Finite Group Databasebeta

← Group #13136935

Character table — Group #13136935

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
χ91-11-111-1-111-1-11-111-1-11-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−ii−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ101-11-111-1-111-1-11-111-1-11-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−ii−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ111-11-111-1-111-1-11-111-1-11-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−ii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ121-11-111-1-111-1-11-111-1-11-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−iiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ131-11-111-1-111-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i−iiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ141-11-111-1-111-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i−ii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ151-11-111-1-111-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiiii−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ161-11-111-1-111-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiiii−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ17222222222222-2-2-2-2-2-200000022-2-2-2-22222-2-2-2-22200000000000000002-22-222-2-222-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-200000022-2-2-2-22222-2-2-2-2220000000000000000-22-22-2-222-2-222000000000000000000000000000000
χ192-22-222-2-222-2-2-22-2-22200000022-2-2-2-2-2-2-2-222222200000000000000002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ202-22-222-2-222-2-2-22-2-22200000022-2-2-2-2-2-2-2-22222220000000000000000−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
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+i32ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22
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−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22
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−i32ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
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−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
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−i32ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14
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−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14
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+i32ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14
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−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14
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+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3200000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14i−i−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ22ζ14−ζ22−ζ14ζ5ζ13−ζ5−ζ13ζ5ζ13−ζ5−ζ13−ζ23−ζ7ζ23ζ7−ζ23−ζ7ζ23ζ7
χ383-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3200000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14i−iζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ22ζ14−ζ22−ζ14−ζ5−ζ13ζ5ζ13−ζ5−ζ13ζ5ζ13ζ23ζ7−ζ23−ζ7ζ23ζ7−ζ23−ζ7
χ393-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3200000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14−iiζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ22−ζ14ζ22ζ14−ζ23−ζ7ζ23ζ7−ζ23−ζ7ζ23ζ7ζ5ζ13−ζ5−ζ13ζ5ζ13−ζ5−ζ13
χ403-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3200000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14−ii−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ22−ζ14ζ22ζ14ζ23ζ7−ζ23−ζ7ζ23ζ7−ζ23−ζ7−ζ5−ζ13ζ5ζ13−ζ5−ζ13ζ5ζ13
χ413-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i3200000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ii−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ22−ζ14ζ22ζ14ζ5ζ13−ζ5−ζ13−ζ5−ζ13ζ5ζ13−ζ23−ζ7ζ23ζ7ζ23ζ7−ζ23−ζ7
χ423-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i3200000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−iiζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ22−ζ14ζ22ζ14−ζ5−ζ13ζ5ζ13ζ5ζ13−ζ5−ζ13ζ23ζ7−ζ23−ζ7−ζ23−ζ7ζ23ζ7
χ433-33-3−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i3200000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14i−iζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ22ζ14−ζ22−ζ14−ζ23−ζ7ζ23ζ7ζ23ζ7−ζ23−ζ7ζ5ζ13−ζ5−ζ13−ζ5−ζ13ζ5ζ13
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.