Finite Group Databasebeta

← Group #149125

Character table — Group #149125

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order1222222244444444222244448888888888888888444444448888888816161616161616161616161616161616161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-200000000000000000000000022-2-222-2-22222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−20000000000000000
χ202222222222222222-2-2-2-2-2-2-2-200000000000000000000000022-2-222-2-2−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222220000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2000000000000000000000000-2-222-2-2222222−2−2−2−22222−2−2−2−2−2−2−2−22222−2−2−2−222220000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2000000000000000000000000-2-222-2-222−2−2−2−22222−2−2−2−222222222−2−2−2−22222−2−2−2−20000000000000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i2222−2−2−2−2−2−2−2−22222i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i−2−2−2−222222222−2−2−2−2−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i2222−2−2−2−2−2−2−2−22222−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2−2−2−222222222−2−2−2−2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ292222-2-2-2-222-2-222-2-222-2-22-2-222222-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000000000000000000000002-22-2
χ302222-2-2-2-222-2-222-2-222-2-22-2-222222-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000000000000000000000-22-22
χ312222-2-2-2-222-2-222-2-222-2-22-2-22-2-2-2-222-2-2-2-222222200000000000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ322222-2-2-2-222-2-222-2-222-2-22-2-22-2-2-2-222-2-2-2-22222220000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ332222-2-2-2-2-2-222-2-222-2-2222-2-222222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-2-2-222-2-222-2-2222-2-222222-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-2-2-222-2-222-2-2222-2-22-2-2-2-2222222-2-222-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ362222-2-2-2-2-2-222-2-222-2-2222-2-22-2-2-2-2222222-2-222-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ3722-2-222-2-22i−2i2i−2i2i−2i2i−2i0000000022−2−22−2i2i2−i2−i2i2−i22−2i2−i21+i1+i−1−i−1−i1−i1−i−1+i−1+i002ζ2−2ζ2002ζ6−2ζ6ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ3ζ+ζ3ζ+ζ3−ζ−ζ3−ζ−ζ3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70000000000000000
χ3822-2-222-2-22i−2i2i−2i2i−2i2i−2i0000000022−2−22−2i2i2−i2−i2i2−i22−2i2−i21+i1+i−1−i−1−i1−i1−i−1+i−1+i002ζ2−2ζ2002ζ6−2ζ6−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ+ζ3−ζ+ζ3ζ−ζ3ζ−ζ3−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70000000000000000
χ3922-2-222-2-22i−2i2i−2i2i−2i2i−2i0000000022−2−22−2i2i2−i2−i2i2−i22−2i2−i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2ζ22ζ200−2ζ62ζ6ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ+ζ3−ζ+ζ3ζ−ζ3ζ−ζ3−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70000000000000000
χ4022-2-222-2-22i−2i2i−2i2i−2i2i−2i0000000022−2−22−2i2i2−i2−i2i2−i22−2i2−i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2ζ22ζ200−2ζ62ζ6−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ3ζ+ζ3ζ+ζ3−ζ−ζ3−ζ−ζ3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70000000000000000
χ4122-2-222-2-22i−2i2i−2i2i−2i2i−2i00000000−2−222−22−i2−i2i2i2−i2i2−22−i2i21+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2ζ22ζ200−2ζ62ζ6ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ3−ζ+ζ3ζ−ζ3ζ−ζ3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ30000000000000000
χ4222-2-222-2-22i−2i2i−2i2i−2i2i−2i00000000−2−222−22−i2−i2i2i2−i2i2−22−i2i21+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2ζ22ζ200−2ζ62ζ6−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ+ζ3ζ+ζ3−ζ−ζ3−ζ−ζ30000000000000000
χ4322-2-222-2-22i−2i2i−2i2i−2i2i−2i00000000−2−222−22−i2−i2i2i2−i2i2−22−i2i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i002ζ2−2ζ2002ζ6−2ζ6ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ+ζ3ζ+ζ3−ζ−ζ3−ζ−ζ30000000000000000
χ4422-2-222-2-22i−2i2i−2i2i−2i2i−2i00000000−2−222−22−i2−i2i2i2−i2i2−22−i2i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i002ζ2−2ζ2002ζ6−2ζ6−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ3−ζ+ζ3ζ−ζ3ζ−ζ3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ30000000000000000
χ4522-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000000022−2−22−2−i2−i2i2i2−i2i22−2−i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2ζ62ζ600−2ζ22ζ2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ+ζ3ζ+ζ3−ζ−ζ3−ζ−ζ3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ+ζ3−ζ+ζ3ζ−ζ3ζ−ζ30000000000000000
χ4622-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000000022−2−22−2−i2−i2i2i2−i2i22−2−i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2ζ62ζ600−2ζ22ζ2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ30000000000000000
χ4722-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000000022−2−22−2−i2−i2i2i2−i2i22−2−i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i002ζ6−2ζ6002ζ2−2ζ2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ30000000000000000
χ4822-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000000022−2−22−2−i2−i2i2i2−i2i22−2−i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i002ζ6−2ζ6002ζ2−2ζ2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ+ζ3ζ+ζ3−ζ−ζ3−ζ−ζ3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ+ζ3−ζ+ζ3ζ−ζ3ζ−ζ30000000000000000
χ4922-2-222-2-2−2i2i−2i2i−2i2i−2i2i00000000−2−222−22i2i2−i2−i2i2−i2−22i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i002ζ6−2ζ6002ζ2−2ζ2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ+ζ3ζ+ζ3−ζ−ζ3−ζ−ζ3−ζ+ζ3−ζ+ζ3ζ−ζ3ζ−ζ3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ70000000000000000
χ5022-2-222-2-2−2i2i−2i2i−2i2i−2i2i00000000−2−222−22i2i2−i2−i2i2−i2−22i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i002ζ6−2ζ6002ζ2−2ζ2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ3ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ70000000000000000
χ5122-2-222-2-2−2i2i−2i2i−2i2i−2i2i00000000−2−222−22i2i2−i2−i2i2−i2−22i2−i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2ζ62ζ600−2ζ22ζ2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ−ζ3−ζ−ζ3ζ+ζ3ζ+ζ3ζ−ζ3ζ−ζ3−ζ+ζ3−ζ+ζ3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ70000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.