Finite Group Databasebeta

← Group #10619607

Character table — Group #10619607

Order 648.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size1111112223333333333336666666666181818181818181818181818181818181818181818181818181818181818
order12336641212333333666666361212121212121212344699121212121212121212121212121212121212181836363636
χ11111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ3111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ4111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111-1-11−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ5111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ6111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111-1-11−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ7111111-1-1-111111111111111-1-1-1-1-1-1-1-111-111111-1-1111-1-1-1111-1-1-1-1-111-1-1-1-1
χ8111111-1-1-111111111111111-1-1-1-1-1-1-1-11-11111-1-111-1-1-1111-1-1-1111-1-111-1-1-1-1
χ9111111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111+i321+i321+i321−i321−i321−i32-1-111-11−1−i32−1+i3211-1-1−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i32-1-1−1−i32−1+i321+i321+i321−i321−i32
χ10111111-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111+i321+i321+i321−i321−i321−i32-1-11-111−1−i32−1+i32-1-1111+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i32
χ11111111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−i321−i321−i321+i321+i321+i32-1-111-11−1+i32−1−i3211-1-1−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i32-1-1−1+i32−1−i321−i321−i321+i321+i32
χ12111111-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−i321−i321−i321+i321+i321+i32-1-11-111−1+i32−1−i32-1-1111−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i32
χ132222222222222222222222222222222-100-1-1-10000000000000000-1-1-1-1-1-1-1-1
χ14222222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-100-11+i321−i320000000000000000-1-11+i321−i321+i321+i321−i321−i32
χ15222222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322-100-11−i321+i320000000000000000-1-11−i321+i321−i321−i321+i321+i32
χ16222222-2-2-222222222222222-2-2-2-2-2-2-2-2-100-1-1-1000000000000000011-1-11111
χ17222222-2-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3221+i31+i31+i31−i31−i31−i3-2-2-100-11+i321−i320000000000000000111+i321−i32−1−i32−1−i32−1+i32−1+i32
χ18222222-2-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3221−i31−i31−i31+i31+i31+i3-2-2-100-11−i321+i320000000000000000111−i321+i32−1+i32−1+i32−1−i32−1−i32
χ192-222-2-2000222222-2-2-2-2-2-22-200000000200-222000000000000000000-2-20000
χ202-222-2-2000222222-2-2-2-2-2-22-200000000-1001-1-100000000000000003−3113−33−3
χ212-222-2-2000222222-2-2-2-2-2-22-200000000-1001-1-10000000000000000−3311−33−33
χ222-222-2-2000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i32-200000000200-2−1−i3−1+i30000000000000000001+i31−i30000
χ232-222-2-2000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i32-200000000-10011+i321−i3200000000000000003−3−1−i32−1+i322ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11
χ242-222-2-2000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i32-200000000-10011+i321−i320000000000000000−33−1−i32−1+i32−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11
χ252-222-2-2000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i32-200000000200-2−1+i3−1−i30000000000000000001−i31+i30000
χ262-222-2-2000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i32-200000000-10011−i321+i3200000000000000003−3−1+i32−1−i32−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11
χ272-222-2-2000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i32-200000000-10011−i321+i320000000000000000−33−1+i32−1−i32ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11
χ2833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i32003+i32−i3−3+i323−i32i3−3−i3200011000−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000
χ2933−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i32003+i32−i3−3+i323−i32i3−3−i32000-1-10001+i321−i321+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000
χ3033−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i3200−i3−3+i323+i32i3−3−i323−i3200011000−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1+i321−1−i32−1+i321−1−i3200000000
χ3133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i3200−i3−3+i323+i32i3−3−i323−i32000-1-10001+i321−i321+i321−i321+i321−i32-11+i321−i32-11−i32-11+i321−i32-11+i3200000000
χ3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i300−3+i323+i32−i3−3−i323−i32i300011000−1−i32−1+i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1−i32−1+i321−1−i32−1+i32100000000
