Finite Group Databasebeta

← Group #13047462

Character table — Group #13047462

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11222223333444666666666666121212121212121212181818181818272727272727363636363636363636545454545454545454
order12344463366121212333666121212121212121212121212121212369918184412121212121212363636363636222666666
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ31111-1-1111111-1-111111111-1-1-1-1111-1-1-1-1-1-11111111111111-1-111-1-1-1-11-1-111-1-1-1-1
χ41111-1-1111111-1-111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111-1-11111
χ5111-11-111111-11-1111111-1-111-1-1-1-1-1111-1-1-1111111111111-11-1-1-111-1-1-11-1-1-111-1-1
χ6111-11-111111-11-1111111-1-111-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-11-1-1-111-1-11-1111-1-111
χ7111-1-1111111-1-11111111-1-1-1-111-1-1-1-1-1-1111111111111111-1-11-1-1-1-111-1-11-1-1-1-111
χ8111-1-1111111-1-11111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-11111-11111-1-1
χ922222222222222222222222222222222222-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1000000000
χ1022222222222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-122-1-1-1-1000000222-1-1-1-1-1-1000000000
χ1122222222222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-12-12-1000000-1-1-12-12-12-1000000000
χ1222222222222222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12-12000000-1-1-1-12-12-12000000000
χ132222-2-2222222-2-222222222-2-2-2-2222-2-2-2-2-2-2-1-1-1-1-1-1000000-111-1-11111000000000
χ142222-2-2222222-2-2-1-1-1-1-1-122-2-2-2-2-1-1-111111122-1-1-1-10000002-2-2-1-11111000000000
χ152222-2-2222222-2-2-1-1-1-1-1-122-2-2-2-2-1-1-1111111-1-12-12-1000000-1112-1-21-21000000000
χ162222-2-2222222-2-2-1-1-1-1-1-122-2-2-2-2-1-1-1111111-1-1-12-12000000-111-121-21-2000000000
χ17222-22-222222-22-2222222-2-222-2-2-2-2-2222-2-2-2-1-1-1-1-1-10000001-1111-1-111000000000
χ18222-22-222222-22-2-1-1-1-1-1-1-2-222-2-2111-1-1-111122-1-1-1-1000000-22-211-1-111000000000
χ19222-22-222222-22-2-1-1-1-1-1-1-2-222-2-2111-1-1-1111-1-12-12-10000001-11-212-1-21000000000
χ20222-22-222222-22-2-1-1-1-1-1-1-2-222-2-2111-1-1-1111-1-1-12-120000001-111-2-121-2000000000
χ21222-2-2222222-2-22222222-2-2-2-222-2-2-2-2-2-2222-1-1-1-1-1-100000011-11111-1-1000000000
χ22222-2-2222222-2-22-1-1-1-1-1-1-2-2-2-222111111-1-1-122-1-1-1-1000000-2-221111-1-1000000000
χ23222-2-2222222-2-22-1-1-1-1-1-1-2-2-2-222111111-1-1-1-1-12-12-100000011-1-21-212-1000000000
χ24222-2-2222222-2-22-1-1-1-1-1-1-2-2-2-222111111-1-1-1-1-1-12-1200000011-11-21-2-12000000000
χ252-22000-222-2-2000222-2-2-20000000000000002-222-2-22i−2i2i2i−2i−2i000000000000000000
χ262-22000-222-2-2000222-2-2-20000000000000002-222-2-2−2i2i−2i−2i2i2i000000000000000000
χ273333333−3−3i32−3+3i32−3−3i32−3+3i32333000000−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000011−1−i32−1+i32−1−i32−1+i32000000000111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ283333333−3−3i32−3+3i32−3−3i32−3+3i32333000000−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000-1-11+i321−i321+i321−i32000000000-1-1-11+i321−i321+i321−i321+i321−i32
χ293333333−3+3i32−3−3i32−3+3i32−3−3i32333000000−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3200000000000000011−1+i32−1−i32−1+i32−1−i32000000000111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ303333333−3+3i32−3−3i32−3+3i32−3−3i32333000000−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000-1-11−i321+i321−i321+i32000000000-1-1-11−i321+i321−i321+i321−i321+i32
χ313333-3-33−3−3i32−3+3i32−3−3i32−3+3i323-3-3000000−3−3i32−3+3i323+3i323−3i323+3i323−3i3200000000000000011−1−i32−1+i32−1−i32−1+i320000000001-1-1−1−i32−1+i321+i321−i321+i321−i32
χ323333-3-33−3−3i32−3+3i32−3−3i32−3+3i323-3-3000000−3−3i32−3+3i323+3i323−3i323+3i323−3i32000000000000000-1-11+i321−i321+i321−i32000000000-1111+i321−i32−1−i32−1+i32−1−i32−1+i32
