Finite Group Databasebeta

← Group #11789734

Character table — Group #11789734

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order12442444443366661212121212121212121212121212612121212128888888824242424242424242424242424242424224424884461224244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ511111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ611111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ711111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ811111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1
χ911-1-1-1ii−i−i1111-1-11iiii−i−i−i−i11-1-1-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1-111-1i−ii−i1-1i−ii−i1-1
χ1011-1-1-1ii−i−i1111-1-11iiii−i−i−i−i11-1-1-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1-11-11−iii−i-11−ii−ii-11
χ1111-1-1-1ii−i−i1111-1-11iiii−i−i−i−i11-1-1-1-1-11ii−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-111-1i−ii−i1-1i−i−ii-11
χ1211-1-1-1ii−i−i1111-1-11iiii−i−i−i−i11-1-1-1-1-11ii−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-11-11−iii−i-11−iii−i1-1
χ1311-1-1-1−i−iii1111-1-11−i−i−i−iiiii11-1-1-1-1-11−i−iiiii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1-111-1−ii−ii1-1−iii−i-11
χ1411-1-1-1−i−iii1111-1-11−i−i−i−iiiii11-1-1-1-1-11−i−iiiii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1-11-11i−i−ii-11i−i−ii1-1
χ1511-1-1-1−i−iii1111-1-11−i−i−i−iiiii11-1-1-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1-111-1−ii−ii1-1−ii−ii1-1
χ1611-1-1-1−i−iii1111-1-11−i−i−i−iiiii11-1-1-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1-11-11i−i−ii-11i−ii−i-11
χ17222222222222222222222222222222222222000000000000000000000000-2-2-2-20000-2-200000000
χ1822222-2-2-2-22222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-2-2-200002200000000
χ192222-20000-2222-2-2200000000-2-22222-2-2000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i2-22-200000000000000
χ202222-20000-2222-2-2200000000-2-22222-2-200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-22-200000000000000
χ212222-20000-2222-2-2200000000-2-22222-2-200002-22-2000022-2-222-2-200000000-22-2200000000000000
χ222222-20000-2222-2-2200000000-2-22222-2-20000-22-220000-2-222-2-22200000000-22-2200000000000000
χ2322-2-220000-222222200000000-2-2-2-2-2-22-2000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i22-2-200000000000000
χ2422-2-220000-222222200000000-2-2-2-2-2-22-200000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i22-2-200000000000000
χ2522-2-220000-222222200000000-2-2-2-2-2-22-200002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000-2-22200000000000000
χ2622-2-220000-222222200000000-2-2-2-2-2-22-20000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000-2-22200000000000000
χ2722-2-2-22i2i−2i−2i2222-2-222i2i2i2i−2i−2i−2i−2i22-2-2-2-2-222i2i−2i−2i000000000000000000000000-222-20000−2i2i00000000
χ2822-2-2-2−2i−2i2i2i2222-2-22−2i−2i−2i−2i2i2i2i2i22-2-2-2-2-22−2i−2i2i2i000000000000000000000000-222-200002i−2i00000000
χ2944444444441-2111-2111111111111-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-2111-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ314444444444-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2111111110000000000000000000000000000222200-1-1-1-10000
