Finite Group Databasebeta

← Group #11775915

Character table — Group #11775915

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order12222244443366666666661212121212121212661212121288888888242424242424242424242424242424244444444444121212128888
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
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-11-11-11-11-11-1ii−i−i
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1-11-111-1-11-11−i−iii
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-11-11-11-11-11-1−i−iii
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11-111-1-11-11ii−i−i
χ91111-1-111-1-111111-1-1-1-11111111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-111-1-111-1-111i−ii−i
χ101111-1-111-1-111111-1-1-1-11111111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1111111-1-1−ii−ii
χ111111-1-111-1-111111-1-1-1-11111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111-1-111-1-111−ii−ii
χ121111-1-111-1-111111-1-1-1-11111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1111111-1-1i−ii−i
χ131111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-111-1-111-11-1-11
χ141111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-11-11-1-11-111-1
χ151111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-111-1-111-1
χ161111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-11-11-1-111-1-11
χ17222222222222222222222222222222222222000000000000000000000000-2-2-2-20000-2-200000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2220000-2200000000
χ192222-2-222-2-222222-2-2-2-22222222-2-2-2-2-2-222-2-200000000000000000000000022220000-2-200000000
χ202222-2-2-2-22222222-2-2-2-2222-2-2-2-22222-2-2-2-22200000000000000000000000022-2-20000-2200000000
χ2122-2-2002-20022-2-2-200002-2222-2-20000002-2001+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i00000000000000
χ2222-2-2002-20022-2-2-200002-2222-2-20000002-2001−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i00000000000000
χ2322-2-2002-20022-2-2-200002-2222-2-20000002-200−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i00000000000000
χ2422-2-2002-20022-2-2-200002-2222-2-20000002-200−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i00000000000000
χ2522-2-200-220022-2-2-200002-22-2-222000000-22001+i−1−i−1+i1−i−1−i1+i1−i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−2i2i2i−2i00000000000000
χ2622-2-200-220022-2-2-200002-22-2-222000000-22001−i−1+i−1−i1+i−1+i1−i1+i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i2i−2i−2i2i00000000000000
χ2722-2-200-220022-2-2-200002-22-2-222000000-2200−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i2i−2i−2i2i00000000000000
χ2822-2-200-220022-2-2-200002-22-2-222000000-2200−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−2i2i2i−2i00000000000000
χ2944444444441-211-211111-2-211111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-211-211111-2-211111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ314444444444-21-2-21-2-2-2-2-211-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ324444444444-21-2-21-2-2-2-2-211-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ33444444-4-4-4-41-211-211111-2-2-1-1-1-1-1-1-1-1-2-222222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii000000000000000000
χ34444444-4-4-4-41-211-211111-2-2-1-1-1-1-1-1-1-1-2-22222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i000000000000000000
χ35444444-4-4-4-4-21-2-21-2-2-2-2-2112222222211-1-1-1-100000000000000000000000000002-22-200-11-110000
χ36444444-4-4-4-4-21-2-21-2-2-2-2-2112222222211-1-1-1-10000000000000000000000000000-22-22001-11-10000
χ374444-4-444-4-41-211-2-1-1-1-11-2-21111-1-1-1-122-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ384444-4-444-4-41-211-2-1-1-1-11-2-21111-1-1-1-122-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ394444-4-444-4-4-21-2-212222-211-2-2-2-22222-1-111-1-1000000000000000000000000000022-2-20011-1-10000
χ404444-4-444-4-4-21-2-212222-211-2-2-2-22222-1-111-1-10000000000000000000000000000-2-22200-1-1110000
χ414444-4-4-4-4441-211-2-1-1-1-11-2-2-1-1-1-111112222-2-222-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000