χ333333-3-33−3+3i32−3−3i32−3+3i32−3−3i323-3-3000000−3+3i32−3−3i323−3i323+3i323−3i323+3i3200000000000000011−1+i32−1−i32−1+i32−1−i320000000001-1-1−1+i32−1−i321−i321+i321−i321+i32
χ343333-3-33−3+3i32−3−3i32−3+3i32−3−3i323-3-3000000−3+3i32−3−3i323−3i323+3i323−3i323+3i32000000000000000-1-11−i321+i321−i321+i32000000000-1111−i321+i32−1+i32−1−i32−1+i32−1−i32
χ35333-33-33−3−3i32−3+3i32−3−3i32−3+3i32-33-30000003+3i323−3i32−3−3i32−3+3i323+3i323−3i3200000000000000011−1−i32−1+i32−1−i32−1+i32000000000-11-11+i321−i32−1−i32−1+i321+i321−i32
χ36333-33-33−3−3i32−3+3i32−3−3i32−3+3i32-33-30000003+3i323−3i32−3−3i32−3+3i323+3i323−3i32000000000000000-1-11+i321−i321+i321−i320000000001-11−1−i32−1+i321+i321−i32−1−i32−1+i32
χ37333-33-33−3+3i32−3−3i32−3+3i32−3−3i32-33-30000003−3i323+3i32−3+3i32−3−3i323−3i323+3i3200000000000000011−1+i32−1−i32−1+i32−1−i32000000000-11-11−i321+i32−1+i32−1−i321−i321+i32
χ38333-33-33−3+3i32−3−3i32−3+3i32−3−3i32-33-30000003−3i323+3i32−3+3i32−3−3i323−3i323+3i32000000000000000-1-11−i321+i321−i321+i320000000001-11−1+i32−1−i321−i321+i32−1+i32−1−i32
χ39333-3-333−3−3i32−3+3i32−3−3i32−3+3i32-3-330000003+3i323−3i323+3i323−3i32−3−3i32−3+3i3200000000000000011−1−i32−1+i32−1−i32−1+i32000000000-1-111+i321−i321+i321−i32−1−i32−1+i32
χ40333-3-333−3−3i32−3+3i32−3−3i32−3+3i32-3-330000003+3i323−3i323+3i323−3i32−3−3i32−3+3i32000000000000000-1-11+i321−i321+i321−i3200000000011-1−1−i32−1+i32−1−i32−1+i321+i321−i32
χ41333-3-333−3+3i32−3−3i32−3+3i32−3−3i32-3-330000003−3i323+3i323−3i323+3i32−3+3i32−3−3i3200000000000000011−1+i32−1−i32−1+i32−1−i32000000000-1-111−i321+i321−i321+i32−1+i32−1−i32
χ42333-3-333−3+3i32−3−3i32−3+3i32−3−3i32-3-330000003−3i323+3i323−3i323+3i32−3+3i32−3−3i32000000000000000-1-11−i321+i321−i321+i3200000000011-1−1+i32−1−i32−1+i32−1−i321−i321+i32
χ434-44000-444-4-4000444-4-4-4000000000000000-22-2-222000000000000000000000000
χ444-44000-444-4-4000-2-2-22220000000000000004-4-2-222000000000000000000000000
χ454-44000-444-4-4000-2-2-2222000000000000000-224-2-42000000000000000000000000
χ464-44000-444-4-4000-2-2-2222000000000000000-22-242-4000000000000000000000000
χ4766-3666-30000-3-3-303-303-300000003-303-303-3000000000000000000000000000000
χ4866-3666-30000-3-3-33-303-300000003-303-303-30000000000000000000000000000000
χ4966-3666-30000-3-3-3-303-303000000-303-303-303000000000000000000000000000000
χ5066-36-6-6-30000-33303-303-300000003-30-330-33000000000000000000000000000000
χ5166-36-6-6-30000-3333-303-300000003-30-330-330000000000000000000000000000000
χ5266-36-6-6-30000-333-303-303000000-30330-330-3000000000000000000000000000000
χ5366-3-66-6-300003-3303-303-30000000-3303-30-33000000000000000000000000000000
χ5466-3-66-6-300003-333-303-30000000-3303-30-330000000000000000000000000000000
χ5566-3-66-6-300003-33-303-30300000030-3-30330-3000000000000000000000000000000
χ5666-3-6-66-3000033-303-303-30000000-330-3303-3000000000000000000000000000000
χ5766-3-6-66-3000033-33-303-30000000-330-3303-30000000000000000000000000000000
χ5866-3-6-66-3000033-3-303-30300000030-330-3-303000000000000000000000000000000
χ596-66000-6−3−3i3−3+3i33+3i33−3i30000000000000000000000000000002i−2i2ζ112ζ7−2ζ11−2ζ7000000000000000000
χ606-66000-6−3−3i3−3+3i33+3i33−3i3000000000000000000000000000000−2i2i−2ζ11−2ζ72ζ112ζ7000000000000000000
χ616-66000-6−3+3i3−3−3i33−3i33+3i30000000000000000000000000000002i−2i2ζ72ζ11−2ζ7−2ζ11000000000000000000
χ626-66000-6−3+3i3−3−3i33−3i33+3i3000000000000000000000000000000−2i2i−2ζ7−2ζ112ζ72ζ11000000000000000000
χ6312-12-60006000000006-60-66000000000000000000000000000000000000000000000
χ6412-12-6000600000006-60-660000000000000000000000000000000000000000000000
χ6512-12-600060000000-60660-6000000000000000000000000000000000000000000000

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