12-1-120022-1-1-1-1222222-1-1200-1-1-1-1-1-1-1-1222-1-1-1-1-1-100222222-1-1-1-100-1-1-1-10000000000
χ14222-12-12-1-122-1-12-1-120022-1-1-1-1222222-1-1200-1-1-1-1-1-1-1-1222-1-1-1-1-1-100-2-2-2-2-2-211110011110000000000
χ15222-1-2-121122-1-1-211-20022-1-111222222-1-1-20011-1-1-1-1-1-1-2-2-2111111002222-2-211-1-100-1-1110000000000
χ16222-1-2-121122-1-1-211-20022-1-111222222-1-1-20011-1-1-1-1-1-1-2-2-211111100-2-2-2-222-1-1110011-1-10000000000
χ1722-1222-12222-1-1-1-1-1222-1-122222-1-12-1-1-1-1-1-1-1-1-12-1-12-1-12-1-122-1-1-1-1220000000000-1-100002-1-12-1-10000
χ1822-1222-12222-1-1-1-1-1222-1-12222-12-1-12-1-1-1-1-1-1-1-1-12-1-12-1-12-1-1-122-1-1220000000000-1-10000-12-1-12-10000
χ1922-1222-12222-1-1-1-1-1222-1-12222-1-12-1-12-1-1-1-1-1-1-1-1-12-1-12-1-12-1-1-1-122220000000000-1-10000-1-12-1-120000
χ2022-1222-12222-1-1-1-1-12-2-2-1-122222-1-12-1-1-1-1-111-1-12-1-12-1-12-1-122-1-1-1-1-2-20000000000110000-211-2110000
χ2122-1222-12222-1-1-1-1-12-2-2-1-12222-12-1-12-1-1-1-111-1-1-12-1-12-1-12-1-1-122-1-1-2-200000000001100001-211-210000
χ2222-1222-12222-1-1-1-1-12-2-2-1-12222-1-12-1-12-1-1-111-1-1-1-12-1-12-1-12-1-1-1-122-2-2000000000011000011-211-20000
χ2322-12-22-1-2-222-1-1111-22-2-1-122-2-22-1-12-1-1-1-11-11112-1-12-1-1-211-2-211112-20000000000-1100002-1-1-2110000
χ2422-12-22-1-2-222-1-1111-22-2-1-122-2-2-12-1-12-1-1-11-1111-12-1-12-11-2111-2-2112-20000000000-110000-12-11-210000
χ2522-12-22-1-2-222-1-1111-22-2-1-122-2-2-1-12-1-12-1-11-1111-1-12-1-1211-21111-2-22-20000000000-110000-1-1211-20000
χ2622-12-22-1-2-222-1-1111-2-22-1-122-2-22-1-12-1-1-1-111-1112-1-12-1-1-211-2-21111-2200000000001-10000-2112-1-10000
χ2722-12-22-1-2-222-1-1111-2-22-1-122-2-2-12-1-12-1-1-111-111-12-1-12-11-2111-2-211-2200000000001-100001-21-12-10000
χ2822-12-22-1-2-222-1-1111-2-22-1-122-2-2-1-12-1-12-1-111-111-1-12-1-1211-21111-2-2-2200000000001-1000011-2-1-120000
χ292-2220-2-200-222-20000002-22-200222-2-2-22-200000222-2-2-2000000000002i−2i2i−2i00002i−2i002i−2i000000000000
χ302-2220-2-200-222-20000002-22-200222-2-2-22-200000222-2-2-200000000000−2i2i−2i2i0000−2i2i00−2i2i000000000000
χ312-22-101-23−3-22-1103−30002-2-113−3222-2-2-2-110003−3-1-1-11110003−33−33−3002i−2i2i−2i00−i3i3−ii00−ii−i3i30000000000
χ322-22-101-23−3-22-1103−30002-2-113−3222-2-2-2-110003−3-1-1-11110003−33−33−300−2i2i−2i2i00i3−i3i−i00i−ii3−i30000000000
χ332-22-101-2−33-22-110−330002-2-11−33222-2-2-2-11000−33-1-1-1111000−33−33−33002i−2i2i−2i00i3−i3−ii00−iii3−i30000000000
χ342-22-101-2−33-22-110−330002-2-11−33222-2-2-2-11000−33-1-1-1111000−33−33−3300−2i2i−2i2i00−i3i3i−i00i−i−i3i30000000000
