Finite Group Databasebeta

← Group #11785330

Character table — Group #11785330

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order1222444444443366666612121212121212121212121212121212121212122244444466661212121212121212121212122244888824242424242424244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111
χ711111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111i−ii−iii−i−iii−i−i1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111−ii−ii−i−iii−i−iii1-1−i−iii−i−iii
χ111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111i−ii−iii−i−iii−i−i1-1−i−iii−i−iii
χ121111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111−ii−ii−i−iii−i−iii1-1ii−i−iii−i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111i−i−iiii−i−i−i−iii-11ii−i−i−i−iii
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111−iii−i−i−iiiii−i−i-11−i−iiiii−i−i
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111i−i−iiii−i−i−i−iii-11−i−iiiii−i−i
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111−iii−i−i−iiiii−i−i-11ii−i−i−i−iii
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-2000000000000-2-200000000
χ1822222222-2-2-2-222222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2-2-20000000000002200000000
χ192222-2-2-2-222-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-200000000000000000000000022-2-2000000000000-2200000000
χ202222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000000022-2-20000000000002-200000000
χ2122-2-222-2-20000222-2-22-2-22222-2-200000000-2-2000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i-222-20000000000000000000000
χ2222-2-222-2-20000222-2-22-2-22222-2-200000000-2-200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i-222-20000000000000000000000
χ2322-2-222-2-20000222-2-22-2-22222-2-200000000-2-200002-22-2000022-2-222-2-2000000002-2-220000000000000000000000
χ2422-2-222-2-20000222-2-22-2-22222-2-200000000-2-20000-22-220000-2-222-2-222000000002-2-220000000000000000000000
χ2522-2-2-2-2220000222-2-22-2-2-2-2-2-2220000000022000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i2-22-20000000000000000000000
χ2622-2-2-2-2220000222-2-22-2-2-2-2-2-222000000002200000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i2-22-20000000000000000000000
χ2722-2-2-2-2220000222-2-22-2-2-2-2-2-222000000002200002-2-22000022-2-2-2-22200000000-22-220000000000000000000000
χ2822-2-2-2-2220000222-2-22-2-2-2-2-2-22200000000220000-222-20000-2-22222-2-200000000-22-220000000000000000000000
χ292-22-22i−2i2i−2i2-22i−2i22-22-2-22-22i−2i2i−2i2i−2i22-2-22i2i−2i−2i2i−2i2-22i−2i0000000000000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ302-22-22i−2i2i−2i2-22i−2i22-22-2-22-22i−2i2i−2i2i−2i22-2-22i2i−2i−2i2i−2i2-22i−2i000000000000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ312-22-22i−2i2i−2i-22−2i2i22-22-2-22-22i−2i2i−2i2i−2i-2-222−2i−2i2i2i2i−2i-22−2i2i0000000000000000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ322-22-22i−2i2i−2i-22−2i2i22-22-2-22-22i−2i2i−2i2i−2i-2-222−2i−2i2i2i2i−2i-22−2i2i000000000000000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ332-22-2−2i2i−2i2i2-2−2i2i22-22-2-22-2−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i−2i2i2-2−2i2i0000000000000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ342-22-2−2i2i−2i2i2-2−2i2i22-22-2-22-2−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i−2i2i2-2−2i2i000000000000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ352-22-2−2i2i−2i2i-222i−2i22-22-2-22-2−2i2i−2i2i−2i2i-2-2222i2i−2i−2i−2i2i-222i−2i0000000000000000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ362-22-2−2i2i−2i2i-222i−2i22-22-2-22-2−2i2i−2i2i−2i2i-2-2222i2i−2i−2i−2i2i-222i−2i000000000000000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ374444444444441-2111-2-2-211-2-2-2-2-2-2-2-2-2-2-2-211111100000000000000000000000000002222-1-1-1-1-1-1-1-10000000000
