Finite Group Databasebeta

← Group #11788320

Character table — Group #11788320

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order122222444433666666666612121212121212126612121212888888882424242424242424242424242424242422442244246612128888
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
χ91111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-1-11-111-1-11i−ii−i
χ101111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-11-111-1−ii−ii
χ111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11-1-11-111-1-11−ii−ii
χ121111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-11-111-1i−ii−i
χ131111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11-1-11
χ141111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-111-1
χ151111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-111-1
χ161111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1111-1-11
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
χ192222-2-222-2-22222-2-2-2-222222222-2-2-2-2-2-222-2-2000000000000000000000000-2-22200002-200000000
χ202222-2-2-2-2222222-2-2-2-22222-2-2-2-22222-2-2-2-222000000000000000000000000-2-2-2-200002200000000
χ212-2-2200002-222-2-20000-222-2000022-2-200002-2002i−2i2i−2i0000002i2i−2i−2i2i2i−2i−2i00002-22-200000000000000
χ222-2-2200002-222-2-20000-222-2000022-2-200002-200−2i2i−2i2i000000−2i−2i2i2i−2i−2i2i2i00002-22-200000000000000
χ232-2-2200002-222-2-20000-222-2000022-2-200002-22i−2i00002i−2i2i2i−2i−2i000000002i2i−2i−2i-22-2200000000000000
χ242-2-2200002-222-2-20000-222-2000022-2-200002-2−2i2i0000−2i2i−2i−2i2i2i00000000−2i−2i2i2i-22-2200000000000000
χ252-2-220000-2222-2-20000-222-20000-2-2220000-22002-2-2200000022-2-2-2-22200002-2-2200000000000000
χ262-2-220000-2222-2-20000-222-20000-2-2220000-2200-222-2000000-2-22222-2-200002-2-2200000000000000
χ272-2-220000-2222-2-20000-222-20000-2-2220000-222-20000-2222-2-200000000-2-222-222-200000000000000
χ282-2-220000-2222-2-20000-222-20000-2-2220000-22-2200002-2-2-2220000000022-2-2-222-200000000000000
χ2944444444441-2111111-21-2-211111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-2111111-21-2-211111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ314444444444-21-2-2-2-2-2-21-211-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ324444444444-21-2-2-2-2-2-21-211-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ33444444-4-4-4-41-2111111-21-2-2-1-1-1-1-1-1-1-1-2-222222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii000000000000000000
χ34444444-4-4-4-41-2111111-21-2-2-1-1-1-1-1-1-1-1-2-22222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i000000000000000000
χ35444444-4-4-4-4-21-2-2-2-2-2-21-2112222222211-1-1-1-100000000000000000000000000002-22-200-11-110000
χ36444444-4-4-4-4-21-2-2-2-2-2-21-2112222222211-1-1-1-10000000000000000000000000000-22-22001-11-10000
χ374444-4-444-4-41-211-1-1-1-1-21-2-21111-1-1-1-122-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ384444-4-444-4-41-211-1-1-1-1-21-2-21111-1-1-1-122-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ394444-4-444-4-4-21-2-222221-211-2-2-2-22222-1-111-1-100000000000000000000000000002-2-2200-111-10000
χ404444-4-444-4-4-21-2-222221-211-2-2-2-22222-1-111-1-10000000000000000000000000000-222-2001-1-110000
χ414444-4-4-4-4441-211-1-1-1-1-21-2-2-1-1-1-111112222-2-222-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000
χ424444-4-4-4-4441-211-1-1-1-1-21-2-2-1-1-1-111112222-2-2-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000
χ434444-4-4-4-444-21-2-222221-2112222-2-2-2-2-1-1-1-111000000000000000000000000000022-2-200-1-1110000
χ444444-4-4-4-444-21-2-222221-2112222-2-2-2-2-1-1-1-1110000000000000000000000000000-2-2220011-1-10000