χ35333333333-1-133333-133-1-1-1-1-1-1000000-1-1-133-1-1000000000000000-1-111-1-11-11111-1-1-1-1-1-100000011-1-1
χ36333333333-1-133333-133-1-1-1-1-1-1000000-1-1-133-1-1000000000000000-1-1-1-111-11-1-1-1-1-1-11111000000-1-111
χ37333333333-1-133333-1-3-3-1-1-1-1-1-1000000-1-1-1-3-3-1-10000000000000001111-1-11-1111111-1-1-1-1000000-1-111
χ38333333333-1-133333-1-3-3-1-1-1-1-1-1000000-1-1-1-3-3-1-100000000000000011-1-111-11-1-1-1-111111100000011-1-1
χ393333-333-3-3-1-133-3-3-313-3-1-1-1-111000000-1-113-311000000000000000-1111-1-1-11-1-111-11-1-1110000001-1-11
χ403333-333-3-3-1-133-3-3-313-3-1-1-1-111000000-1-113-311000000000000000-11-1-1111-111-1-1-1111-1-1000000-111-1
χ413333-333-3-3-1-133-3-3-31-33-1-1-1-111000000-1-11-33110000000000000001-111-1-1-11-1-1111-1-1-111000000-111-1
χ423333-333-3-3-1-133-3-3-31-33-1-1-1-111000000-1-11-33110000000000000001-1-1-1111-111-1-11-111-1-10000001-1-11
χ43444-24-24-2-244-2-24-2-240044-2-2-2-2-2-2-2-2-2-2-2-2400-2-2111111-2-2-21111110000000000000000000000000000
χ44444-2-4-242244-2-2-422-40044-2-222-2-2-2-2-2-2-2-2-40022111111222-1-1-1-1-1-10000000000000000000000000000
χ4544-2-24-2-2-2-24411-211400-2-2-2-2-2-24-2-24-2-211-20011-211-2114-2-2-2-211110000000000000000000000000000
χ4644-2-24-2-2-2-24411-211400-2-2-2-2-2-2-24-2-24-211-200111-211-21-24-211-2-2110000000000000000000000000000
χ4744-2-24-2-2-2-24411-211400-2-2-2-2-2-2-2-24-2-2411-2001111-211-2-2-241111-2-20000000000000000000000000000
χ4844-2-2-4-2-22244112-1-1-400-2-2-2-2224-2-24-2-211200-1-1-211-211-42222-1-1-1-10000000000000000000000000000
χ4944-2-2-4-2-22244112-1-1-400-2-2-2-222-24-2-24-211200-1-11-211-212-42-1-122-1-10000000000000000000000000000
χ5044-2-2-4-2-22244112-1-1-400-2-2-2-222-2-24-2-2411200-1-111-211-222-4-1-1-1-1220000000000000000000000000000
χ514-4440-4-400-444-40000004-44-400-2-2-22224-400000-2-2-22220000000000000000000000000000000000000
χ524-44-202-423−23-44-22023−230004-4-2223−23-2-2-2222-2200023−23111-1-1-1000−33−33−330000000000000000000000000000
χ534-44-202-4−2323-44-220−23230004-4-22−2323-2-2-2222-22000−2323111-1-1-10003−33−33−30000000000000000000000000000
χ544-4-240-4200-44-22000000-224-4004-2-2-422-22000004-2-2-4220000000000000000000000000000000000000
χ554-4-240-4200-44-22000000-224-400-24-22-42-2200000-24-22-420000000000000000000000000000000000000
χ564-4-240-4200-44-22000000-224-400-2-2422-4-2200000-2-2422-40000000000000000000000000000000000000
χ574-4-2-202223−23-441-10−33000-22-2223−234-2-2-4221-1000−33-2112-1-100023−23−33−330000000000000000000000000000
χ584-4-2-202223−23-441-10−33000-22-2223−23-24-22-421-1000−331-21-12-1000−3323−23−330000000000000000000000000000
