Finite Group Databasebeta

← Group #13147394

Character table — Group #13147394

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111111112222224444441212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order123344661212121224661212246612123366666666666666121212121212121212121212121212122244666612121212246688888888121224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ5111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-111-1-1-1-11-111-1-11-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-1i−ii−ii−ii−i11ii−i−iii−i−iii−i−iii−i−i
χ101111-1-111-1-1-1-11-111-1-11-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-1−ii−ii−ii−ii11−i−iii−i−iii−i−iii−i−iii
χ111111-1-111-1-1-1-11-111-1-11-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1111-11-1-11-11-1-111-1-111-1-1-1-111-1-111
χ121111-1-111-1-1-1-11-111-1-11-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-11-111-11-1-1-1-1-111-1-11111-1-111-1-1
χ131111-1-111-1-1-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11-111i−i−iii−i−ii-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-111-1-1-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11-111−iii−i−iii−i-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-111-1-1-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-11-1-11-1-11-111-11111-1-1-1-111-1-11111-1-1
χ161111-1-111-1-1-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-11-1-1-111-11-1-1111-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-200000022-2-2-2-200000000222222-2-2-2-2000000002-22-222-2-222-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-200000022-2-2-2-200000000222222-2-2-2-200000000-22-22-2-222-2-222000000000000000000000000000000
χ192222-2-222-2-2-2-2-22-2-22200000022-2-2-2-20000000022-2-2-2-22222000000002-2-2222-2-2-2-222000000000000000000000000000000
χ202222-2-222-2-2-2-2-22-2-22200000022-2-2-2-20000000022-2-2-2-2222200000000-222-2-2-22222-2-2000000000000000000000000000000
χ2133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32iiii−i−i−i−i−1−i32−1+i32ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11
χ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−i−i−i−iiiii−1−i32−1+i32−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11
χ2333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i32111111111+i321−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+i32−1−i32
χ2433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i32-1-1-1-1-1-1-1-11+i321−i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ2533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i32ii−i−i−i−iii1+i321−i32ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11
χ2633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i32−i−iiiii−i−i1+i321−i32−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11
χ2733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i3211-1-111-1-1−1−i32−1+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ2833−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32-1-111-1-111−1−i32−1+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ2933−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-111+i321−i321-11-1-11-11−1−i32−1+i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ3033−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-111+i321−i32-11-111-11-1−1−i32−1+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ3133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3200000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i32i−ii−ii−ii−i1+i321−i32ζ7ζ11−ζ7−ζ11ζ7ζ11−ζ7−ζ11ζ7ζ11−ζ7−ζ11ζ7ζ11−ζ7−ζ11
χ3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3200000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i32−ii−ii−ii−ii1+i321−i32−ζ7−ζ11ζ7ζ11−ζ7−ζ11ζ7ζ11−ζ7−ζ11ζ7ζ11−ζ7−ζ11ζ7ζ11
χ3333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i320000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−1−i32−1+i321-1-11-111-11+i321−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32
χ3433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i320000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−1−i32−1+i32-111-11-1-111+i321−i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
χ3533−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i3200000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-111+i321−i32i−i−iii−i−ii−1−i32−1+i32ζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11
χ3633−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i3200000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-111+i321−i32−iii−i−iii−i−1−i32−1+i32−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11
χ3733−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32iiii−i−i−i−i−1+i32−1−i32ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7
χ3833−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−i−i−i−iiiii−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7
χ3933−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i32111111111−i321+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−i32−1+i32
χ4033−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i32-1-1-1-1-1-1-1-11−i321+i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ4133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i32ii−i−i−i−iii1−i321+i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ4233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i32−i−iiiii−i−i1−i321+i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ4333−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i3211-1-111-1-1−1+i32−1−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ4433−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32-1-111-1-111−1+i32−1−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ4533−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i323-3−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i320000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-111−i321+i321-11-1-11-11−1+i32−1−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ4633−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i323-3−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i320000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-111−i321+i32-11-111-11-1−1+i32−1−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ4733−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i323-3−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i3200000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i32i−ii−ii−ii−i1−i321+i32ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7
χ4833−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i323-3−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i3200000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i32−ii−ii−ii−ii1−i321+i32−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7
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χ5133−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i323-3−3+3i32−3−3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i3200000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-111−i321+i32i−i−iii−i−ii−1+i32−1−i32ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ5233−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i323-3−3+3i32−3−3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i3200000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-111−i321+i32−iii−i−iii−i−1+i32−1−i32−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
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χ9812-12−6+6i3−6−6i3−12i12i6−6i36+6i3−12ζ712ζ7−12ζ1112ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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