Finite Group Databasebeta

← Group #13147872

Character table — Group #13147872

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222344446664121212121212336666661212121212121212366612121212121212121212121212121212121212124444444422224444121212121212121212121212121212126666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-111111-1-1-1-1-1-1-1-11111-1-111
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-1-1-11111-1-1-1-1111111-1-1
χ911111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-11-11-1-1-111-1-111-1-111-1-111-1-11-11-1
χ1011111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11-111-11111-1-111-1-1-1-111-1-111-11-11
χ1111111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-11-11-1-1-1-111-1-11111-1-111-1-1-11-11
χ1211111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-11-1-1111-1-111-1-111-1-111-1-1111-11-1
χ1311111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11-1-11-11-1111-1-1-1-11111-1-1-1-1111-1-11
χ1411111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111-1-111-111-1-1-1-111-1-11111-1-1-111-1
χ1511111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-11-1-11-1-11111-1-111-1-1-1-111-111-1
χ1611111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-111-11-1-1-11111-1-1-1-11111-1-11-1-11
χ1722222222222222222222-12-122-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000002200-1-1-1-1-1-1-1-1000000000000
χ1822222222222222222222-12-122-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20011111111000000000000
χ192222222222222222222-12-12-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000022220000002200000000-1-1-1-1-1-1-1-10000
χ202222222222222222222-12-12-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000111111110000
χ212222222-2-2222-222-2-2-2-22-12-122-1-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111222200000000-2-200-1-1-1-11111000000000000
χ222222222-2-2222-222-2-2-2-22-12-122-1-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111-2-2-2-20000000022001111-1-1-1-1000000000000
χ232222222-2-2222-222-2-2-2-2-12-12-1-122-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-111111111000022-2-20000002-200000000-1-1-1-111110000
χ242222222-2-2222-222-2-2-2-2-12-12-1-122-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-1111111110000-2-222000000-22000000001111-1-1-1-10000
χ2522222-2-222222-2-2-222-2-22-12-122-1-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-1111122-2-2000000002-200-1-111-1-111000000000000
χ2622222-2-222222-2-2-222-2-22-12-122-1-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-11111-2-22200000000-220011-1-111-1-1000000000000
χ2722222-2-222222-2-2-222-2-2-12-12-1-12211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-1111100002222000000-2-200000000-1-111-1-1110000
χ2822222-2-222222-2-2-222-2-2-12-12-1-12211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-111110000-2-2-2-2000000220000000011-1-111-1-10000
χ2922222-2-2-2-22222-2-2-2-2222-12-122-1-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-122-2-200000000-2200-1-11111-1-1000000000000
χ3022222-2-2-2-22222-2-2-2-2222-12-122-1-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-1-2-222000000002-20011-1-1-1-111000000000000
χ3122222-2-2-2-22222-2-2-2-222-12-12-1-1221111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-1000022-2-2000000-2200000000-1-11111-1-10000
χ3222222-2-2-2-22222-2-2-2-222-12-12-1-1221111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-10000-2-2220000002-20000000011-1-1-1-1110000
χ3322-2-22002-22-2-20002-20022-222-2-2-2000022-2-222-2-2002-20000000022-2-2000000002i−2i2i−2i00000000000000002i−2i002i−2i000000
