Finite Group Databasebeta

← Group #10695148

Character table — Group #10695148

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122244442234444444444666121212126688888888121212121212121212122424242424242424242424242424242488888888888888882466881212242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii-11−ii
χ111111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-111i−i-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i1111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1-1−ii11−i−iii1-1i−i
χ131111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii1-1−ii
χ141111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i-11i−i
χ151111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-111−ii-1-1−i−iii-11i−i
χ161111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii1111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-11-1-1i−i11ii−i−i1-1−ii
χ1722222222222-2-2-2-2-2-2-2-22222222222200000000-2-2-2-2-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-22222222222200000000-2-2-2-2-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-122-1-1-1-1-1-10000
χ202222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-211-2-21111110000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-1-1-2-2-1-111110000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2112211-1-1-1-10000
χ2322222222-2-2222-2-222-2-2-2-22222222-2-222-2-222-2-222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2222-2-222-2-2-2-22222222-2-2-2-222-2-22222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-22-2-222-2-222-2-22222222-2-200000000-2-22222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ2622222222-2-22-2-222-2-222-2-22222222-2-200000000-2-22222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2722222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-11122-2-222-2-2-1-1111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000−i3i300−i3i3−i3i3−i3i30000
χ2822222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-11122-2-222-2-2-1-1111111-1-1-1-1-1-11111-1-1-1-11111000000000000000000i3−i300i3−i3i3−i3i3−i30000
χ2922222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-111-2-222-2-222-1-1111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000−i3i300−i3i3i3−i3i3−i30000
χ3022222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-111-2-222-2-222-1-1111111-1-11111-1-1-1-11111-1-1-1-1000000000000000000i3−i300i3−i3−i3i3−i3i30000
χ312222-2-2-2-222222-2-2-2-222-2-2222-2-2-2-2222i2i−2i−2i−2i−2i2i2i22-2-222-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ322222-2-2-2-222222-2-2-2-222-2-2222-2-2-2-222−2i−2i2i2i2i2i−2i−2i22-2-222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ332222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-222-2-2-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ342222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-222-2-2-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ352222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-12i2i−2i−2i−2i−2i2i2i-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000−i3i300i3−i33−3−330000
χ362222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-12i2i−2i−2i−2i−2i2i2i-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000i3−i300−i3i3−333−30000
χ372222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-1−2i−2i2i2i2i2i−2i−2i-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii000000000000000000−i3i300i3−i3−333−30000
χ382222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-1−2i−2i2i2i2i2i−2i−2i-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii000000000000000000i3−i300−i3i33−3−330000
χ392222-2-2-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-200000000-2-2-2-2222222000000000000000022-2-2-2-222000000000000000000000000
χ402222-2-2-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-200000000-2-2-2-22222220000000000000000-2-22222-2-2000000000000000000000000
χ412222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111112i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-2-1-12i−2i11−i−iii0000
χ422222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111112i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-2211−2i2i-1-1ii−i−i0000
χ432222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2-1-1−2i2i11ii−i−i0000
χ442222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-22112i−2i-1-1−i−iii0000
χ4522-2-22i−2i2i−2i0022-2002i−2i00002-2-22i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232-20000002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4622-2-22i−2i2i−2i0022-2002i−2i00002-2-22i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232-20000002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4722-2-22i−2i2i−2i0022-2002i−2i00002-2-22i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232-20000002i−2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4822-2-22i−2i2i−2i0022-2002i−2i00002-2-22i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232-20000002i−2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4922-2-22i−2i2i−2i002-2200−2i2i00002-2-22i−2i2i−2i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300-22000000−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300002−2−22−i2i2i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ5022-2-22i−2i2i−2i002-2200−2i2i00002-2-22i−2i2i−2i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300-22000000−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−222−2i2−i2−i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ5122-2-22i−2i2i−2i002-2200−2i2i00002-2-22i−2i2i−2i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300-22000000−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002−2−22−i2i2i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ5222-2-22i−2i2i−2i002-2200−2i2i00002-2-22i−2i2i−2i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300-22000000−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ230000−222−2i2−i2−i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ5322-2-2−2i2i−2i2i0022-200−2i2i00002-2-2−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132-2000000−2i2i00002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5422-2-2−2i2i−2i2i0022-200−2i2i00002-2-2−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132-2000000−2i2i00002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5522-2-2−2i2i−2i2i0022-200−2i2i00002-2-2−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132-2000000−2i2i0000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5622-2-2−2i2i−2i2i0022-200−2i2i00002-2-2−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132-2000000−2i2i0000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5722-2-2−2i2i−2i2i002-22002i−2i00002-2-2−2i2i−2i2i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300-220000002i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002−2−22i2−i2−i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ5822-2-2−2i2i−2i2i002-22002i−2i00002-2-2−2i2i−2i2i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300-220000002i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ130000−222−2−i2i2i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ5922-2-2−2i2i−2i2i002-22002i−2i00002-2-2−2i2i−2i2i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300-220000002i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300002−2−22i2−i2−i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ6022-2-2−2i2i−2i2i002-22002i−2i00002-2-2−2i2i−2i2i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300-220000002i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−222−2−i2i2i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ614444444444-2-4-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-200000000222222-2-222000000000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-444-4-444-4-4-2-2-2-2-2-2-2220000000022-2-2-2-22222000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-2-4-44444-4-4-4-4-2-2-22222-2-20000000022-2-22222-2-2000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-2-4-4-4-4444444-2-2-2222222000000002222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ6544-4-44i−4i4i−4i00-24-4004i−4i0000-222−2i2i−2i2i0000−4ζ5−4ζ134ζ5+4ζ13004ζ7+4ζ23−4ζ7−4ζ23-22000000−2i2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000
χ6644-4-44i−4i4i−4i00-24-4004i−4i0000-222−2i2i−2i2i00004ζ5+4ζ13−4ζ5−4ζ1300−4ζ7−4ζ234ζ7+4ζ23-22000000−2i2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ6744-4-44i−4i4i−4i00-2-4400−4i4i0000-222−2i2i−2i2i00−4ζ5−4ζ134ζ5+4ζ13004ζ7+4ζ23−4ζ7−4ζ23002-20000002i−2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.