χ384444444444441-2111-2-2-211-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-2111111110000000000
χ39444444444444-21-2-2-2111-2-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ40444444444444-21-2-2-2111-2-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000000000000000000000
χ4144444444-4-4-4-41-2111-2-2-211-2-2-2-22222222211-1-1-1-1000000000000000000000000000022-2-2-1-1-1-111110000000000
χ4244444444-4-4-4-41-2111-2-2-211-2-2-2-22222222211-1-1-1-10000000000000000000000000000-2-2221111-1-1-1-10000000000
χ4344444444-4-4-4-4-21-2-2-2111-2-21111-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000000000
χ4444444444-4-4-4-4-21-2-2-2111-2-21111-1-1-1-1-1-1-1-1-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000000000
χ454444-4-4-4-444-4-41-2111-2-2-2-1-12222-2-2-2-22222-1-111-1-100000000000000000000000000002i−2i2i−2i−i−iii−i−iii0000000000
χ464444-4-4-4-444-4-41-2111-2-2-2-1-12222-2-2-2-22222-1-111-1-10000000000000000000000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ474444-4-4-4-444-4-4-21-2-2-211122-1-1-1-11111-1-1-1-122-2-22222-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000000000
χ484444-4-4-4-444-4-4-21-2-2-211122-1-1-1-11111-1-1-1-122-2-222-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000000000
χ494444-4-4-4-4-4-4441-2111-2-2-2-1-122222222-2-2-2-2-1-1-1-11100000000000000000000000000002i−2i−2i2i−i−iiiii−i−i0000000000
χ504444-4-4-4-4-4-4441-2111-2-2-2-1-122222222-2-2-2-2-1-1-1-1110000000000000000000000000000−2i2i2i−2iii−i−i−i−iii0000000000
χ514444-4-4-4-4-4-444-21-2-2-211122-1-1-1-1-1-1-1-111112222-2-222-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000000000
χ524444-4-4-4-4-4-444-21-2-2-211122-1-1-1-1-1-1-1-111112222-2-2-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000000000
χ5344-4-444-4-40000-21-2221-1-1-2-211-1-13i−3i3i−3i3i−3i3i−3i2200002-22-22i−2i2i−2i-1-111-1-111−i−iii−i−iii00000000000000000000000000
χ5444-4-444-4-40000-21-2221-1-1-2-211-1-13i−3i3i−3i3i−3i3i−3i220000-22-22−2i2i−2i2i11-1-111-1-1ii−i−iii−i−i00000000000000000000000000
χ5544-4-444-4-40000-21-2221-1-1-2-211-1-1−3i3i−3i3i−3i3i−3i3i2200002-22-2−2i2i−2i2i-1-111-1-111ii−i−iii−i−i00000000000000000000000000
χ5644-4-444-4-40000-21-2221-1-1-2-211-1-1−3i3i−3i3i−3i3i−3i3i220000-22-222i−2i2i−2i11-1-111-1-1−i−iii−i−iii00000000000000000000000000
χ5744-4-4-4-4440000-21-2221-1-122-1-1113i−3i3i−3i−3i3i−3i3i-2-200002-2-222i−2i−2i2i-1-11111-1-1−i−iiiii−i−i00000000000000000000000000
χ5844-4-4-4-4440000-21-2221-1-122-1-1113i−3i3i−3i−3i3i−3i3i-2-20000-222-2−2i2i2i−2i11-1-1-1-111ii−i−i−i−iii00000000000000000000000000
χ5944-4-4-4-4440000-21-2221-1-122-1-111−3i3i−3i3i3i−3i3i−3i-2-200002-2-22−2i2i2i−2i-1-11111-1-1ii−i−i−i−iii00000000000000000000000000
χ6044-4-4-4-4440000-21-2221-1-122-1-111−3i3i−3i3i3i−3i3i−3i-2-20000-222-22i−2i−2i2i11-1-1-1-111−i−iiiii−i−i00000000000000000000000000
χ614-44-44i−4i4i−4i4-44i−4i1-2-11-12-22i−i−2i2i−2i2i-2-222−2i−2i2i2ii−i1-1i−i00000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ624-44-44i−4i4i−4i4-44i−4i1-2-11-12-22i−i−2i2i−2i2i-2-222−2i−2i2i2ii−i1-1i−i00000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ634-44-44i−4i4i−4i4-44i−4i-212-22-11-1−2i2ii−ii−i11-1-1ii−i−i−2i2i-22−2i2i00000000−i3i3−i3i33−33−3−i3i3−i3i33−33−300000000000000000000000000
