Finite Group Databasebeta

← Group #10692008

Character table — Group #10692008

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122234444444466612121212244888888881212121212121212688881224242424242424242424242424242424224444448888888844121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911111-1-111-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-1ii−i−i1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111-1-1i−i1-1
χ1011111-1-111-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-1ii−i−i1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-111-1-1−ii-11
χ1111111-1-111-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-1−i−iii1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-1-111−ii-11
χ1211111-1-111-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-1−i−iii1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1-111i−i1-1
χ1311111-1-111-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-1ii−i−i1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-1-111i−i-11
χ1411111-1-111-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-1ii−i−i1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-1-111−ii1-1
χ1511111-1-111-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-1−i−iii1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-111-1-1−ii1-1
χ1611111-1-111-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-1−i−iii1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-111-1-1i−i-11
χ1722222222222-2-22222222-2-2-20000000022-2-222-2-2-20000-2000000000000000022-2-222-2-2000000000000000000
χ1822222222222-2-22222222-2-2-20000000022-2-222-2-2-20000-20000000000000000-2-222-2-222000000000000000000
χ192222222-2-2-2-2222222222-2-2222-2-222-2-2-2-222-2-222-20000-20000000022-2-222-2-200000000000000000000000000
χ202222222-2-2-2-2222222222-2-22-2-222-2-222-2-222-2-222-20000-200000000-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-2222222222-200000000-2-2-2-2-2-2-2-22000020000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ222222222-2-2-2-2-2-2222222222-200000000-2-2-2-2-2-2-2-2200002000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ2322222-2-222-2-222222-2-2-2-22-2-20000000022-2-2-2-22220000-2000000000000000022-2-2-2-222000000000000000000
χ2422222-2-222-2-222222-2-2-2-22-2-20000000022-2-2-2-22220000-20000000000000000-2-22222-2-2000000000000000000
χ2522222-2-2-2-22222222-2-2-2-2-22-200000000-2-2-2-22222-20000200000000000000000000000022-2-2-2-2220000000000
χ2622222-2-2-2-22222222-2-2-2-2-22-200000000-2-2-2-22222-200002000000000000000000000000-2-22222-2-20000000000
χ2722222-2-2-2-222-2-2222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i-2-22222-2-220000-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-222-2-2222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-220000-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-122222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ302222-122222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ312222-122222222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ322222-122222222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-2-2-2-2-11111111111111111000000000000000022-1-1-1-10000
χ332222-122-2-2-2-222-1-1-1-1-1-1-1-2-2222-2-222-2-211-1-111-1-1100001−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000000000000000−i3i3−i3i30000
χ342222-122-2-2-2-222-1-1-1-1-1-1-1-2-2222-2-222-2-211-1-111-1-1100001i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000000000000000i3−i3i3−i30000
χ352222-122-2-2-2-222-1-1-1-1-1-1-1-2-22-2-222-2-22211-1-111-1-1100001−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000000000000000i3−i3i3−i30000
χ362222-122-2-2-2-222-1-1-1-1-1-1-1-2-22-2-222-2-22211-1-111-1-1100001i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000000000000000−i3i3−i3i30000
χ372222-1-2-222-2-2-2-2-1-1-11111-2222i2i2i2i−2i−2i−2i−2i-1-1-1-1111112i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii00000000000000002-2-1-1110000
χ382222-1-2-222-2-2-2-2-1-1-11111-2222i2i2i2i−2i−2i−2i−2i-1-1-1-111111−2i−2i2i2i-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000-2211-1-10000
χ392222-1-2-222-2-2-2-2-1-1-11111-222−2i−2i−2i−2i2i2i2i2i-1-1-1-1111112i2i−2i−2i-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000-2211-1-10000
χ402222-1-2-222-2-2-2-2-1-1-11111-222−2i−2i−2i−2i2i2i2i2i-1-1-1-111111−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i00000000000000002-2-1-1110000
χ412222-1-2-2-2-222-2-2-1-1-111112-222i2i−2i−2i−2i−2i2i2i11-1-1-1-111-10000133−3−3−3−333−i−iiiii−i−i000000000000000000−i3i3i3−i30000
χ422222-1-2-2-2-222-2-2-1-1-111112-222i2i−2i−2i−2i−2i2i2i11-1-1-1-111-100001−3−33333−3−3−i−iiiii−i−i000000000000000000i3−i3−i3i30000
χ432222-1-2-2-2-222-2-2-1-1-111112-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-111-10000133−3−3−3−333ii−i−i−i−iii000000000000000000i3−i3−i3i30000
χ442222-1-2-2-2-222-2-2-1-1-111112-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-111-100001−3−33333−3−3ii−i−i−i−iii000000000000000000−i3i3i3−i30000
χ452-22-222i−2i2-22i−2i00-22-22i2i−2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2002i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ462-22-222i−2i2-22i−2i00-22-22i2i−2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2002i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ472-22-222i−2i2-22i−2i00-22-22i2i−2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-2002i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ482-22-222i−2i2-22i−2i00-22-22i2i−2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-2002i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ492-22-222i−2i-22−2i2i00-22-22i2i−2i−2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200−2i2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i2-2002i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000
χ502-22-222i−2i-22−2i2i00-22-22i2i−2i−2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200−2i2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000
