Finite Group Databasebeta

← Group #13136944

Character table — Group #13136944

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111111111114448881212121212121212181818181818181818181818242424242424242424242424363636363636363636363636363636363636363636363636727272
order1222336666664121226633666666444412121212121212126666666612121212888888882424242424242424242424242424242441212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1
χ5111111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1
χ6111111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1
χ7111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii111
χ8111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i111
χ9222222222222-2-2-20002222222222-2-22222-2-2-2-200000000-2-2-2-2000000000000000000000000000
χ10222222222222-2-2-200022222222-2-222-2-2-2-2222200000000-2-2-2-2000000000000000000000000000
χ1122-2-22222-2-2-2-20000002222-2-2-2-2002i−2i00002i2i−2i−2i0000000000001+i−1−i001−i−1+i001+i1+i−1−i−1−i00001−i1−i−1+i−1+i0000000
χ1222-2-22222-2-2-2-20000002222-2-2-2-2002i−2i00002i2i−2i−2i000000000000−1−i1+i00−1+i1−i00−1−i−1−i1+i1+i0000−1+i−1+i1−i1−i0000000
χ1322-2-22222-2-2-2-20000002222-2-2-2-200−2i2i0000−2i−2i2i2i0000000000001−i−1+i001+i−1−i001−i1−i−1+i−1+i00001+i1+i−1−i−1−i0000000
χ1422-2-22222-2-2-2-20000002222-2-2-2-200−2i2i0000−2i−2i2i2i000000000000−1+i1−i00−1−i1+i00−1+i−1+i1−i1−i0000−1−i−1−i1+i1+i0000000
χ152-22-222-2-222-2-200000022-2-222-2-22i−2i002i2i−2i−2i0000000000000000001+i−1−i001−i−1+i00001+i1+i−1−i−1−i00001−i1−i−1+i−1+i000
χ162-22-222-2-222-2-200000022-2-222-2-22i−2i002i2i−2i−2i000000000000000000−1−i1+i00−1+i1−i0000−1−i−1−i1+i1+i0000−1+i−1+i1−i1−i000
χ172-22-222-2-222-2-200000022-2-222-2-2−2i2i00−2i−2i2i2i0000000000000000001−i−1+i001+i−1−i00001−i1−i−1+i−1+i00001+i1+i−1−i−1−i000
χ182-22-222-2-222-2-200000022-2-222-2-2−2i2i00−2i−2i2i2i000000000000000000−1+i1−i00−1−i1+i0000−1+i−1+i1−i1−i0000−1−i−1−i1+i1+i000
χ193333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000iiii−i−i−i−iζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ111−1−i32−1+i32
χ203333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000−i−i−i−iiiii−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ111−1−i32−1+i32
χ213333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000011111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11+i321−i32
χ223333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32-11+i321−i32
χ233333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000ii−i−i−i−iiiζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11-11+i321−i32
χ243333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000−i−iiiii−i−i−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11-11+i321−i32
χ253333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3200000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000011-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−1−i32−1+i32
χ263333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3200000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000-1-111-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−1−i32−1+i32
χ273333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000iiii−i−i−i−iζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ71−1+i32−1−i32
χ283333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000−i−i−i−iiiii−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ71−1+i32−1−i32
χ293333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000011111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11−i321+i32