χ3422-2-22002-22-2-20002-20022-222-2-2-2000022-2-222-2-2002-20000000022-2-200000000−2i2i−2i2i0000000000000000−2i2i00−2i2i000000
χ3522-2-22002-22-2-20002-200-1212-11-2-233−3−322-2-2-1-11100-113−30033−3−3-1-11133−3−300002i−2i2i−2i0000000000000000−ii−i3i3−ii−i3i30000
χ3622-2-22002-22-2-20002-200-1212-11-2-233−3−322-2-2-1-11100-113−30033−3−3-1-11133−3−30000−2i2i−2i2i0000000000000000i−ii3−i3i−ii3−i30000
χ3722-2-22002-22-2-20002-200-1212-11-2-2−3−33322-2-2-1-11100-11−3300−3−333-1-111−3−33300002i−2i2i−2i0000000000000000−iii3−i3−iii3−i30000
χ3822-2-22002-22-2-20002-200-1212-11-2-2−3−33322-2-2-1-11100-11−3300−3−333-1-111−3−3330000−2i2i−2i2i0000000000000000i−i−i3i3i−i−i3i30000
χ3922-2-2200-222-2-2000-220022-222-2-2-20000-2-22222-2-200-2200000000-2-222000000002i−2i−2i2i00000000000000002i−2i00−2i2i000000
χ4022-2-2200-222-2-2000-220022-222-2-2-20000-2-22222-2-200-2200000000-2-22200000000−2i2i2i−2i0000000000000000−2i2i002i−2i000000
χ4122-2-2200-222-2-2000-2200-1212-11-2-233−3−3-2-222-1-111001-1−330033−3−311-1-1−3−33300002i−2i−2i2i0000000000000000−ii−i3i3i−ii3−i30000
χ4222-2-2200-222-2-2000-2200-1212-11-2-233−3−3-2-222-1-111001-1−330033−3−311-1-1−3−3330000−2i2i2i−2i0000000000000000i−ii3−i3−ii−i3i30000
χ4322-2-2200-222-2-2000-2200-1212-11-2-2−3−333-2-222-1-111001-13−300−3−33311-1-133−3−300002i−2i−2i2i0000000000000000−iii3−i3i−i−i3i30000
χ4422-2-2200-222-2-2000-2200-1212-11-2-2−3−333-2-222-1-111001-13−300−3−33311-1-133−3−30000−2i2i2i−2i0000000000000000i−i−i3i3−iii3−i30000
χ452-22-222-200-22-202-20000222-2-2-22-22-22-200002-22-22-20000002-22-2000000002i−2i2i−2i0000000000002i−2i2i−2i0000000000000000
χ462-22-222-200-22-202-20000222-2-2-22-22-22-200002-22-22-20000002-22-200000000−2i2i−2i2i000000000000−2i2i−2i2i0000000000000000
χ472-22-222-200-22-202-200002-121-2-2-112-22-23−33−3-11-11-1100003−3-11-113−33−33−33−32i−2i2i−2i000000000000−ii−ii−i3i3−i3i3000000000000
χ482-22-222-200-22-202-200002-121-2-2-112-22-23−33−3-11-11-1100003−3-11-113−33−33−33−3−2i2i−2i2i000000000000i−ii−ii3−i3i3−i3000000000000
χ492-22-222-200-22-202-200002-121-2-2-112-22-2−33−33-11-11-110000−33-11-11−33−33−33−332i−2i2i−2i000000000000−ii−iii3−i3i3−i3000000000000
χ502-22-222-200-22-202-200002-121-2-2-112-22-2−33−33-11-11-110000−33-11-11−33−33−33−33−2i2i−2i2i000000000000i−ii−i−i3i3−i3i3000000000000
χ512-22-22-2200-22-20-220000222-2-2-22-2-22-2200002-22-2-22000000-22-22000000002i−2i−2i2i0000000000002i−2i−2i2i0000000000000000
χ522-22-22-2200-22-20-220000222-2-2-22-2-22-2200002-22-2-22000000-22-2200000000−2i2i2i−2i000000000000−2i2i2i−2i0000000000000000
χ532-22-22-2200-22-20-2200002-121-2-2-11-22-223−33−3-11-111-10000−331-11-13−33−3−33−332i−2i−2i2i000000000000−iii−i−i3i3i3−i3000000000000
χ542-22-22-2200-22-20-2200002-121-2-2-11-22-223−33−3-11-111-10000−331-11-13−33−3−33−33−2i2i2i−2i000000000000i−i−iii3−i3−i3i3000000000000
χ552-22-22-2200-22-20-2200002-121-2-2-11-22-22−33−33-11-111-100003−31-11-1−33−333−33−32i−2i−2i2i000000000000−iii−ii3−i3−i3i3000000000000
χ562-22-22-2200-22-20-2200002-121-2-2-11-22-22−33−33-11-111-100003−31-11-1−33−333−33−3−2i2i2i−2i000000000000i−i−ii−i3i3i3−i3000000000000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ584444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221111-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5944444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-22222-2-2-2-2111122-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ6044444-4-4-4-44444-4-4-4-444-2-2-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ6144-4-44004-44-4-40004-4004-2-4-24-4220000-2-222-2-222004-400000000-2-2220000000000000000000000000000000000000000