χ512-22-222i−2i-22−2i2i00-22-22i2i−2i−2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200−2i2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2-2002i−2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000
χ522-22-222i−2i-22−2i2i00-22-22i2i−2i−2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200−2i2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200−2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000
χ532-22-22−2i2i2-2−2i2i00-22-2−2i−2i2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-200−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002i−2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ542-22-22−2i2i2-2−2i2i00-22-2−2i−2i2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-200−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ552-22-22−2i2i2-2−2i2i00-22-2−2i−2i2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002i−2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ562-22-22−2i2i2-2−2i2i00-22-2−2i−2i2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ572-22-22−2i2i-222i−2i00-22-2−2i−2i2i2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i-22002i−2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2-200−2i2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000
χ582-22-22−2i2i-222i−2i00-22-2−2i−2i2i2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i-22002i−2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i-22002i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000
χ592-22-22−2i2i-222i−2i00-22-2−2i−2i2i2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-22002i−2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2-200−2i2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000
χ602-22-22−2i2i-222i−2i00-22-2−2i−2i2i2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-22002i−2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-22002i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000
χ614444-2444444-4-4-2-2-2-2-2-2-2-4-4-400000000-2-222-2-222200002000000000000000000000000000000000000000000
χ624444-244-4-4-4-4-4-4-2-2-2-2-2-2-244-40000000022222222-20000-2000000000000000000000000000000000000000000
χ634444-2-4-444-4-444-2-2-222224-4-400000000-2-22222-2-2-200002000000000000000000000000000000000000000000
χ644444-2-4-4-4-44444-2-2-22222-44-4000000002222-2-2-2-220000-2000000000000000000000000000000000000000000
χ654-44-4-24i−4i4-44i−4i002-22−2i−2i2i2i0002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i-2200−2i2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ664-44-4-24i−4i4-44i−4i002-22−2i−2i2i2i000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i-2200−2i2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ674-44-4-24i−4i-44−4i4i002-22−2i−2i2i2i0002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2-2002i−2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000000000
χ684-44-4-24i−4i-44−4i4i002-22−2i−2i2i2i000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i2-2002i−2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000000000
χ694-44-4-2−4i4i4-4−4i4i002-222i2i−2i−2i0002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i-22002i−2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ704-44-4-2−4i4i4-4−4i4i002-222i2i−2i−2i000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i-22002i−2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ714-44-4-2−4i4i-444i−4i002-222i2i−2i−2i0002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i2-200−2i2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000000000
χ724-44-4-2−4i4i-444i−4i002-222i2i−2i−2i000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i2-200−2i2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000000000
χ734-4-4440000004i−4i-4-440000000000000000000004i−4i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000
χ744-4-4440000004i−4i-4-440000000000000000000004i−4i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2302ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000
χ754-4-444000000−4i4i-4-44000000000000000000000−4i4i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1302ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000
χ764-4-444000000−4i4i-4-44000000000000000000000−4i4i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000
χ774-4-44-20000004i−4i22-223−2323−230000000000000−2i32i300−2i2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2302ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000000000000000
χ784-4-44-20000004i−4i22-223−2323−230000000000000−2i32i300−2i2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000000000000000
χ794-4-44-20000004i−4i22-2−2323−232300000000000002i3−2i300−2i2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2302ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000000000000000
χ804-4-44-20000004i−4i22-2−2323−232300000000000002i3−2i300−2i2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000000000000000
χ814-4-44-2000000−4i4i22-223−2323−2300000000000002i3−2i3002i−2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ130000000000000000000000000000000000
χ824-4-44-2000000−4i4i22-223−2323−2300000000000002i3−2i3002i−2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1302ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ130000000000000000000000000000000000
χ834-4-44-2000000−4i4i22-2−2323−23230000000000000−2i32i3002i−2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ50000000000000000000000000000000000
χ844-4-44-2000000−4i4i22-2−2323−23230000000000000−2i32i3002i−2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1302ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ50000000000000000000000000000000000
χ8588-8-88000000008-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-400000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-400000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000000

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