χ644-44-44i−4i4i−4i4-44i−4i-212-22-11-1−2i2ii−ii−i11-1-1ii−i−i−2i2i-22−2i2i00000000i3−i3i3−i3−33−33i3−i3i3−i3−33−3300000000000000000000000000
χ654-44-44i−4i4i−4i-44−4i4i1-2-11-12-22i−i−2i2i−2i2i22-2-22i2i−2i−2ii−i-11−ii00000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ664-44-44i−4i4i−4i-44−4i4i1-2-11-12-22i−i−2i2i−2i2i22-2-22i2i−2i−2ii−i-11−ii00000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ674-44-44i−4i4i−4i-44−4i4i-212-22-11-1−2i2ii−ii−i-1-111−i−iii−2i2i2-22i−2i00000000−i3i3−i3i33−33−3i3−i3i3−i3−33−3300000000000000000000000000
χ684-44-44i−4i4i−4i-44−4i4i-212-22-11-1−2i2ii−ii−i-1-111−i−iii−2i2i2-22i−2i00000000i3−i3i3−i3−33−33−i3i3−i3i33−33−300000000000000000000000000
χ694-44-4−4i4i−4i4i4-4−4i4i1-2-11-12-22−ii2i−2i2i−2i-2-2222i2i−2i−2i−ii1-1−ii00000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ704-44-4−4i4i−4i4i4-4−4i4i1-2-11-12-22−ii2i−2i2i−2i-2-2222i2i−2i−2i−ii1-1−ii00000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ714-44-4−4i4i−4i4i4-4−4i4i-212-22-11-12i−2i−ii−ii11-1-1−i−iii2i−2i-222i−2i00000000−i3i3−i3i3−33−33−i3i3−i3i3−33−3300000000000000000000000000
χ724-44-4−4i4i−4i4i4-4−4i4i-212-22-11-12i−2i−ii−ii11-1-1−i−iii2i−2i-222i−2i00000000i3−i3i3−i33−33−3i3−i3i3−i33−33−300000000000000000000000000
χ734-44-4−4i4i−4i4i-444i−4i1-2-11-12-22−ii2i−2i2i−2i22-2-2−2i−2i2i2i−ii-11i−i00000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ744-44-4−4i4i−4i4i-444i−4i1-2-11-12-22−ii2i−2i2i−2i22-2-2−2i−2i2i2i−ii-11i−i00000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ754-44-4−4i4i−4i4i-444i−4i-212-22-11-12i−2i−ii−ii-1-111ii−i−i2i−2i2-2−2i2i00000000−i3i3−i3i3−33−33i3−i3i3−i33−33−300000000000000000000000000
χ764-44-4−4i4i−4i4i-444i−4i-212-22-11-12i−2i−ii−ii-1-111ii−i−i2i−2i2-2−2i2i00000000i3−i3i3−i33−33−3−i3i3−i3i3−33−3300000000000000000000000000
χ774-4-444i−4i−4i4i000044-4-44-4-444i−4i4i−4i−4i4i00000000−4i4i000000000000000000000000000000000000000000000000000000
χ784-4-444i−4i−4i4i0000-2122-2-1-11−2i2ii−i−ii3i−3i−3i3i-333-32i−2i000000000000−i3i3i3−i33−3−333−3−33i3−i3−i3i300000000000000000000000000
χ794-4-444i−4i−4i4i0000-2122-2-1-11−2i2ii−i−ii3i−3i−3i3i-333-32i−2i000000000000i3−i3−i3i3−333−3−333−3−i3i3i3−i300000000000000000000000000
χ804-4-444i−4i−4i4i0000-2122-2-1-11−2i2ii−i−ii−3i3i3i−3i3-3-332i−2i000000000000−i3i3i3−i33−3−33−333−3−i3i3i3−i300000000000000000000000000
χ814-4-444i−4i−4i4i0000-2122-2-1-11−2i2ii−i−ii−3i3i3i−3i3-3-332i−2i000000000000i3−i3−i3i3−333−33−3−33i3−i3−i3i300000000000000000000000000
χ824-4-44−4i4i4i−4i000044-4-44-4-44−4i4i−4i4i4i−4i000000004i−4i000000000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i0000-2122-2-1-112i−2i−iii−i3i−3i−3i3i3-3-33−2i2i000000000000−i3i3i3−i3−333−33−3−33−i3i3i3−i300000000000000000000000000
χ844-4-44−4i4i4i−4i0000-2122-2-1-112i−2i−iii−i3i−3i−3i3i3-3-33−2i2i000000000000i3−i3−i3i33−3−33−333−3i3−i3−i3i300000000000000000000000000
χ854-4-44−4i4i4i−4i0000-2122-2-1-112i−2i−iii−i−3i3i3i−3i-333-3−2i2i000000000000−i3i3i3−i3−333−3−333−3i3−i3−i3i300000000000000000000000000
χ864-4-44−4i4i4i−4i0000-2122-2-1-112i−2i−iii−i−3i3i3i−3i-333-3−2i2i000000000000i3−i3−i3i33−3−333−3−33−i3i3i3−i300000000000000000000000000
χ8788-8-888-8-800002-42-2-2-44422-4-44400000000-2-2000000000000000000000000000000000000000000000000000000
χ8888-8-8-8-88800002-42-2-2-444-2-244-4-40000000022000000000000000000000000000000000000000000000000000000
χ898-8-888i−8i−8i8i00002-4-2-2244-42i−2i−4i4i4i−4i00000000−2i2i000000000000000000000000000000000000000000000000000000
χ908-8-88−8i8i8i−8i00002-4-2-2244-4−2i2i4i−4i−4i4i000000002i−2i000000000000000000000000000000000000000000000000000000

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