χ324444444444-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2111111110000000000000000000000000000-2-2-2-20011110000
χ3344444-4-4-4-441-2111-2-1-1-1-1-1-1-1-11111-2-2-2-222222222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000
χ3444444-4-4-4-441-2111-2-1-1-1-1-1-1-1-11111-2-2-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000
χ3544444-4-4-4-44-21-2-2-2122222222-2-2-2-21111-1-1-1-1000000000000000000000000000022-2-200-1-1110000
χ3644444-4-4-4-44-21-2-2-2122222222-2-2-2-21111-1-1-1-10000000000000000000000000000-2-2220011-1-10000
χ374444-40000-41-21-1-1-23i3i−3i−3i3i3i−3i−3i-1-111-2-22200002-22-22i−2i2i−2i-1-111-1-111−i−iii−i−iii000000000000000000
χ384444-40000-41-21-1-1-23i3i−3i−3i3i3i−3i−3i-1-111-2-2220000-22-22−2i2i−2i2i11-1-111-1-1ii−i−iii−i−i000000000000000000
χ394444-40000-41-21-1-1-2−3i−3i3i3i−3i−3i3i3i-1-111-2-22200002-22-2−2i2i−2i2i-1-111-1-111ii−i−iii−i−i000000000000000000
χ404444-40000-41-21-1-1-2−3i−3i3i3i−3i−3i3i3i-1-111-2-2220000-22-222i−2i2i−2i11-1-111-1-1−i−iii−i−iii000000000000000000
χ4144-4-440000-41-2111-233-3-3-3-333-1-1-1-122-2200002i−2i−2i2i−2i2i2i−2i−i−iiiii−i−iii−i−i−i−iii000000000000000000
χ4244-4-440000-41-2111-233-3-3-3-333-1-1-1-122-220000−2i2i2i−2i2i−2i−2i2iii−i−i−i−iii−i−iiiii−i−i000000000000000000
χ4344-4-440000-41-2111-2-3-33333-3-3-1-1-1-122-2200002i−2i−2i2i2i−2i−2i2i−i−iiiii−i−i−i−iiiii−i−i000000000000000000
χ4444-4-440000-41-2111-2-3-33333-3-3-1-1-1-122-220000−2i2i2i−2i−2i2i2i−2iii−i−i−i−iiiii−i−i−i−iii000000000000000000
χ4544-4-4-44i4i−4i−4i41-21-1-1-2iiii−i−i−i−i11-1-1222-2−2i−2i2i2i2i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-11111000000000000000000
χ4644-4-4-44i4i−4i−4i41-21-1-1-2iiii−i−i−i−i11-1-1222-2−2i−2i2i2i−2i−2i2i2i-2-222iiii−i−i−i−i1111-1-1-1-1000000000000000000
χ4744-4-4-44i4i−4i−4i4-21-2221−2i−2i−2i−2i2i2i2i2i-2-222-1-1-11ii−i−i00000000000000000000000000002-22i−2i00-11−ii0000
χ4844-4-4-44i4i−4i−4i4-21-2221−2i−2i−2i−2i2i2i2i2i-2-222-1-1-11ii−i−i0000000000000000000000000000-22−2i2i001-1i−i0000
χ4944-4-4-4−4i−4i4i4i41-21-1-1-2−i−i−i−iiiii11-1-1222-22i2i−2i−2i2i2i−2i−2i-2-222−i−i−i−iiiii1111-1-1-1-1000000000000000000
χ5044-4-4-4−4i−4i4i4i41-21-1-1-2−i−i−i−iiiii11-1-1222-22i2i−2i−2i−2i−2i2i2i22-2-2iiii−i−i−i−i-1-1-1-11111000000000000000000
χ5144-4-4-4−4i−4i4i4i4-21-22212i2i2i2i−2i−2i−2i−2i-2-222-1-1-11−i−iii00000000000000000000000000002-2−2i2i00-11i−i0000
χ5244-4-4-4−4i−4i4i4i4-21-22212i2i2i2i−2i−2i−2i−2i-2-222-1-1-11−i−iii0000000000000000000000000000-222i−2i001-1−ii0000
χ534-44i−4i02+2i−2−2i2−2i−2+2i01-2-13-321−2i−1+2i2−i−2+i2+i−2−i1+2i−1−2i3i−3ii−i2i−2i001+i−1−i1−i−1+i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ544-44i−4i02+2i−2−2i2−2i−2+2i01-2-13-321−2i−1+2i2−i−2+i2+i−2−i1+2i−1−2i3i−3ii−i2i−2i001+i−1−i1−i−1+i00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ554-44i−4i02+2i−2−2i2−2i−2+2i01-2-1-332−2+i2−i−1+2i1−2i−1−2i1+2i−2−i2+i−3i3ii−i2i−2i001+i−1−i1−i−1+i00000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ564-44i−4i02+2i−2−2i2−2i−2+2i01-2-1-332−2+i2−i−1+2i1−2i−1−2i1+2i−2−i2+i−3i3ii−i2i−2i001+i−1−i1−i−1+i00000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ574-44i−4i02+2i−2−2i2−2i−2+2i044-400-4−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i004i−4i−4i4i00−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000000000
