Finite Group Databasebeta

← Group #13166498

Character table — Group #13166498

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222444444448888888888888888888899991212181818181818181818181818181818181818181818181818181818181818181818182424242424242424108108108108108108
order12223446661212121233666666336666661212121212121212121212124444244488888888121212121212121224242424242424242424242424242424666612121212248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1ii−i−i
χ6111111111111111111111111111111111111111111-1-1-1-111-1-1−i−iii−i−iii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1−i−iii
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111−i−iii
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111ii−i−i
χ911111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-11-1
χ1011111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11-11
χ1111111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-11
χ1211111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-11-1
χ1311111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111ii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11-1i−i−ii
χ1411111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11-1−iii−i
χ1511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11−iii−i
χ1611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11i−i−ii
χ172222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222002222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ182222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220022-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000
χ192222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200-2-22i2i−2i−2i2i2i−2i−2i11111111−i−i−i−i−i−i−i−iiiiiiiii00000000000000
χ202222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200-2-2−2i−2i2i2i−2i−2i2i2i11111111iiiiiiii−i−i−i−i−i−i−i−i00000000000000
χ212222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111222200-2-22222-2-2-2-21111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000
χ222222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111222200-2-2-2-2-2-222221111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000
χ232222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-200222i2i−2i−2i−2i−2i2i2i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ242222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-20022−2i−2i2i2i2i2i−2i−2i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ2522-2-22002-2-2000022-2-222-2-222-2-2-2-2220000000000002i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002i2i−2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000
χ2622-2-22002-2-2000022-2-222-2-222-2-2-2-2220000000000002i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000002i2i−2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000
χ2722-2-22002-2-2000022-2-222-2-222-2-2-2-222000000000000−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2i−2i2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000
χ2822-2-22002-2-2000022-2-222-2-222-2-2-2-222000000000000−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−2i−2i2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000
χ2922-2-2-100-111−i3−i3i3i322-2-222-2-2-1-11111-1-10000−i3−i3−i3−i3i3i3i3i32i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000033−3−3−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300000000000000
χ3022-2-2-100-111−i3−i3i3i322-2-222-2-2-1-11111-1-10000−i3−i3−i3−i3i3i3i3i32i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000033−3−3−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300000000000000
χ3122-2-2-100-111−i3−i3i3i322-2-222-2-2-1-11111-1-10000−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−3−333ii−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+ζ2300000000000000
χ3222-2-2-100-111−i3−i3i3i322-2-222-2-2-1-11111-1-10000−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−3−333ii−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−ζ2300000000000000
χ3322-2-2-100-111i3i3−i3−i322-2-222-2-2-1-11111-1-10000i3i3i3i3−i3−i3−i3−i32i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−3−333−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−ζ1300000000000000
χ3422-2-2-100-111i3i3−i3−i322-2-222-2-2-1-11111-1-10000i3i3i3i3−i3−i3−i3−i32i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−3−333−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+ζ1300000000000000
χ3522-2-2-100-111i3i3−i3−i322-2-222-2-2-1-11111-1-10000i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000033−3−3ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ2300000000000000
χ3622-2-2-100-111i3i3−i3−i322-2-222-2-2-1-11111-1-10000i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000033−3−3ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ2300000000000000