χ6244-4-44004-44-4-40004-400-2-22-2-22222323−23−23-2-22211-1-100-2223−2300−3−33311-1-1−3−333000000000000000000000000000000000000
χ6344-4-44004-44-4-40004-400-2-22-2-2222−23−232323-2-22211-1-100-22−23230033−3−311-1-133−3−3000000000000000000000000000000000000
χ6444-4-4400-444-4-4000-44004-2-4-24-422000022-2-2-2-22200-440000000022-2-20000000000000000000000000000000000000000
χ6544-4-4400-444-4-4000-4400-2-22-2-22222323−23−2322-2-211-1-1002-2−232300−3−333-1-11133−3−3000000000000000000000000000000000000
χ6644-4-4400-444-4-4000-4400-2-22-2-2222−23−23232322-2-211-1-1002-223−230033−3−3-1-111−3−333000000000000000000000000000000000000
χ674-44-444-400-44-404-40000-24-2-4224-4-22-220000-22-224-4000000-22-2200000000000000000000000000000000000000000000
χ684-44-444-400-44-404-40000-2-2-2222-22-22-2223−2323−231-11-1-22000023−231-11-1−33−33−33−33000000000000000000000000000000000000
χ694-44-444-400-44-404-40000-2-2-2222-22-22-22−2323−23231-11-1-220000−23231-11-13−33−33−33−3000000000000000000000000000000000000
χ704-44-44-4400-44-40-440000-24-2-4224-42-22-20000-22-22-440000002-22-200000000000000000000000000000000000000000000
χ714-44-44-4400-44-40-440000-2-2-2222-222-22-223−2323−231-11-12-20000−2323-11-11−33−333−33−3000000000000000000000000000000000000
χ724-44-44-4400-44-40-440000-2-2-2222-222-22-2−2323−23231-11-12-2000023−23-11-113−33−3−33−33000000000000000000000000000000000000
χ734-4-4440000-4-44000000044-4-4-44-44000000004-4-4400000000000000000000000000000000000000000000000000000000
χ744-4-4440000-4-4400000004-2-42-442-2000023−23−2323-222-200000000000023−23−23230000000000000000000000000000000000000000
χ754-4-4440000-4-4400000004-2-42-442-20000−232323−23-222-2000000000000−232323−230000000000000000000000000000000000000000
χ764-4-4440000-4-440000000-242-42-2-4423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ774-4-4440000-4-440000000-242-42-2-44−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ784-4-4440000-4-440000000-2-2222-22-223−23−232323−23−23231-1-1100000000−333−3−333−33-3-33000000000000000000000000000000000000
χ794-4-4440000-4-440000000-2-2222-22-223−23−2323−232323−231-1-1100000000−333−33−3−33-333-3000000000000000000000000000000000000
χ804-4-4440000-4-440000000-2-2222-22-2−232323−2323−23−23231-1-11000000003−3−33−333−3-333-3000000000000000000000000000000000000
χ814-4-4440000-4-440000000-2-2222-22-2−232323−23−232323−231-1-11000000003−3−333−3−333-3-33000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000222200000000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000-2-2-2-2000000000000000000001111
χ846666-366-6-6-3-3-3-6-3-3333300000000000000000000000000000000000000000000000022-2-200000000000000000000-1-111
χ856666-366-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000-2-2220000000000000000000011-1-1
χ866666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000002-22-200000000000000000000-11-11
χ876666-3-6-666-3-3-3-633-3-333000000000000000000000000000000000000000000000000-22-22000000000000000000001-11-1
χ886666-3-6-6-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000002-2-2200000000000000000000-111-1
χ896666-3-6-6-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000-222-2000000000000000000001-1-11
χ901212-12-12-60012-12-666000-66000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-600-1212-6660006-6000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-612-12006-660-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6-1212006-6606-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-600000−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-6000006i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000000

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