χ594-4-2-202223−23-441-10−33000-22-2223−23-2-2422-41-1000−3311-2-1-12000−33−3323−230000000000000000000000000000
χ604-4-2-2022−2323-441-103−3000-22-22−23234-2-2-4221-10003−3-2112-1-1000−23233−33−30000000000000000000000000000
χ614-4-2-2022−2323-441-103−3000-22-22−2323-24-22-421-10003−31-21-12-10003−3−23233−30000000000000000000000000000
χ624-4-2-2022−2323-441-103−3000-22-22−2323-2-2422-41-10003−311-2-1-120003−33−3−23230000000000000000000000000000
χ63666-36-36-3-3-2-2-3-36-3-3-200-2-2111100000011-200110000000000000000022-2-22-2-1-1-1-10011110000000000
χ64666-36-36-3-3-2-2-3-36-3-3-200-2-2111100000011-2001100000000000000000-2-222-22111100-1-1-1-10000000000
χ65666-3-6-3633-2-2-3-3-633200-2-211-1-100000011200-1-10000000000000000022-2-2-2211-1-10011-1-10000000000
χ66666-3-6-3633-2-2-3-3-633200-2-211-1-100000011200-1-100000000000000000-2-2222-2-1-11100-1-1110000000000
χ6766-3666-366-2-2-3-3-3-3-3-26611-2-2-2-2000000111-3-311000000000000000-2-200000000001100000000000000
χ6866-3666-366-2-2-3-3-3-3-3-2-6-611-2-2-2-20000001113311000000000000000220000000000-1-100000000000000
χ6966-36-66-3-6-6-2-2-3-333326-611-2-22200000011-1-33-1-1000000000000000-2200000000001-100000000000000
χ7066-36-66-3-6-6-2-2-3-33332-6611-2-22200000011-13-3-1-10000000000000002-20000000000-1100000000000000
χ716-6660-6-6002-26-6000000-22-2200000000-2200000000000000000000002i−2i−2i2i00002i−2i00−2i2i000000000000
χ726-6660-6-6002-26-6000000-22-2200000000-220000000000000000000000−2i2i2i−2i0000−2i2i002i−2i000000000000
χ736-66-303-633−332-2-33033−33000-221-1−330000001-1000−33000000000000000002i−2i−2i2i00−i3i3−ii00i−ii3−i30000000000
χ746-66-303-633−332-2-33033−33000-221-1−330000001-1000−3300000000000000000−2i2i2i−2i00i3−i3i−i00−ii−i3i30000000000
χ756-66-303-6−33332-2-330−3333000-221-13−30000001-10003−3000000000000000002i−2i−2i2i00i3−i3−ii00i−i−i3i30000000000
χ766-66-303-6−33332-2-330−3333000-221-13−30000001-10003−300000000000000000−2i2i2i−2i00−i3i3i−i00−iii3−i30000000000
χ771212-6-612-6-6-6-6-4-433-633-400222222000000-1-1200-1-10000000000000000000000000000000000000000000
χ781212-6-6-12-6-666-4-4336-3-34002222-2-2000000-1-1-200110000000000000000000000000000000000000000000
χ7912-12-6120-126004-4-660000002-2-44000000002-2000000000000000000000000000000000000000000000000
χ8012-12-6-606663−634-43-30−33330002-22-2−2323000000-110003−30000000000000000000000000000000000000000000
χ8112-12-6-6066−63634-43-3033−330002-22-223−23000000-11000−330000000000000000000000000000000000000000000

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