χ372-22-222i−2i-22-22i−2i2i−2i2222-2-2-2-22222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i−2i2i002-2000000002-22-22i−2i2i−2i000000000000000000000000000000
χ382-22-222i−2i-22-22i−2i2i−2i2222-2-2-2-22222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i2i2i−2i00-2200000000-22-22−2i2i−2i2i000000000000000000000000000000
χ392-22-22−2i2i-22-2−2i2i−2i2i2222-2-2-2-22222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i−2i−2i2i00-2200000000-22-222i−2i2i−2i000000000000000000000000000000
χ402-22-22−2i2i-22-2−2i2i−2i2i2222-2-2-2-22222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i2i2i−2i002-2000000002-22-2−2i2i−2i2i000000000000000000000000000000
χ412-22-2-12i−2i1-11−ii−ii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−iii−i−iii2i−2i−2i2i002-200000000-11-11−ii−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000
χ422-22-2-12i−2i1-11−ii−ii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−iii−i−iii2i−2i−2i2i002-200000000-11-11−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000
χ432-22-2-12i−2i1-11−ii−ii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−iii−i−iii−2i2i2i−2i00-22000000001-11-1i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000
χ442-22-2-12i−2i1-11−ii−ii2222-2-2-2-2-1-1-1-111112i2i−2i−2i−i−iii−i−iii−2i2i2i−2i00-22000000001-11-1i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000
χ452-22-2-1−2i2i1-11i−ii−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iii−i−iii−i−i2i−2i−2i2i00-22000000001-11-1−ii−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000
χ462-22-2-1−2i2i1-11i−ii−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iii−i−iii−i−i2i−2i−2i2i00-22000000001-11-1−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000
χ472-22-2-1−2i2i1-11i−ii−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iii−i−iii−i−i−2i2i2i−2i002-200000000-11-11i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000
χ482-22-2-1−2i2i1-11i−ii−i2222-2-2-2-2-1-1-1-11111−2i−2i2i2iii−i−iii−i−i−2i2i2i−2i002-200000000-11-11i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000
χ492-2-22200-2-22000022-2-2-2-22222-2-222-2-200000000000022-2-2000000002i−2i2i−2i00002-2-2200002i−2i−2i2i0000−2i2i2i−2i00000000000000
χ502-2-22200-2-22000022-2-2-2-22222-2-222-2-200000000000022-2-200000000−2i2i−2i2i00002-2-220000−2i2i2i−2i00002i−2i−2i2i00000000000000
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χ522-2-22200-2-22000022-2-2-2-22222-2-222-2-2000000000000-2-22200000000-222-20000-222-20000-222-20000-222-200000000000000
χ532-2-22-10011-13−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−33322-2-2000000002i−2i2i−2i−333−3-111-1−i3i3i3−i3−iii−ii3−i3−i3i3i−i−ii00000000000000
χ542-2-22-10011-13−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−33322-2-200000000−2i2i−2i2i−333−3-111-1i3−i3−i3i3i−i−ii−i3i3i3−i3−iii−i00000000000000
χ552-2-22-10011-13−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−333-2-222000000002-2-223−3−331-1-11−333−3-111-1−333−3-111-100000000000000
χ562-2-22-10011-13−3−3322-2-2-2-222-1-111-1-111000033−3−3−3−333-2-22200000000-222-23−3−331-1-113−3−331-1-113−3−331-1-1100000000000000
χ572-2-22-10011-1−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−322-2-2000000002i−2i2i−2i3−3−33-111-1i3−i3−i3i3−iii−i−i3i3i3−i3i−i−ii00000000000000
χ582-2-22-10011-1−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−322-2-200000000−2i2i−2i2i3−3−33-111-1−i3i3i3−i3i−i−iii3−i3−i3i3−iii−i00000000000000
χ592-2-22-10011-1−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−3-2-222000000002-2-22−333−31-1-113−3−33-111-13−3−33-111-100000000000000
χ602-2-22-10011-1−333−322-2-2-2-222-1-111-1-1110000−3−33333−3−3-2-22200000000-222-2−333−31-1-11−333−31-1-11−333−31-1-1100000000000000
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χ62444444444444441-21-21-21-21-21-21-21-21-21-21-21-21-21-20000-4-40000000000000000000000000000000000-1-122-1-122000000
χ6344444444444444-21-21-21-21-21-21-21-21-21-21-21-21-21-210000440000000000000000000000000000000000-2-211-2-211000000
χ6444444444444444-21-21-21-21-21-21-21-21-21-21-21-21-21-210000-4-4000000000000000000000000000000000022-1-122-1-1000000
χ6544444-4-4444-4-4-4-41-21-21-21-21-21-21-21-2-12-12-12-12-12-1200004-4000000000000000000000000000000000011-2-2-1-122000000
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χ6744444-4-4444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-12-12-100004-40000000000000000000000000000000000-2-21122-1-1000000
χ6844444-4-4444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-12-12-10000-44000000000000000000000000000000000022-1-1-2-211000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.