Finite Group Databasebeta

← Group #13135215

Character table — Group #13135215

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1122222444446666881212121212121212121224242424242424242424363636363636727272727272727272727272727272
order12236664441212336612123666661212121212121212121212121212441212121226688882424242424242424
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111-1-1111111-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1i−ii−iii−i−iii−i−i
χ611111111-1-1111111-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1−ii−ii−i−iii−i−iii
χ711111111-1-1111111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111i−i−iiii−i−i−i−iii
χ811111111-1-1111111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111−iii−i−i−iiiii−i−i
χ92222222222222-12-122-12-1-1-1-122-1-12-12-1-1-1-1-1-1-100000000000220000-1-1-1-1
χ102222222222222-12-122-12-1-1-1-122-1-12-12-1-1-1-1-1-1-100000000000-2-200001111
χ11222222222222-12-1222-1-12-1-1-1-1-122-12-12-1-1-1-1-1-10000000002200-1-1-1-10000
χ12222222222222-12-1222-1-12-1-1-1-1-122-12-12-1-1-1-1-1-1000000000-2-20011110000
χ1322222222-2-2222-12-1-2-2-12-1-1-1-1-2-2112-1-21-1-11111000000000002i−2i0000−i−iii
χ1422222222-2-2222-12-1-2-2-12-1-1-1-1-2-2112-1-21-1-1111100000000000−2i2i0000ii−i−i
χ1522222222-2-222-12-12-2-2-1-12-1-1-111-2-2-121-2-1-111110000000002i−2i00−i−iii0000
χ1622222222-2-222-12-12-2-2-1-12-1-1-111-2-2-121-2-1-11111000000000−2i2i00ii−i−i0000
χ172222222-22-2-2-222222-222222222-2-2-2-2-22-2-222-2-2000000000000000000000
χ182222222-22-2-2-22-12-12-2-12-1-1-1-12211-21-2-111-1-111000000000000000003−33−3
χ192222222-22-2-2-22-12-12-2-12-1-1-1-12211-21-2-111-1-11100000000000000000−33−33
χ202222222-22-2-2-2-12-122-2-1-12-1-1-1-1-1-2-21-21211-1-1110000000000000−i3i3−i3i30000
χ212222222-22-2-2-2-12-122-2-1-12-1-1-1-1-1-2-21-21211-1-1110000000000000i3−i3i3−i30000
χ222222222-2-22-2-22222-22222222-2-222-2-22-2-2-2-2-222000000000000000000000
χ232222222-2-22-2-22-12-1-22-12-1-1-1-1-2-2-1-1-21211111-1-100000000000000000−i3i3i3−i3
χ242222222-2-22-2-22-12-1-22-12-1-1-1-1-2-2-1-1-21211111-1-100000000000000000i3−i3−i3i3
χ252222222-2-22-2-2-12-12-22-1-12-1-1-111221-2-1-21111-1-100000000000003−3−330000
χ262222222-2-22-2-2-12-12-22-1-12-1-1-111221-2-1-21111-1-10000000000000−333−30000
χ27444444444444-2-2-2-2441-2-2111-2-2-2-2-2-2-2-2111111000000000000000000000
χ2844444444-4-444-2-2-2-2-4-41-2-21112222-2-22211-1-1-1-1000000000000000000000
χ294444444-44-4-4-4-2-2-2-24-41-2-2111-2-222222-2-1-111-1-1000000000000000000000
χ304444444-4-44-4-4-2-2-2-2-441-2-211122-2-222-22-1-1-1-111000000000000000000000
χ3144-444-4-4000004444004-4-4-4-4400000000000000000000000000000000000
χ3244-444-4-4000004-24-200-2-4222-200−2i32i300000000−2i32i3000000000000000000000
χ3344-444-4-4000004-24-200-2-4222-2002i3−2i3000000002i3−2i3000000000000000000000
χ3444-444-4-400000-24-2400-22-422-2−2i32i300000000−2i32i300000000000000000000000
χ3544-444-4-400000-24-2400-22-422-22i3−2i3000000002i3−2i300000000000000000000000
χ3644-444-4-400000-2-2-2-200122-1-11−2i32i3−2i32i300003-3i3−i3i3−i3000000000000000000000
χ3744-444-4-400000-2-2-2-200122-1-11−2i32i32i3−2i30000-33i3−i3−i3i3000000000000000000000
χ3844-444-4-400000-2-2-2-200122-1-112i3−2i3−2i32i30000-33−i3i3i3−i3000000000000000000000
χ3944-444-4-400000-2-2-2-200122-1-112i3−2i32i3−2i300003-3−i3i3−i3i3000000000000000000000
χ404-404-4000000044-4-40040000-4000000000000002i−2i2i2i−2i−2i000000000000000
χ414-404-4000000044-4-40040000-400000000000000−2i2i−2i−2i2i2i000000000000000
χ42666-3-3-3-3666-3-30000-3-30000000000000000000022-1-1-1-12-1-1000000000000
χ43666-3-3-3-3666-3-30000-3-300000000000000000000-2-21111-211000000000000
χ44666-3-3-3-36-6-6-3-30000330000000000000000000022-1-1-1-1-211000000000000
χ45666-3-3-3-36-6-6-3-300003300000000000000000000-2-211112-1-1000000000000
χ46666-3-3-3-3-66-6330000-330000000000000000000000−i3i3−i3i30−i3i3000000000000
χ47666-3-3-3-3-66-6330000-330000000000000000000000i3−i3i3−i30i3−i3000000000000
χ48666-3-3-3-3-6-663300003-30000000000000000000000−i3i3−i3i30i3−i3000000000000
χ49666-3-3-3-3-6-663300003-30000000000000000000000i3−i3i3−i30−i3i3000000000000
χ508-808-800000008-4-8400-40000400000000000000000000000000000000000
χ518-808-80000000-484-800-40000400000000000000000000000000000000000
χ528-808-80000000-4-444002006-6-200000000000000000000000000000000000
χ538-808-80000000-4-44400200-66-200000000000000000000000000000000000
χ541212-12-6-666000−6i36i300000000000000000000000000000000000000000000000
χ551212-12-6-6660006i3−6i300000000000000000000000000000000000000000000000
χ5612-120-66−6i36i300000000000000000000000000000002i−2i2ζ72ζ11−2ζ7−2ζ11000000000000000
χ5712-120-66−6i36i30000000000000000000000000000000−2i2i−2ζ7−2ζ112ζ72ζ11000000000000000
χ5812-120-666i3−6i300000000000000000000000000000002i−2i2ζ112ζ7−2ζ11−2ζ7000000000000000
χ5912-120-666i3−6i30000000000000000000000000000000−2i2i−2ζ11−2ζ72ζ112ζ7000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.