Finite Group Databasebeta

← Group #10705298

Character table — Group #10705298

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122244443444466688888888121212122444668888121212121212121212122424242424242424242424242424242416161616161616161616161616161616444412121212121212128888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ101111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ121111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ131111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222-2-2-2-222200000000222222-2-222000022-2-2-2-2-2-2-2-2000000000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222-2-2-2-222200000000222222-2-222000022-2-2-2-2-2-2-2-20000000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222-2-2-2-2222000000002222-2-222-2-20000-2-2-2-22222-2-2000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222-2-2-2-2222000000002222-2-222-2-20000-2-2-2-22222-2-20000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-12222-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2422222222-12222-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2522222222-12222-1-1-122222222-1-1-1-1-2-2-2-211-2-2-2-211-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2622222222-12222-1-1-122222222-1-1-1-1-2-2-2-211-2-2-2-211-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2722222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-211222211-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-211222211-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2-2-2222-2-222200000000-2-2-2-22-2-22220000-2-222-2-222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ322222-2-2-2-2222-2-222200000000-2-2-2-22-2-22220000-2-222-2-222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ332222-2-2-2-2222-2-222200000000-2-2-2-2-222-2-2-20000222222-2-2-2-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2222-2-222200000000-2-2-2-2-222-2-2-20000222222-2-2-2-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-22-22-222-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ362222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-2-22-22-2-222-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-2-2-1-2-222-1-1-12222-2-2-2-211112-22-2-1-122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ382222-2-2-2-2-1-2-222-1-1-12222-2-2-2-211112-22-2-1-122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ392222-2-2-2-2-1-2-222-1-1-12222-2-2-2-21111-22-2211-2-222-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ402222-2-2-2-2-1-2-222-1-1-12222-2-2-2-21111-22-2211-2-222-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ412222-2-2-2-2-1-2-222-1-1-1-2-2-2-2222211112-22-2-1-1-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ422222-2-2-2-2-1-2-222-1-1-1-2-2-2-2222211112-22-2-1-1-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ432222-2-2-2-2-1-2-222-1-1-1-2-2-2-222221111-22-221122-2-2-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-2-2-1-2-222-1-1-1-2-2-2-222221111-22-221122-2-2-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ452-22-22i2i−2i−2i22i−2i2-2-22-2000000002i2i−2i−2i0000002i−2i2-2002i−2i00002-2000000002i2i−2i−2i22-2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ462-22-22i2i−2i−2i22i−2i2-2-22-2000000002i2i−2i−2i0000002i−2i2-2002i−2i00002-2000000002i2i−2i−2i22-2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ472-22-22i2i−2i−2i22i−2i2-2-22-2000000002i2i−2i−2i000000−2i2i-22002i−2i00002-200000000−2i−2i2i2i-2-2221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ482-22-22i2i−2i−2i22i−2i2-2-22-2000000002i2i−2i−2i000000−2i2i-22002i−2i00002-200000000−2i−2i2i2i-2-222−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-22-22i2i−2i−2i2−2i2i-22-22-222-2-22i2i−2i−2i2i2i−2i−2i000000000000−2i2i0000-2222-2-22i2i−2i−2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ502-22-22i2i−2i−2i2−2i2i-22-22-222-2-22i2i−2i−2i2i2i−2i−2i000000000000−2i2i0000-2222-2-22i2i−2i−2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ512-22-22i2i−2i−2i2−2i2i-22-22-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000−2i2i0000-22-2-222−2i−2i2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ522-22-22i2i−2i−2i2−2i2i-22-22-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000−2i2i0000-22-2-222−2i−2i2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ532-22-2−2i−2i2i2i22i−2i-22-22-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000002i−2i0000-2222-2-2−2i−2i2i2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ542-22-2−2i−2i2i2i22i−2i-22-22-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000002i−2i0000-2222-2-2−2i−2i2i2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ552-22-2−2i−2i2i2i22i−2i-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000002i−2i0000-22-2-2222i2i−2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ562-22-2−2i−2i2i2i22i−2i-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000002i−2i0000-22-2-2222i2i−2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ572-22-2−2i−2i2i2i2−2i2i2-2-22-200000000−2i−2i2i2i0000002i−2i-2200−2i2i00002-2000000002i2i−2i−2i-2-2221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ582-22-2−2i−2i2i2i2−2i2i2-2-22-200000000−2i−2i2i2i0000002i−2i-2200−2i2i00002-2000000002i2i−2i−2i-2-222−