Finite Group Databasebeta

← Group #13047448

Character table — Group #13047448

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11222223333444666666666666121212121212121212181818181818272727272727363636363636363636545454545454545454
order1222346336666123336666666121266666612121236991818441212121266121818181836362446612121212
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1
χ3111-11-1111111-1-111111-1-1111-1-1111-1-1-1-1-1-11111111111111-1-111-1-1-1-1-11-1-1-111-1-1
χ4111-11-1111111-1-111111-1-1111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-11-1111-1-111
χ511-111-111111-11-1111-1-111111-1-1-1-1-1111-1-1-1111111111111-11-1-1-111-1-1-1-11-1-1-1-111
χ611-111-111111-11-1111-1-111111-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-11-1-1-111-1-111-11111-1-1
χ711-1-11111111-1-11111-1-1-1-111111-1-1-1-1-1-1111111111111111-1-11-1-1-1-1111-1-111-1-1-1-1
χ811-1-11111111-1-11111-1-1-1-111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-111-111-1-11111
χ922222222222222222222222222222222222-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1000000000
χ1022222222222222-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1000000222-1-1-1-1-1-1000000000
χ1122222222222222-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-12-12-1000000-1-1-12-12-12-1000000000
χ1222222222222222-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12-12000000-1-1-1-12-12-12000000000
χ13222-22-2222222-2-222222-2-2222-2-2222-2-2-2-2-2-2-1-1-1-1-1-1000000-111-1-11111000000000
χ14222-22-2222222-2-2-1-1-122-2-2-1-1-1-2-2-1-1-111111122-1-1-1-10000002-2-2-1-11111000000000
χ15222-22-2222222-2-2-1-1-122-2-2-1-1-1-2-2-1-1-1111111-1-12-12-1000000-1112-1-21-21000000000
χ16222-22-2222222-2-2-1-1-122-2-2-1-1-1-2-2-1-1-1111111-1-1-12-12000000-111-121-21-2000000000
χ1722-222-222222-22-2222-2-222222-2-2-2-2-2222-2-2-2-1-1-1-1-1-10000001-1111-1-111000000000
χ1822-222-222222-22-2-1-1-1-2-222-1-1-1-2-2111-1-1-111122-1-1-1-1000000-22-211-1-111000000000
χ1922-222-222222-22-2-1-1-1-2-222-1-1-1-2-2111-1-1-1111-1-12-12-10000001-11-212-1-21000000000
χ2022-222-222222-22-2-1-1-1-2-222-1-1-1-2-2111-1-1-1111-1-1-12-120000001-111-2-121-2000000000
χ2122-2-22222222-2-22222-2-2-2-222222-2-2-2-2-2-2222-1-1-1-1-1-100000011-11111-1-1000000000
χ2222-2-22222222-2-22-1-1-1-2-2-2-2-1-1-122111111-1-1-122-1-1-1-1000000-2-221111-1-1000000000
χ2322-2-22222222-2-22-1-1-1-2-2-2-2-1-1-122111111-1-1-1-1-12-12-100000011-1-21-212-1000000000
χ2422-2-22222222-2-22-1-1-1-2-2-2-2-1-1-122111111-1-1-1-1-1-12-1200000011-11-21-2-12000000000
χ252-20020-222-2-20002220000-2-2-2000000000002-222-2-22i−2i2i2i−2i−2i000000000000000000
χ262-20020-222-2-20002220000-2-2-2000000000002-222-2-2−2i2i−2i−2i2i2i000000000000000000
χ273333333−3−3i32−3+3i32−3−3i32−3+3i32333000−3−3i32−3+3i32−3−3i32−3+3i32000−3−3i32−3+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+3i32333000−3−3i32−3+3i32−3−3i32−3+3i32000−3−3i32−3+3i32000000000000000-1-11+i321−i321+i321−i32000000000-1-1-11+i321−i321+i321−i321+i321−i32
χ293333333−3+3i32−3−3i32−3+3i32−3−3i32333000−3+3i32−3−3i32−3+3i32−3−3i32000−3+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+3i32−3−3i32333000−3+3i32−3−3i32−3+3i32−3−3i32000−3+3i32−3−3i32000000000000000-1-11−i321+i321−i321+i32000000000-1-1-11−i321+i321−i321+i321−i321+i32
χ31333-33-33−3−3i32−3+3i32−3−3i32−3+3i323-3-3000−3−3i32−3+3i323+3i323−3i320003+3i323−3i3200000000000000011−1−i32−1+i32−1−i32−1+i32000000000-11-11+i321−i32−1−i32−1+i321+i321−i32
χ32333-33-33−3−3i32−3+3i32−3−3i32−3+3i323-3-3000−3−3i32−3+3i323+3i323−3i320003+3i323−3i32000000000000000-1-11+i321−i321+i321−i320000000001-11−1−i32−1+i321+i321−i32−1−i32−1+i32