χ3333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i300−3+i323+i32−i3−3−i323−i32i3000-1-10001+i321−i321+i321−i321−i32-11+i321−i32-11+i321+i321−i32-11+i321−i32-100000000
χ3433−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i3200−3−i32i33−i32−3+i32−i33+i320001-1000−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i3200000000
χ3533−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i3200−3−i32i33−i32−3+i32−i33+i32000-110001+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i3200000000
χ3633−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i3200i33−i32−3−i32−i33+i32−3+i320001-1000−1−i32−1+i321+i321−i32−1−i32−1+i3211+i321−i32-1−1+i321−1−i321−i32-11+i3200000000
χ3733−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i3200i33−i32−3−i32−i33+i32−3+i32000-110001+i321−i32−1−i32−1+i321+i321−i32-1−1−i32−1+i3211−i32-11+i32−1+i321−1−i3200000000
χ3833−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3003−i32−3−i32i33+i32−3+i32−i30001-1000−1−i32−1+i321+i321−i32−1+i321−1−i321−i32-11+i32−1−i32−1+i3211+i321−i32-100000000
χ3933−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3003−i32−3−i32i33+i32−3+i32−i3000-110001+i321−i32−1−i32−1+i321−i32-11+i32−1+i321−1−i321+i321−i32-1−1−i32−1+i32100000000
χ4033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i32003−i32i3−3−i323+i32−i3−3+i3200011000−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000
χ4133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i32003−i32i3−3−i323+i32−i3−3+i32000-1-10001−i321+i321−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000
χ4233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i3200i3−3−i323−i32−i3−3+i323+i3200011000−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1−i321−1+i32−1−i321−1+i3200000000
χ4333−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i3200i3−3−i323−i32−i3−3+i323+i32000-1-10001−i321+i321−i321+i321−i321+i32-11−i321+i32-11+i32-11−i321+i32-11−i3200000000
χ4433−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i300−3−i323−i32i3−3+i323+i32−i300011000−1+i32−1−i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1+i32−1−i321−1+i32−1−i32100000000
χ4533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i300−3−i323−i32i3−3+i323+i32−i3000-1-10001−i321+i321−i321+i321+i32-11−i321+i32-11−i321−i321+i32-11−i321+i32-100000000
χ4633−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i3200−3+i32−i33+i32−3−i32i33−i320001-1000−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i3200000000
χ4733−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i323−i32i3−3−i323+i32−i3−3+i323−i32i3−3−i323+i32−i3−3+i3200−3+i32−i33+i32−3−i32i33−i32000-110001−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i3200000000
χ4833−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i3200−i33+i32−3+i32i33−i32−3−i320001-1000−1+i32−1−i321−i321+i32−1+i32−1−i3211−i321+i32-1−1−i321−1+i321+i32-11−i3200000000
χ4933−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32i3−3−i323−i32−i3−3+i323+i32i3−3−i323−i32−i3−3+i323+i3200−i33+i32−3+i32i33−i32−3−i32000-110001−i321+i32−1+i32−1−i321−i321+i32-1−1+i32−1−i3211+i32-11−i32−1−i321−1+i3200000000
χ5033−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3003+i32−3+i32−i33−i32−3−i32i30001-1000−1+i32−1−i321−i321+i32−1−i321−1+i321+i32-11−i32−1+i32−1−i3211−i321+i32-100000000
χ5133−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32−3−i323−i32i3−3+i323+i32−i3−3−i323−i32i3−3+i323+i32−i3003+i32−3+i32−i33−i32−3−i32i3000-110001−i321+i32−1+i32−1−i321+i32-11−i32−1−i321−1+i321−i321+i32-1−1+i32−1−i32100000000
χ52666666666000000000000-3-3000000-3-3000000000000000000000000000000
χ53666666-6-6-6000000000000-3-300000033000000000000000000000000000000
χ546-666-6-6000000000000000-3300000033−33000000000000000000000000000000
χ556-666-6-6000000000000000-33000000−3333000000000000000000000000000000
χ566-6−3−3i3−3+3i33+3i33−3i30003+i3−2i3−3+i33−i32i3−3−i3−3−i32i33−i3−3+i3−2i33+i30000000000000000000000000000000000000000
χ576-6−3−3i3−3+3i33+3i33−3i3000−2i3−3+i33+i32i3−3−i33−i32i33−i3−3−i3−2i33+i3−3+i30000000000000000000000000000000000000000
χ586-6−3−3i3−3+3i33+3i33−3i3000−3+i33+i3−2i3−3−i33−i32i33−i3−3−i32i33+i3−3+i3−2i30000000000000000000000000000000000000000
χ596-6−3+3i3−3−3i33−3i33+3i30003−i32i3−3−i33+i3−2i3−3+i3−3+i3−2i33+i3−3−i32i33−i30000000000000000000000000000000000000000
χ606-6−3+3i3−3−3i33−3i33+3i30002i3−3−i33−i3−2i3−3+i33+i3−2i33+i3−3+i32i33−i3−3−i30000000000000000000000000000000000000000
χ616-6−3+3i3−3−3i33−3i33+3i3000−3−i33−i32i3−3+i33+i3−2i33+i3−3+i3−2i33−i3−3−i32i30000000000000000000000000000000000000000

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