Finite Group Databasebeta

← Group #13146543

Character table — Group #13146543

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
χ1122-2-22-22-2000222-22-2-2-2200-222-2-200002-20000000000000000002-2000000
χ1222-2-22-22-2000222-22-2-2-2200-222-2-20000-22000000000000000000-22000000
χ1322-2-22-22-2000222-22-2-2-2-2002-2-2220000002i−2i0000000000000000002i−2i0000
χ1422-2-22-22-2000222-22-2-2-2-2002-2-222000000−2i2i000000000000000000−2i2i0000
χ152-22-22-2-2200022-22-2-22-202-20000000000000−i2i2−i2i22-2−i2−i2i2i2−i2−i2i2i20000000000
χ162-22-22-2-2200022-22-2-22-202-20000000000000i2−i2i2−i22-2i2i2−i2−i2i2i2−i2−i20000000000
χ172-22-22-2-2200022-22-2-22-20-220000000000000−i2i2i2−i2-22−i2−i2i2i2i2i2−i2−i20000000000
χ182-22-22-2-2200022-22-2-22-20-220000000000000i2−i2−i2i2-22i2i2−i2−i2−i2−i2i2i20000000000
χ19444444444441-211-2-2-2100000000-2-211000000000000000000220000-1-1-1-1
χ20444444444441-211-2-2-2100000000-2-211000000000000000000-2-200001111
χ2144444444444-21-2-2111-20000000011-2-222220000000000000000-1-1-1-10000
χ2244444444444-21-2-2111-20000000011-2-2-2-2-2-2000000000000000011110000
χ2344444444-4-4-41-211-2-2-210000000022-1-10000000000000000002-20000-1-111
χ2444444444-4-4-41-211-2-2-210000000022-1-1000000000000000000-22000011-1-1
χ2544444444-4-4-4-21-2-2111-200000000-1-12222-2-20000000000000000-1-1110000
χ2644444444-4-4-4-21-2-2111-200000000-1-122-2-222000000000000000011-1-10000
χ2744-4-44-44-4000-21-221-1-12000000003i−3i002-22i−2i0000000000000000-11−ii0000
χ2844-4-44-44-4000-21-221-1-12000000003i−3i00-22−2i2i00000000000000001-1i−i0000
χ2944-4-44-44-4000-21-221-1-1200000000−3i3i002-2−2i2i0000000000000000-11i−i0000
χ3044-4-44-44-4000-21-221-1-1200000000−3i3i00-222i−2i00000000000000001-1−ii0000
χ314-4-4444-4-40001-2-1-12-22100000000003-3000000000000000000000000−i3i3−i3i3
χ324-4-4444-4-40001-2-1-12-22100000000003-3000000000000000000000000i3−i3i3−i3
χ334-4-4444-4-40001-2-1-12-2210000000000-33000000000000000000000000−i3i3i3−i3
χ344-4-4444-4-40001-2-1-12-2210000000000-33000000000000000000000000i3−i3−i3i3
χ354-4-4444-4-400044-4-4-44-440000000000000000000000000000000000000000
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
χ446-66-6-333-3033−330000000002-203−33−300000000−i2i2i2−i2-11ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ456-66-6-333-3033−330000000002-203−33−300000000i2−i2−i2i2-11−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ466-66-6-333-3033−33000000000-220−33−3300000000−i2i2−i2i21-1ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ476-66-6-333-3033−33000000000-220−33−3300000000i2−i2i2−i21-1−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ486-66-6-333-30−33330000000002-20−33−3300000000−i2i2i2−i2-11ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ496-66-6-333-30−33330000000002-20−33−3300000000i2−i2−i2i2-11−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ506-66-6-333-30−3333000000000-2203−33−300000000−i2i2−i2i21-1ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ516-66-6-333-30−3333000000000-2203−33−300000000i2−i2i2−i21-1−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ5288-8-88-88-80002-42-2-444-20000000000000000000000000000000000000000
χ538-88-88-8-880002-4-2244-4-20000000000000000000000000000000000000000
χ548-88-88-8-88000-424-4-2-2240000000000000000000000000000000000000000
χ558-8-8888-8-8000-4244-22-2-40000000000000000000000000000000000000000
χ561212-12-12-66-6600000000000400-4-2-22200000000000000000000000000000000
χ571212-12-12-66-6600000000000-400422-2-200000000000000000000000000000000
χ5812-12-1212-6-66600000000000000023−23−232300000000000000000000000000000000
χ5912-12-1212-6-666000000000000000−232323−2300000000000000000000000000000000

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