χ303333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32-11−i321+i32
χ313333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000ii−i−i−i−iiiζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7-11−i321+i32
χ323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32000000000000−i−iiiii−i−i−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7-11−i321+i32
χ333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3200000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000011-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321−1+i32−1−i32
χ343333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3200000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32000000000000-1-111-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321−1+i32−1−i32
χ354444444444444444441-21-21-21-20000000000001111-2-2-2-211-2-2000000000000000000000000000
χ36444444444444444444-21-21-21-21000000000000-2-2-2-21111-2-211000000000000000000000000000
χ37444444444444444-4-4-41-21-21-21-2000000000000-1-1-1-1222211-2-2000000000000000000000000000
χ38444444444444444-4-4-4-21-21-21-210000000000002222-1-1-1-1-2-211000000000000000000000000000
χ39444444444444-4-4-40001-21-21-21-200000000000033-3-30000-1-122000000000000000000000000000
χ40444444444444-4-4-40001-21-21-21-2000000000000-3-3330000-1-122000000000000000000000000000
χ41444444444444-4-4-4000-21-21-21-21000000000000000033-3-322-1-1000000000000000000000000000
χ42444444444444-4-4-4000-21-21-21-210000000000000000-3-33322-1-1000000000000000000000000000
χ434-4-4444-4-4-4-4440000001-2-12-121-2000000000000−i3i3−i3i300−2i32i33-300000000000000000000000000000
χ444-4-4444-4-4-4-4440000001-2-12-121-2000000000000−i3i3i3−i3−2i32i300-3300000000000000000000000000000
χ454-4-4444-4-4-4-4440000001-2-12-121-2000000000000i3−i3−i3i32i3−2i300-3300000000000000000000000000000
χ464-4-4444-4-4-4-4440000001-2-12-121-2000000000000i3−i3i3−i3002i3−2i33-300000000000000000000000000000
χ474-4-4444-4-4-4-44400000044-4-4-4-444000000000000000000000000000000000000000000000000000
χ484-4-4444-4-4-4-444000000-212-12-1-2100000000000000−2i32i3−i3i3i3−i3003-3000000000000000000000000000
χ494-4-4444-4-4-4-444000000-212-12-1-21000000000000002i3−2i3i3−i3−i3i3003-3000000000000000000000000000
χ504-4-4444-4-4-4-444000000-212-12-1-21000000000000−2i32i300i3−i3i3−i300-33000000000000000000000000000
χ514-4-4444-4-4-4-444000000-212-12-1-210000000000002i3−2i300−i3i3−i3i300-33000000000000000000000000000
χ526666−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i30000000000022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000000000000000000000000000000000000
χ536666−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000000-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000000000000000000000000000000
χ546666−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i30000000000022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000000000000000000000000000000000000
χ556666−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300000000000-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000000000000000000000000000000
χ5666-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i300000000000000002i−2i00002ζ112ζ7−2ζ11−2ζ70000000000001−i−1+i001+i−1−i00−ζ7−ζ10−ζ2−ζ11ζ7+ζ10ζ2+ζ110000ζ7−ζ10−ζ2+ζ11−ζ7+ζ10ζ2−ζ110000000
χ5766-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i300000000000000002i−2i00002ζ112ζ7−2ζ11−2ζ7000000000000−1+i1−i00−1−i1+i00ζ7+ζ10ζ2+ζ11−ζ7−ζ10−ζ2−ζ110000−ζ7+ζ10ζ2−ζ11ζ7−ζ10−ζ2+ζ110000000
