Finite Group Databasebeta

← Group #13136942

Character table — Group #13136942

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111111112222224444441212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12223366666622666644121212123366666666666666121212121212121212121212121212124444121212121212121244888888881212121224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ5111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i
χ91-11-111-1-111-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-111-1-1i−i1-1i−i1-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-11-111-1-111-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-111-1-1i−i-11−ii-11−iiii−i−i-1-111−i−iii-1-111−i−iii
χ111-11-111-1-111-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111-1-111−iii−i-11−ii1-1−i−iiiii−i−i-1-111−i−iii11-1-1
χ121-11-111-1-111-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111-1-111−ii−ii1-1i−i-11−i−iii−i−iii11-1-1ii−i−i-1-111
χ131-11-111-1-111-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-111-1-1−ii1-1−ii1-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii
χ141-11-111-1-111-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-111-1-1−ii-11i−i-11i−i−i−iii-1-111ii−i−i-1-111ii−i−i
χ151-11-111-1-111-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111-1-111i−ii−i1-1−ii-11ii−i−iii−i−i11-1-1−i−iii-1-111
χ161-11-111-1-111-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111-1-111i−i−ii-11i−i1-1ii−i−i−i−iii-1-111ii−i−i11-1-1
χ17222222222222-2-2-2-2-2-20000002222-2-2-2-222-2-2-2-22200000000000000002-2-2222-2-2-2-222000000000000000000000000000000
χ18222222222222-2-2-2-2-2-20000002222-2-2-2-222-2-2-2-2220000000000000000-222-2-2-22222-2-2000000000000000000000000000000
χ192-22-222-2-222-2-2-22-2-2220000002222-2-2-2-2-2-22222-2-2000000000000000022-2-22222-2-2-2-2000000000000000000000000000000
χ202-22-222-2-222-2-2-22-2-2220000002222-2-2-2-2-2-22222-2-20000000000000000-2-222-2-2-2-22222000000000000000000000000000000
χ213333−3−3i32−3+3i32−3−3i32−3+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+i3211iiii−i−i−i−i−1−i32−1+i32−1−i32−1+i32ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11
χ223333−3−3i32−3+3i32−3−3i32−3+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−i−i−i−iiiii−1−i32−1+i32−1−i32−1+i32−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11
χ233333−3−3i32−3+3i32−3−3i32−3+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−i32-1-1111111111+i321−i321+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
χ243333−3−3i32−3+3i32−3−3i32−3+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−i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ253333−3−3i32−3+3i32−3−3i32−3+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+i32-1-1ii−i−i−i−iii1+i321−i321+i321−i32ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11
χ263333−3−3i32−3+3i32−3−3i32−3+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+i32-1-1−i−iiiii−i−i1+i321−i321+i321−i32−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11
χ273333−3−3i32−3+3i32−3−3i32−3+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−i321111-1-111-1-1−1−i32−1+i32−1−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
χ283333−3−3i32−3+3i32−3−3i32−3+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−i3211-1-111-1-111−1−i32−1+i32−1−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
χ293333−3+3i32−3−3i32−3+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−i3211iiii−i−i−i−i−1+i32−1−i32−1+i32−1−i32ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7
χ303333−3+3i32−3−3i32−3+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−i−i−i−iiiii−1+i32−1−i32−1+i32−1−i32−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7
χ313333−3+3i32−3−3i32−3+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+i32-1-1111111111−i321+i321−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
χ323333−3+3i32−3−3i32−3+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+i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ333333−3+3i32−3−3i32−3+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−i32-1-1ii−i−i−i−iii1−i321+i321−i321+i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ343333−3+3i32−3−3i32−3+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−i32-1-1−i−iiiii−i−i1−i321+i321−i321+i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ353333−3+3i32−3−3i32−3+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+i321111-1-111-1-1−1+i32−1−i32−1+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
χ363333−3+3i32−3−3i32−3+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+i3211-1-111-1-111−1+i32−1−i32−1+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
χ373-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ7000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32i−ii−i-11−ii1-1ζ11ζ7−ζ11−ζ7ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32
χ383-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ7000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32i−i−ii1-1i−i-11ζ11ζ7−ζ11−ζ7−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32
χ393-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ700000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−ii1-1i−i1-1i−i−ζ11−ζ7ζ11ζ7−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32ζ7ζ11−ζ7−ζ11
χ403-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ113ζ7−3ζ11−3ζ700000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−ii-11−ii-11−ii−ζ11−ζ7ζ11ζ71−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32−ζ7−ζ11ζ7ζ11
χ413-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ7000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−iii−i1-1−ii-11−ζ11−ζ7ζ11ζ7ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32
χ423-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ7000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−ii−ii-11i−i1-1−ζ11−ζ7ζ11ζ7−ζ7−ζ11ζ7ζ111−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ11−1+i32−1−i321−i321+i32
χ433-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ700000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32i−i1-1−ii1-1−iiζ11ζ7−ζ11−ζ7−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11−1+i32−1−i321−i321+i32−ζ7−ζ11ζ7ζ11
χ443-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ11−3ζ73ζ113ζ700000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32i−i-11i−i-11i−iζ11ζ7−ζ11−ζ71−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ111−i321+i32−1+i32−1−i32ζ7ζ11−ζ7−ζ11
χ453-33-3−3+3i32−3−3i323−3i323+3i32−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i323i−3i3ζ73ζ11−3ζ7−3ζ11000000000000000000000000000000001-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32i−ii−i-11−ii1-1ζ7ζ11−ζ7−ζ11ζ11ζ7−ζ11−ζ71+i321−i32−1−i32−1+i32−ζ11−ζ7ζ11ζ7−1−i32−1+i321+i321−i32
χ463-33-3−3+3i32−3−3i323−3i323+3i32−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i323i−3i3ζ73ζ11−3ζ7−3ζ11000000000000000000000000000000001-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32i−i−ii1-1i−i-11ζ7ζ11−ζ7−ζ11−ζ11−ζ7ζ11ζ7−1−i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ71+i321−i32−1−i32−1+i32
χ473-33-3−3+3i32−3−3i323−3i323+3i32−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i323i−3i3ζ73ζ11−3ζ7−3ζ1100000000000000000000000000000000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−ii1-1i−i1-1i−i−ζ7−ζ11ζ7ζ11−1−i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ7−1−i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ7
χ483-33-3−3+3i32−3−3i323−3i323+3i32−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i323i−3i3ζ73ζ11−3ζ7−3ζ1100000000000000000000000000000000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−ii-11−ii-11−ii−ζ7−ζ11ζ7ζ111+i321−i32−1−i32−1+i32−ζ11−ζ7ζ11ζ71+i321−i32−1−i32−1+i32−ζ11−ζ7ζ11ζ7
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χ513-33-3−3+3i32−3−3i323−3i323+3i32−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i32−3i3i−3ζ7−3ζ113ζ73ζ1100000000000000000000000000000000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32i−i1-1−ii1-1−iiζ7ζ11−ζ7−ζ11−1−i32−1+i321+i321−i32−ζ11−ζ7ζ11ζ7−1−i32−1+i321+i321−i32−ζ11−ζ7ζ11ζ7
χ523-33-3−3+3i32−3−3i323−3i323+3i32−3+3i32−3−3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i32−3i3i−3ζ7−3ζ113ζ73ζ1100000000000000000000000000000000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32i−i-11i−i-11i−iζ7ζ11−ζ7−ζ111+i321−i32−1−i32−1+i32ζ11ζ7−ζ11−ζ71+i321−i32−1−i32−1+i32ζ11ζ7−ζ11−ζ7
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.