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ592-22-2−2i−2i2i2i2−2i2i2-2-22-200000000−2i−2i2i2i000000−2i2i2-200−2i2i00002-200000000−2i−2i2i2i22-2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ602-22-2−2i−2i2i2i2−2i2i2-2-22-200000000−2i−2i2i2i000000−2i2i2-200−2i2i00002-200000000−2i−2i2i2i22-2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6144444444-2-4-4-4-4-2-2-200000000-2-2-2-244-4-4-2-20000-2-222222222000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-200000000-2-2-2-2-4-4442200002222-2-2-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-4-4-244-4-4-2-2-20000000022224-4-44-2-2000022-2-222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-244-4-4-2-2-2000000002222-444-4220000-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ6544-4-44-44-4400004-4-422−2222−2222−2222−224-44-40000000000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ6644-4-44-44-4400004-4-4−2222−2222−2222−22224-44-400000000000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ6744-4-44-44-4-20000-22222−2222−2222−2222−22-22-220000−2i32i30000−2i32i300000000−22−22−22−22i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000
χ6844-4-44-44-4-20000-22222−2222−2222−2222−22-22-2200002i3−2i300002i3−2i300000000−22−22−22−22−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ6944-4-44-44-4-20000-222−2222−2222−2222−2222-22-220000−2i32i30000−2i32i3000000002−22−22−22−2−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ7044-4-44-44-4-20000-222−2222−2222−2222−2222-22-2200002i3−2i300002i3−2i3000000002−22−22−22−2i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000
χ7144-4-4-44-44400004-4-422−2222−22−2222−2222-44-440000000000000000000022−2222−22−2222−22220000000000000000000000000000000000000000
χ7244-4-4-44-44400004-4-4−2222−222222−2222−22-44-4400000000000000000000−2222−222222−2222−220000000000000000000000000000000000000000
χ7344-4-4-44-44-20000-22222−2222−22−2222−22222-22-20000−2i32i300002i3−2i300000000−22−222−22−2i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ7444-4-4-44-44-20000-22222−2222−22−2222−22222-22-200002i3−2i30000−2i32i300000000−22−222−22−2−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ7544-4-4-44-44-20000-222−2222−222222−2222−222-22-20000−2i32i300002i3−2i3000000002−22−2−22−22−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ7644-4-4-44-44-20000-222−2222−222222−2222−222-22-200002i3−2i30000−2i32i3000000002−22−2−22−22i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ774-44-44i4i−4i−4i-24i−4i4-42-2200000000−2i−2i2i2i0000004i−4i4-400−2i2i0000-2200000000−2i−2i2i2i-2-22200000000000000000000000000000000
χ784-44-44i4i−4i−4i-24i−4i4-42-2200000000−2i−2i2i2i000000−4i4i-4400−2i2i0000-22000000002i2i−2i−2i22-2-200000000000000000000000000000000
χ794-44-44i4i−4i−4i-2−4i4i-442-2244-4-44i4i−4i−4i−2i−2i2i2i0000000000002i−2i00002-2-2-222−2i−2i2i2i0000000000000000000000000000000000000000
χ804-44-44i4i−4i−4i-2−4i4i-442-22-4-444−4i−4i4i4i−2i−2i2i2i0000000000002i−2i00002-222-2-22i2i−2i−2i0000000000000000000000000000000000000000
χ814-44-4−4i−4i4i4i-24i−4i-442-2244-4-4−4i−4i4i4i2i2i−2i−2i000000000000−2i2i00002-2-2-2222i2i−2i−2i0000000000000000000000000000000000000000
χ824-44-4−4i−4i4i4i-24i−4i-442-22-4-4444i4i−4i−4i2i2i−2i−2i000000000000−2i2i00002-222-2-2−2i−2i2i2i0000000000000000000000000000000000000000
χ834-44-4−4i−4i4i4i-2−4i4i4-42-22000000002i2i−2i−2i0000004i−4i-44002i−2i0000-2200000000−2i−2i2i2i22-2-200000000000000000000000000000000
χ844-44-4−4i−4i4i4i-2−4i4i4-42-22000000002i2i−2i−2i000000−4i4i4-4002i−2i0000-22000000002i2i−2i−2i-2-22200000000000000000000000000000000
χ854-4-444i−4i−4i4i40000-4-4422−22−22222i2−2i2−2i22i24i−4i−4i4i0000000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i40000-4-44−222222−22−2i22i22i2−2i24i−4i−4i4i00000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i-2000022-222−22−22222i2−2i2−2i22i2−2i2i2i−2i0000000000000023−23−2i32i300−222−2−i2i2i2−i26−6−66−i6i6i6−i600000000000000000000000000000000
χ884-4-444i−4i−4i4i-2000022-222−22−22222i2−2i2−2i22i2−2i2i2i−2i00000000000000−23232i3−2i300−222−2−i2i2i2−i2−666−6i6−i6−i6i600000000000000000000000000000000
χ894-4-444i−4i−4i4i-2000022-2−222222−22−2i22i22i2−2i2−2i2i2i−2i0000000000000023−23−2i32i3002−2−22i2−i2−i2i2−666−6i6−i6−i6i600000000000000000000000000000000
χ904-4-444i−4i−4i4i-2000022-2−222222−22−2i22i22i2−2i2−2i2i2i−2i00000000000000−23232i3−2i3002−2−22i2−i2−i2i26−6−66−i6i6i6−i600000000000000000000000000000000
χ914-4-44−4i4i4i−4i40000-4-4422−22−2222−2i22i22i2−2i2−4i4i4i−4i0000000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i40000-4-44−222222−222i2−2i2−2i22i2−4i4i4i−4i00000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i-2000022-222−22−2222−2i22i22i2−2i22i−2i−2i2i0000000000000023−232i3−2i300−222−2i2−i2−i2i26−6−66i6−i6−i6i600000000000000000000000000000000
χ944-4-44−4i4i4i−4i-2000022-222−22−2222−2i22i22i2−2i22i−2i−2i2i00000000000000−2323−2i32i300−222−2i2−i2−i2i2−666−6−i6i6i6−i600000000000000000000000000000000
χ954-4-44−4i4i4i−4i-2000022-2−222222−222i2−2i2−2i22i22i−2i−2i2i0000000000000023−232i3−2i3002−2−22−i2i2i2−i2−666−6−i6i6i6−i600000000000000000000000000000000
χ964-4-44−4i4i4i−4i-2000022-2−222222−222i2−2i2−2i22i22i−2i−2i2i00000000000000−2323−2i32i3002−2−22−i2i2i2−i26−6−66i6−i6−i6i600000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.