Finite Group Databasebeta

← Group #13139209

Character table — Group #13139209

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222244466666688812121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order12234466121233661212824243666121212121261224242424242424242222444412121212466668121212122424
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111
χ311111111111111111111111111111111111111-1-11-11-1111111-1-11-1-1-1-1-1-11-1-1
χ411111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-111-1-1-1-1111-1-1-1
χ51111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-11-1-11-1-1
χ61111111111111111-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-111-1-1-1
χ71111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11-11-1-11-111111
χ81111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11-11111111-11-1-1-111-1-1-111
χ922222222222-1-1222222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1220000000000000-1-120000-1-1
χ1022222222222-1-1222222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2000000000000011-2000011
χ1122222222222-1-1222-2-2-2-1-1-122-1-1-1-1-1-1-2-2111111220000000000000-1-1-2000011
χ1222222222222-1-1222-2-2-2-1-1-122-1-1-1-1-1-1-2-2111111-2-200000000000001120000-1-1
χ132222222222-122-1-1-1222-12-1-1-12-1-12-1-1-1-122-1-1-1-100202022-1-1-1-100-1000000-100
χ142222222222-122-1-1-1222-12-1-1-12-1-12-1-1-1-122-1-1-1-100-20-20-2-21111001000000100
χ152222222222-122-1-1-1-2-2-2-12-1-1-12-1-12-1-111-2-21111002020-2-2111100-1000000-100
χ162222222222-122-1-1-1-2-2-2-12-1-1-12-1-12-1-111-2-2111100-20-2022-1-1-1-1001000000100
χ172222-2-222-2-22222-2-20002222-2-2-2-2-22-2000000002-200000000000002-20000000
χ182222-2-222-2-22222-2-20002222-2-2-2-2-22-200000000-220000000000000-220000000
χ192222-2-222-2-22-1-12-2-2000-1-1-12-21111-11003−333−3−32-20000000000000-11000003−3
χ202222-2-222-2-22-1-12-2-2000-1-1-12-21111-11003−333−3−3-2200000000000001-100000−33
χ212222-2-222-2-22-1-12-2-2000-1-1-12-21111-1100−33−3−3332-20000000000000-1100000−33
χ222222-2-222-2-22-1-12-2-2000-1-1-12-21111-1100−33−3−333-2200000000000001-1000003−3
χ2322-222-22-2-222222220002-22-2-2222-2-2-20000000000020-2000000020000-200000
χ2422-222-22-2-222222220002-22-2-2222-2-2-200000000000-2020000000-20000200000
χ2522-22-222-22-22222-2-20002-22-22-2-2-22-22000000000020-20000000002000000-200
χ2622-22-222-22-22222-2-20002-22-22-2-2-22-220000000000-202000000000-2000000200
χ2722-22-222-22-2-122-111000-1-2-11-1-21121-13−3003−33−30020-200033−3−300-1000000100
χ2822-22-222-22-2-122-111000-1-2-11-1-21121-13−3003−33−300-202000−3−333001000000-100
χ2922-22-222-22-2-122-111000-1-2-11-1-21121-1−3300−33−330020-2000−3−33300-1000000100
χ3022-22-222-22-2-122-111000-1-2-11-1-21121-1−3300−33−3300-20200033−3−3001000000-100
χ314444444444-2-2-2-2-2-24441-21-2-2-211-211-2-2-2-21111000000000000000000000000
χ324444444444-2-2-2-2-2-2-4-4-41-21-2-2-211-2112222-1-1-1-1000000000000000000000000
χ334444-4-444-4-4-244-222000-24-2-22-422-4-2200000000000000000000000000000000
χ344444-4-444-4-4-2-2-2-2220001-21-222-1-121-10023−23−3−333000000000000000000000000
χ354444-4-444-4-4-2-2-2-2220001-21-222-1-121-100−232333−3−3000000000000000000000000
χ3644-444-44-4-444-2-2444000-22-2-4-4-2-2-222200000000000000000000000000000000
χ3744-444-44-4-44-244-2-2-2000-2-4-2224-2-2-42200000000000000000000000000000000
χ3844-444-44-4-44-2-2-2-2-2-200012122-2112-1-100003-3-33000000000000000000000000
χ3944-444-44-4-44-2-2-2-2-2-200012122-2112-1-10000-333-3000000000000000000000000
χ4044-44-444-44-44-2-24-4-4000-22-2-44222-22-200000000000000000000000000000000
χ4144-44-444-44-4-2-2-2-2220001212-22-1-1-2-1123−2300−33−33000000000000000000000000
χ4244-44-444-44-4-2-2-2-2220001212-22-1-1-2-11−2323003−33−3000000000000000000000000
χ434-40400-400044-4-40000040-400000000000000000000002i−2i2i−2i2i−2i000000000000
χ444-40400-400044-4-40000040-40000000000000000000000−2i2i−2i2i−2i2i000000000000
χ454-40400-4000-24-4223−23000-20200023−23000000000000000002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000
χ464-40400-4000-24-4223−23000-20200023−2300000000000000000−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000
χ474-40400-4000-24-42−2323000-202000−2323000000000000000002i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000
χ484-40400-4000-24-42−2323000-202000−232300000000000000000−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000
χ49666-366-3-3-3-30000006-3-300000000000000000000002020000002-10000-1-1-1000
χ50666-366-3-3-3-30000006-3-30000000000000000000000-20-2000000-210000111000
χ51666-366-3-3-3-3000000-6330000000000000000000000202000000-2-10000-111000
χ52666-366-3-3-3-3000000-6330000000000000000000000-20-20000002100001-1-1000
χ5366-6-36-6-333-30000000−3i33i3000000000000000000000020-20000000-100001−i3i3000
χ5466-6-36-6-333-30000000−3i33i30000000000000000000000-202000000010000-1i3−i3000
χ5566-6-36-6-333-300000003i3−3i3000000000000000000000020-20000000-100001i3−i3000
χ5666-6-36-6-333-300000003i3−3i30000000000000000000000-202000000010000-1−i3i3000
χ578-80800-80008-44-800000-4040000000000000000000000000000000000000000
χ588-80800-8000-4-44443−4300020-2000−232300000000000000000000000000000000000
χ598-80800-8000-4-444−434300020-200023−2300000000000000000000000000000000000
χ60121212-6-12-12-6-6660000000000000000000000000000000000000000000000000000
χ611212-12-6-1212-66-660000000000000000000000000000000000000000000000000000
χ6224-240-1200120000000000000000000000000000000000000000000000000000000

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