χ584-44i−4i0−2−2i2+2i−2+2i2−2i01-2-13-32−1+2i1−2i−2+i2−i−2−i2+i−1−2i1+2i3i−3ii−i2i−2i00−1−i1+i−1+i1−i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ594-44i−4i0−2−2i2+2i−2+2i2−2i01-2-13-32−1+2i1−2i−2+i2−i−2−i2+i−1−2i1+2i3i−3ii−i2i−2i00−1−i1+i−1+i1−i00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ604-44i−4i0−2−2i2+2i−2+2i2−2i01-2-1-3322−i−2+i1−2i−1+2i1+2i−1−2i2+i−2−i−3i3ii−i2i−2i00−1−i1+i−1+i1−i00000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ614-44i−4i0−2−2i2+2i−2+2i2−2i01-2-1-3322−i−2+i1−2i−1+2i1+2i−1−2i2+i−2−i−3i3ii−i2i−2i00−1−i1+i−1+i1−i00000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ624-44i−4i0−2−2i2+2i−2+2i2−2i044-400-42+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i004i−4i−4i4i002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000000000
χ634-4−4i4i02−2i−2+2i2+2i−2−2i01-2-13-321+2i−1−2i2+i−2−i2−i−2+i1−2i−1+2i−3i3i−ii−2i2i001−i−1+i1+i−1−i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ644-4−4i4i02−2i−2+2i2+2i−2−2i01-2-13-321+2i−1−2i2+i−2−i2−i−2+i1−2i−1+2i−3i3i−ii−2i2i001−i−1+i1+i−1−i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ654-4−4i4i02−2i−2+2i2+2i−2−2i01-2-1-332−2−i2+i−1−2i1+2i−1+2i1−2i−2+i2−i3i−3i−ii−2i2i001−i−1+i1+i−1−i00000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ664-4−4i4i02−2i−2+2i2+2i−2−2i01-2-1-332−2−i2+i−1−2i1+2i−1+2i1−2i−2+i2−i3i−3i−ii−2i2i001−i−1+i1+i−1−i00000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ674-4−4i4i02−2i−2+2i2+2i−2−2i044-400-4−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00−4i4i4i−4i00−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000000000
χ684-4−4i4i0−2+2i2−2i−2−2i2+2i01-2-13-32−1−2i1+2i−2−i2+i−2+i2−i−1+2i1−2i−3i3i−ii−2i2i00−1+i1−i−1−i1+i00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ694-4−4i4i0−2+2i2−2i−2−2i2+2i01-2-13-32−1−2i1+2i−2−i2+i−2+i2−i−1+2i1−2i−3i3i−ii−2i2i00−1+i1−i−1−i1+i00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ704-4−4i4i0−2+2i2−2i−2−2i2+2i01-2-1-3322+i−2−i1+2i−1−2i1−2i−1+2i2−i−2+i3i−3i−ii−2i2i00−1+i1−i−1−i1+i00000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ714-4−4i4i0−2+2i2−2i−2−2i2+2i01-2-1-3322+i−2−i1+2i−1−2i1−2i−1+2i2−i−2+i3i−3i−ii−2i2i00−1+i1−i−1−i1+i00000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ724-4−4i4i0−2+2i2−2i−2−2i2+2i044-400-42−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00−4i4i4i−4i002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000000000
χ738888-80000-8-42-44420000000044-4-422-2-20000000000000000000000000000000000000000000000
χ7488-8-880000-8-42-4-4-42000000004444-2-22-20000000000000000000000000000000000000000000000
χ758-88i−8i04+4i−4−4i4−4i−4+4i0-42400-22+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00−4i4i−2i2i00−1−i1+i−1+i1−i000000000000000000000000000000000000000000
χ768-88i−8i0−4−4i4+4i−4+4i4−4i0-42400-2−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00−4i4i−2i2i001+i−1−i1−i−1+i000000000000000000000000000000000000000000
χ778-8−8i8i04−4i−4+4i4+4i−4−4i0-42400-22−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i004i−4i2i−2i00−1+i1−i−1−i1+i000000000000000000000000000000000000000000
χ788-8−8i8i0−4+4i4−4i−4−4i4+4i0-42400-2−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i004i−4i2i−2i001−i−1+i1+i−1−i000000000000000000000000000000000000000000

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