χ5866-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i30000000000000000−2i2i0000−2ζ11−2ζ72ζ112ζ70000000000001+i−1−i001−i−1+i00ζ7−ζ10−ζ2+ζ11−ζ7+ζ10ζ2−ζ110000−ζ7−ζ10−ζ2−ζ11ζ7+ζ10ζ2+ζ110000000
χ5966-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i30000000000000000−2i2i0000−2ζ11−2ζ72ζ112ζ7000000000000−1−i1+i00−1+i1−i00−ζ7+ζ10ζ2−ζ11ζ7−ζ10−ζ2+ζ110000ζ7+ζ10ζ2+ζ11−ζ7−ζ10−ζ2−ζ110000000
χ6066-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i300000000000000002i−2i00002ζ72ζ11−2ζ7−2ζ110000000000001−i−1+i001+i−1−i00−ζ2−ζ11−ζ7−ζ10ζ2+ζ11ζ7+ζ100000−ζ2+ζ11ζ7−ζ10ζ2−ζ11−ζ7+ζ100000000
χ6166-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i300000000000000002i−2i00002ζ72ζ11−2ζ7−2ζ11000000000000−1+i1−i00−1−i1+i00ζ2+ζ11ζ7+ζ10−ζ2−ζ11−ζ7−ζ100000ζ2−ζ11−ζ7+ζ10−ζ2+ζ11ζ7−ζ100000000
χ6266-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i30000000000000000−2i2i0000−2ζ7−2ζ112ζ72ζ110000000000001+i−1−i001−i−1+i00−ζ2+ζ11ζ7−ζ10ζ2−ζ11−ζ7+ζ100000−ζ2−ζ11−ζ7−ζ10ζ2+ζ11ζ7+ζ100000000
χ6366-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i30000000000000000−2i2i0000−2ζ7−2ζ112ζ72ζ11000000000000−1−i1+i00−1+i1−i00ζ2−ζ11−ζ7+ζ10−ζ2+ζ11ζ7−ζ100000ζ2+ζ11ζ7+ζ10−ζ2−ζ11−ζ7−ζ100000000
χ646-66-6−3−3i3−3+3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i3000000000000002i−2i002ζ112ζ7−2ζ11−2ζ70000000000000000001−i−1+i001+i−1−i0000−ζ7−ζ10−ζ2−ζ11ζ7+ζ10ζ2+ζ110000ζ7−ζ10−ζ2+ζ11−ζ7+ζ10ζ2−ζ11000
χ656-66-6−3−3i3−3+3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i3000000000000002i−2i002ζ112ζ7−2ζ11−2ζ7000000000000000000−1+i1−i00−1−i1+i0000ζ7+ζ10ζ2+ζ11−ζ7−ζ10−ζ2−ζ110000−ζ7+ζ10ζ2−ζ11ζ7−ζ10−ζ2+ζ11000
χ666-66-6−3−3i3−3+3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i300000000000000−2i2i00−2ζ11−2ζ72ζ112ζ70000000000000000001+i−1−i001−i−1+i0000ζ7−ζ10−ζ2+ζ11−ζ7+ζ10ζ2−ζ110000−ζ7−ζ10−ζ2−ζ11ζ7+ζ10ζ2+ζ11000
χ676-66-6−3−3i3−3+3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i300000000000000−2i2i00−2ζ11−2ζ72ζ112ζ7000000000000000000−1−i1+i00−1+i1−i0000−ζ7+ζ10ζ2−ζ11ζ7−ζ10−ζ2+ζ110000ζ7+ζ10ζ2+ζ11−ζ7−ζ10−ζ2−ζ11000
χ686-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i3000000000000002i−2i002ζ72ζ11−2ζ7−2ζ110000000000000000001−i−1+i001+i−1−i0000−ζ2−ζ11−ζ7−ζ10ζ2+ζ11ζ7+ζ100000−ζ2+ζ11ζ7−ζ10ζ2−ζ11−ζ7+ζ10000
χ696-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i3000000000000002i−2i002ζ72ζ11−2ζ7−2ζ11000000000000000000−1+i1−i00−1−i1+i0000ζ2+ζ11ζ7+ζ10−ζ2−ζ11−ζ7−ζ100000ζ2−ζ11−ζ7+ζ10−ζ2+ζ11ζ7−ζ10000
χ706-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i300000000000000−2i2i00−2ζ7−2ζ112ζ72ζ110000000000000000001+i−1−i001−i−1+i0000−ζ2+ζ11ζ7−ζ10ζ2−ζ11−ζ7+ζ100000−ζ2−ζ11−ζ7−ζ10ζ2+ζ11ζ7+ζ10000
χ716-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i300000000000000−2i2i00−2ζ7−2ζ112ζ72ζ11000000000000000000−1−i1+i00−1+i1−i0000ζ2−ζ11−ζ7+ζ10−ζ2+ζ11ζ7−ζ100000ζ2+ζ11ζ7+ζ10−ζ2−ζ11−ζ7−ζ10000
χ7288-8-88888-8-8-8-80000002-42-4-24-24000000000000000000000000000000000000000000000000000
χ7388-8-88888-8-8-8-8000000-42-424-24-2000000000000000000000000000000000000000000000000000
χ748-88-888-8-888-8-80000002-4-242-4-24000000000000000000000000000000000000000000000000000
χ758-88-888-8-888-8-8000000-424-2-424-2000000000000000000000000000000000000000000000000000
χ7612-12-1212−6−6i3−6+6i36+6i36−6i36+6i36−6i3−6−6i3−6+6i300000000000000000000000000000000000000000000000000000000000000000
χ7712-12-1212−6+6i3−6−6i36−6i36+6i36−6i36+6i3−6+6i3−6−6i300000000000000000000000000000000000000000000000000000000000000000

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