Finite Group Databasebeta

← Group #13146554

Character table — Group #13146554

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222444121212121212121218181818181818182424242436363636363636363636363636363636363672727272727272727272
order1222366641212336666664444121212121212121222448888121224242424242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111-1-1-1111111111-1-111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11-111-1-111-1-1
χ611111111-1-1-1111111111-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-111
χ711111111-1-1-1111111111-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-111
χ811111111-1-1-1111111111-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111-1-1-11111-1-1
χ92222222222222222222-2-2-2-2-2-2-2-2222200000000-2-2000000000000000000
χ1022222222-2-2-222222222-222-2-2-2-2-2-2-2-2-20000000022000000000000000000
χ112-22-22-22-20002222-2-2-2-2200-222-2-200002-20000000000000000002-2000000
χ122-22-22-22-20002222-2-2-2-2200-222-2-20000-22000000000000000000-22000000
χ132-22-22-22-20002222-2-2-2-2-2002-2-2220000002i−2i0000000000000000002i−2i0000
χ142-22-22-22-20002222-2-2-2-2-2002-2-222000000−2i2i000000000000000000−2i2i0000
χ152-2-222-2-2200022-2-2-2-22202-200000000000002−22−22-222−2−222−2−20000000000
χ162-2-222-2-2200022-2-2-2-22202-20000000000000−22−222-2−2−222−2−2220000000000
χ172-2-222-2-2200022-2-2-2-2220-2200000000000002−2−22-2222−2−2−2−2220000000000
χ182-2-222-2-2200022-2-2-2-2220-220000000000000−222−2-22−2−22222−2−20000000000
χ19444444444441-21-21-2-210000000011-2-2000000000000000000220000-1-1-1-1
χ20444444444441-21-21-2-210000000011-2-2000000000000000000-2-200001111
χ2144444444444-21-21-211-200000000-2-21122220000000000000000-1-1-1-10000
χ2244444444444-21-21-211-200000000-2-211-2-2-2-2000000000000000011110000
χ2344444444-4-4-41-21-21-2-2100000000-1-1220000000000000000002-20000-1-111
χ2444444444-4-4-41-21-21-2-2100000000-1-122000000000000000000-22000011-1-1
χ2544444444-4-4-4-21-21-211-20000000022-1-122-2-20000000000000000-1-1110000
χ2644444444-4-4-4-21-21-211-20000000022-1-1-2-222000000000000000011-1-10000
χ2744-4-444-4-40001-2-121-22-1000000003-3000000000000000000000000003−33−3
χ2844-4-444-4-40001-2-121-22-1000000003-300000000000000000000000000−33−33
χ2944-4-444-4-40001-2-121-22-100000000-33000000000000000000000000003−3−33
χ3044-4-444-4-40001-2-121-22-100000000-3300000000000000000000000000−333−3
χ3144-4-444-4-400044-4-444-4-40000000000000000000000000000000000000000
χ324-44-44-44-4000-21-212-1-1200000000003i−3i2-22i−2i0000000000000000-11−ii0000
χ334-44-44-44-4000-21-212-1-1200000000003i−3i-22−2i2i00000000000000001-1i−i0000
χ344-44-44-44-4000-21-212-1-120000000000−3i3i2-2−2i2i0000000000000000-11i−i0000
χ354-44-44-44-4000-21-212-1-120000000000−3i3i-222i−2i00000000000000001-1−ii0000
χ366666-3-3-3-36-3-3000000002222-1-1-1-1000000000000-1-13−33−33−33−30000000000
χ376666-3-3-3-36-3-3000000002222-1-1-1-1000000000000-1-1−33−33−33−330000000000
χ386666-3-3-3-36-3-300000000-2-2-2-2111100000000222211-1-1-1-1-1-1-1-10000000000
χ396666-3-3-3-36-3-300000000-2-2-2-2111100000000-2-2-2-211111111110000000000
χ406666-3-3-3-3-633000000002-2-22-1-1-1-1000000000000113−33−3−33−330000000000
χ416666-3-3-3-3-633000000002-2-22-1-1-1-100000000000011−33−333−33−30000000000
χ426666-3-3-3-3-63300000000-222-211110000000022-2-2-1-1-1-1-1-111110000000000
χ436666-3-3-3-3-63300000000-222-2111100000000-2-222-1-11111-1-1-1-10000000000
χ446-6-66-333-3033−330000000002-203−33−3000000002−2−22-11ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000
χ456-6-66-333-3033−330000000002-203−33−300000000−222−2-11−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000
χ466-6-66-333-3033−33000000000-220−33−33000000002−22−21-1ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000
χ476-6-66-333-3033−33000000000-220−33−3300000000−22−221-1−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000
χ486-6-66-333-30−33330000000002-20−33−33000000002−2−22-11ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000
χ496-6-66-333-30−33330000000002-20−33−3300000000−222−2-11−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000
χ506-6-66-333-30−3333000000000-2203−33−3000000002−22−21-1ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000
χ516-6-66-333-30−3333000000000-2203−33−300000000−22−221-1−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000
χ5288-8-888-8-8000-424-2-42-240000000000000000000000000000000000000000
χ538-88-88-88-80002-42-4-244-20000000000000000000000000000000000000000
χ548-8-888-8-880002-4-24-24-420000000000000000000000000000000000000000
χ558-8-888-8-88000-424-24-22-40000000000000000000000000000000000000000
χ561212-12-12-6-66600000000000000023−23−232300000000000000000000000000000000
χ571212-12-12-6-666000000000000000−232323−2300000000000000000000000000000000
χ5812-1212-12-66-6600000000000400-4-2-22200000000000000000000000000000000
χ5912-1212-12-66-6600000000000-400422-2-200000000000000000000000000000000

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