χ424444-4-4-4-4441-211-2-1-1-1-11-2-2-1-1-1-111112222-2-2-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000
χ434444-4-4-4-444-21-2-212222-2112222-2-2-2-2-1-1-1-11100000000000000000000000000002-2-22001-1-110000
χ444444-4-4-4-444-21-2-212222-2112222-2-2-2-2-1-1-1-1110000000000000000000000000000-222-200-111-10000
χ4544-4-4004-4001-2-1-1233-3-312-211-1-133-3-300-22002-22-22-22-2-1-111-1-111-1-111-1-111000000000000000000
χ4644-4-4004-4001-2-1-1233-3-312-211-1-133-3-300-2200-22-22-22-2211-1-111-1-111-1-111-1-1000000000000000000
χ4744-4-4004-4001-2-1-12-3-33312-211-1-1-3-33300-22002i−2i−2i2i2i−2i−2i2i−i−iiiii−i−i−i−iiiii−i−i000000000000000000
χ4844-4-4004-4001-2-1-12-3-33312-211-1-1-3-33300-2200−2i2i2i−2i−2i2i2i−2iii−i−i−i−iiiii−i−i−i−iii000000000000000000
χ4944-4-400-44001-2-1-1233-3-312-2-1-111-3-333002-2002i−2i2i−2i−2i2i−2i2i−i−iii−i−iiiii−i−iii−i−i000000000000000000
χ5044-4-400-44001-2-1-1233-3-312-2-1-111-3-333002-200−2i2i−2i2i2i−2i2i−2iii−i−iii−i−i−i−iii−i−iii000000000000000000
χ5144-4-400-44001-2-1-12-3-33312-2-1-11133-3-3002-2002-2-22-222-2-1-11111-1-111-1-1-1-111000000000000000000
χ5244-4-400-44001-2-1-12-3-33312-2-1-11133-3-3002-200-222-22-2-2211-1-1-1-111-1-11111-1-1000000000000000000
χ534-44-44-400001-21-1-21-11-1-1223i−3i3i−3i3i−3i3i−3i2-2000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ544-44-44-400001-21-1-21-11-1-1223i−3i3i−3i3i−3i3i−3i2-2000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ554-44-44-400001-21-1-21-11-1-122−3i3i−3i3i−3i3i−3i3i2-2000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ564-44-44-400001-21-1-21-11-1-122−3i3i−3i3i−3i3i−3i3i2-2000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ574-44-44-40000444-444-44-4-4-4-400000000-440000000000000000000000000000000000000000000000
χ584-44-4-4400001-21-1-2-11-11-1223i−3i3i−3i−3i3i−3i3i-22000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ594-44-4-4400001-21-1-2-11-11-1223i−3i3i−3i−3i3i−3i3i-22000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ604-44-4-4400001-21-1-2-11-11-122−3i3i−3i3i3i−3i3i−3i-22000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ614-44-4-4400001-21-1-2-11-11-122−3i3i−3i3i3i−3i3i−3i-22000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ624-44-4-440000444-44-44-44-4-4-4000000004-40000000000000000000000000000000000000000000000
χ634-4-4400004i−4i1-2-1123-3-33-1-223i−3i−3i3ii−i−ii00002i−2i00000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ644-4-4400004i−4i1-2-1123-3-33-1-223i−3i−3i3ii−i−ii00002i−2i00000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ654-4-4400004i−4i1-2-112-333-3-1-22−3i3i3i−3ii−i−ii00002i−2i00000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ664-4-4400004i−4i1-2-112-333-3-1-22−3i3i3i−3ii−i−ii00002i−2i00000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ674-4-4400004i−4i44-44-40000-44-400004i−4i−4i4i0000−4i4i000000000000000000000000000000000000000000
χ684-4-440000−4i4i1-2-1123-3-33-1-22−3i3i3i−3i−iii−i0000−2i2i00000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ694-4-440000−4i4i1-2-1123-3-33-1-22−3i3i3i−3i−iii−i0000−2i2i00000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ704-4-440000−4i4i1-2-112-333-3-1-223i−3i−3i3i−iii−i0000−2i2i00000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ714-4-440000−4i4i1-2-112-333-3-1-223i−3i−3i3i−iii−i0000−2i2i00000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ724-4-440000−4i4i44-44-40000-44-40000−4i4i4i−4i00004i−4i000000000000000000000000000000000000000000
χ7388-8-8008-800-4244-20000-4-22-4-4440000002-200000000000000000000000000000000000000000000
χ7488-8-800-8800-4244-20000-4-2244-4-4000000-2200000000000000000000000000000000000000000000
χ758-88-88-80000-42-442-44-444-2-200000000-220000000000000000000000000000000000000000000000
χ768-88-8-880000-42-4424-44-44-2-2000000002-20000000000000000000000000000000000000000000000
χ778-8-8800008i−8i-424-4-2000042-20000−4i4i4i−4i0000−2i2i000000000000000000000000000000000000000000
χ788-8-880000−8i8i-424-4-2000042-200004i−4i−4i4i00002i−2i000000000000000000000000000000000000000000

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