χ4544-4-4004i−4i001-21-133-3-3-2-122ii−i−i3i−3i3i−3i002i−2i0000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ4644-4-4004i−4i001-21-133-3-3-2-122ii−i−i3i−3i3i−3i002i−2i0000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ4744-4-4004i−4i001-21-1-3-333-2-122ii−i−i−3i3i−3i3i002i−2i0000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ4844-4-4004i−4i001-21-1-3-333-2-122ii−i−i−3i3i−3i3i002i−2i0000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ4944-4-4004i−4i00444-400004-4-4-44i4i−4i−4i000000−4i4i00000000000000000000000000000000000000000000
χ5044-4-400−4i4i001-21-133-3-3-2-122−i−iii−3i3i−3i3i00−2i2i0000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ5144-4-400−4i4i001-21-133-3-3-2-122−i−iii−3i3i−3i3i00−2i2i0000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ5244-4-400−4i4i001-21-1-3-333-2-122−i−iii3i−3i3i−3i00−2i2i0000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ5344-4-400−4i4i001-21-1-3-333-2-122−i−iii3i−3i3i−3i00−2i2i0000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ5444-4-400−4i4i00444-400004-4-4-4−4i−4i4i4i0000004i−4i00000000000000000000000000000000000000000000
χ554-44-44-400001-2-111-11-12-12-23i−3i3i−3i3i−3i−3i3i2-2000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ564-44-44-400001-2-111-11-12-12-23i−3i3i−3i3i−3i−3i3i2-2000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ574-44-44-400001-2-111-11-12-12-2−3i3i−3i3i−3i3i3i−3i2-2000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ584-44-44-400001-2-111-11-12-12-2−3i3i−3i3i−3i3i3i−3i2-2000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ594-44-44-4000044-444-44-4-4-4-4400000000-440000000000000000000000000000000000000000000000
χ604-44-4-4400001-2-11-11-112-12-23i−3i3i−3i−3i3i3i−3i-22000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ614-44-4-4400001-2-11-11-112-12-23i−3i3i−3i−3i3i3i−3i-22000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ624-44-4-4400001-2-11-11-112-12-2−3i3i−3i3i3i−3i−3i3i-22000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ634-44-4-4400001-2-11-11-112-12-2−3i3i−3i3i3i−3i−3i3i-22000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ644-44-4-44000044-44-44-44-4-4-44000000004-40000000000000000000000000000000000000000000000
χ654-4-4400004-41-2-1-13-3-3321-223-3-3311-1-10000-222i−2i2i−2i2i−2i2i−2i−i−iii−i−iii−i−iii−i−iii000000000000000000
χ664-4-4400004-41-2-1-13-3-3321-223-3-3311-1-10000-22−2i2i−2i2i−2i2i−2i2iii−i−iii−i−iii−i−iii−i−i000000000000000000
χ674-4-4400004-41-2-1-1-333-321-22-333-311-1-10000-222i−2i−2i2i−2i2i2i−2i−i−iiiii−i−iii−i−i−i−iii000000000000000000
χ684-4-4400004-41-2-1-1-333-321-22-333-311-1-10000-22−2i2i2i−2i2i−2i−2i2iii−i−i−i−iii−i−iiiii−i−i000000000000000000
χ694-4-440000-441-2-1-13-3-3321-22-333-3-1-11100002-22-22-2-22-22-1-111-1-11111-1-111-1-1000000000000000000
χ704-4-440000-441-2-1-13-3-3321-22-333-3-1-11100002-2-22-222-22-211-1-111-1-1-1-111-1-111000000000000000000
χ714-4-440000-441-2-1-1-333-321-223-3-33-1-11100002-22-2-222-2-22-1-11111-1-1-1-11111-1-1000000000000000000
χ724-4-440000-441-2-1-1-333-321-223-3-33-1-11100002-2-222-2-222-211-1-1-1-11111-1-1-1-111000000000000000000
χ7388-8-8008i−8i00-42-44000024-2-2−4i−4i4i4i000000−2i2i00000000000000000000000000000000000000000000
χ7488-8-800−8i8i00-42-44000024-2-24i4i−4i−4i0000002i−2i00000000000000000000000000000000000000000000
χ758-88-88-80000-424-4-44-44-24-2200000000-220000000000000000000000000000000000000000000000
χ768-88-8-880000-424-44-44-4-24-22000000002-20000000000000000000000000000000000000000000000
χ778-8-8800008-8-42440000-2-42-20000-4-44400002-2000000000000000000000000000000000000000000
χ788-8-880000-88-42440000-2-42-2000044-4-40000-22000000000000000000000000000000000000000000

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