χ33333-33-33−3+3i32−3−3i32−3+3i32−3−3i323-3-3000−3+3i32−3−3i323−3i323+3i320003−3i323+3i3200000000000000011−1+i32−1−i32−1+i32−1−i32000000000-11-11−i321+i32−1+i32−1−i321−i321+i32
χ34333-33-33−3+3i32−3−3i32−3+3i32−3−3i323-3-3000−3+3i32−3−3i323−3i323+3i320003−3i323+3i32000000000000000-1-11−i321+i321−i321+i320000000001-11−1+i32−1−i321−i321+i32−1+i32−1−i32
χ3533-333-33−3−3i32−3+3i32−3−3i32−3+3i32-33-30003+3i323−3i32−3−3i32−3+3i320003+3i323−3i3200000000000000011−1−i32−1+i32−1−i32−1+i32000000000-1-111+i321−i321+i321−i32−1−i32−1+i32
χ3633-333-33−3−3i32−3+3i32−3−3i32−3+3i32-33-30003+3i323−3i32−3−3i32−3+3i320003+3i323−3i32000000000000000-1-11+i321−i321+i321−i3200000000011-1−1−i32−1+i32−1−i32−1+i321+i321−i32
χ3733-333-33−3+3i32−3−3i32−3+3i32−3−3i32-33-30003−3i323+3i32−3+3i32−3−3i320003−3i323+3i3200000000000000011−1+i32−1−i32−1+i32−1−i32000000000-1-111−i321+i321−i321+i32−1+i32−1−i32
χ3833-333-33−3+3i32−3−3i32−3+3i32−3−3i32-33-30003−3i323+3i32−3+3i32−3−3i320003−3i323+3i32000000000000000-1-11−i321+i321−i321+i3200000000011-1−1+i32−1−i32−1+i32−1−i321−i321+i32
χ3933-3-3333−3−3i32−3+3i32−3−3i32−3+3i32-3-330003+3i323−3i323+3i323−3i32000−3−3i32−3+3i3200000000000000011−1−i32−1+i32−1−i32−1+i320000000001-1-1−1−i32−1+i321+i321−i321+i321−i32
χ4033-3-3333−3−3i32−3+3i32−3−3i32−3+3i32-3-330003+3i323−3i323+3i323−3i32000−3−3i32−3+3i32000000000000000-1-11+i321−i321+i321−i32000000000-1111+i321−i32−1−i32−1+i32−1−i32−1+i32
χ4133-3-3333−3+3i32−3−3i32−3+3i32−3−3i32-3-330003−3i323+3i323−3i323+3i32000−3+3i32−3−3i3200000000000000011−1+i32−1−i32−1+i32−1−i320000000001-1-1−1+i32−1−i321−i321+i321−i321+i32
χ4233-3-3333−3+3i32−3−3i32−3+3i32−3−3i32-3-330003−3i323+3i323−3i323+3i32000−3+3i32−3−3i32000000000000000-1-11−i321+i321−i321+i32000000000-1111−i321+i32−1+i32−1−i32−1+i32−1−i32
χ434-40040-444-4-40004440000-4-4-400000000000-22-2-222000000000000000000000000
χ444-40040-444-4-4000-2-2-20000222000000000004-4-2-222000000000000000000000000
χ454-40040-444-4-4000-2-2-2000022200000000000-224-2-42000000000000000000000000
χ464-40040-444-4-4000-2-2-2000022200000000000-22-242-4000000000000000000000000
χ476666-36-30000-3-3-303-3000003-30003-303-303-3000000000000000000000000000000
χ486666-36-30000-3-3-33-3000003-30003-303-303-30000000000000000000000000000000
χ496666-36-30000-3-3-3-3030000-30300-303-303-303000000000000000000000000000000
χ50666-6-3-6-30000-33303-3000003-30003-30-330-33000000000000000000000000000000
χ51666-6-3-6-30000-3333-3000003-30003-30-330-330000000000000000000000000000000
χ52666-6-3-6-30000-333-3030000-30300-30330-330-3000000000000000000000000000000
χ5366-66-3-6-300003-3303-3000003-3000-3303-30-33000000000000000000000000000000
χ5466-66-3-6-300003-333-3000003-3000-3303-30-330000000000000000000000000000000
χ5566-66-3-6-300003-33-3030000-3030030-3-30330-3000000000000000000000000000000
χ5666-6-6-36-3000033-303-3000003-3000-330-3303-3000000000000000000000000000000
χ5766-6-6-36-3000033-33-3000003-3000-330-3303-30000000000000000000000000000000
χ5866-6-6-36-3000033-3-3030000-3030030-330-3-303000000000000000000000000000000
χ596-60060-6−3−3i3−3+3i33+3i33−3i30000000000000000000000000000002i−2i2ζ112ζ7−2ζ11−2ζ7000000000000000000
χ606-60060-6−3−3i3−3+3i33+3i33−3i3000000000000000000000000000000−2i2i−2ζ11−2ζ72ζ112ζ7000000000000000000
χ616-60060-6−3+3i3−3−3i33−3i33+3i30000000000000000000000000000002i−2i2ζ72ζ11−2ζ7−2ζ11000000000000000000
χ626-60060-6−3+3i3−3−3i33−3i33+3i3000000000000000000000000000000−2i2i−2ζ7−2ζ112ζ72ζ11000000000000000000
χ6312-1200-606000000006-600000-6600000000000000000000000000000000000000000
χ6412-1200-60600000006-600000-66000000000000000000000000000000000000000000
χ6512-1200-6060000000-606000060-600000000000000000000000000000000000000000

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