Finite Group Databasebeta

← Group #11791883

Character table — Group #11791883

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order12224444443366666612121212121212121212121212121212121288888888242424242424242424242424242424242244444444121212128888
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−i11-1-111-1-11-111-1-1ii−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−i11-1-1-1-1111-1-1-111−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−iiiiiiiii11-1-111-1-11-111-1-1−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−iiiiiiiii11-1-1-1-1111-1-1-111ii−i−i
χ91111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1-111-11-1i−ii−i
χ101111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-11-11-11-11-11−ii−ii
χ111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1-111-11-1−ii−ii
χ121111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-11-11-11-11i−ii−i
χ131111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-11-1-11-1-111-1-11
χ141111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-111-1-1-1-111-1-111-1
χ151111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111-1-11-1-11-1-11-111-1
χ161111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-111-1-1-1-111-11-1-11
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
χ192222-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222000000000000000000000000-2-22200002-200000000
χ202222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000-2-2-2-200002200000000
χ2122-2-200002-22222-2-2-2-20000000022-2-2002-200002i−2i2i−2i0000002i2i−2i−2i2i2i−2i−2i00002-2-2200000000000000
χ2222-2-200002-22222-2-2-2-20000000022-2-2002-20000−2i2i−2i2i000000−2i−2i2i2i−2i−2i2i2i00002-2-2200000000000000
χ2322-2-200002-22222-2-2-2-20000000022-2-2002-2002-200002-222-2-20000000022-2-2-222-200000000000000
χ2422-2-200002-22222-2-2-2-20000000022-2-2002-200-220000-22-2-22200000000-2-222-222-200000000000000
χ2522-2-20000-222222-2-2-2-200000000-2-22200-2200002-2-2200000022-2-2-2-22200002-22-200000000000000
χ2622-2-20000-222222-2-2-2-200000000-2-22200-220000-222-2000000-2-22222-2-200002-22-200000000000000
χ2722-2-20000-222222-2-2-2-200000000-2-22200-22002i−2i0000−2i2i2i2i−2i−2i00000000−2i−2i2i2i-22-2200000000000000
χ2822-2-20000-222222-2-2-2-200000000-2-22200-2200−2i2i00002i−2i−2i−2i2i2i000000002i2i−2i−2i-22-2200000000000000
χ2944444444441-21-211-2-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-21-211-2-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ314444444444-21-21-2-211-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ324444444444-21-21-2-211-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ33444444-4-4-4-41-21-211-2-21111-1-1-1-1-1-1-1-1-2-222222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii000000000000000000
χ34444444-4-4-4-41-21-211-2-21111-1-1-1-1-1-1-1-1-2-22222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i000000000000000000
χ35444444-4-4-4-4-21-21-2-211-2-2-2-22222222211-1-1-1-1000000000000000000000000000022-2-200-1-1110000
χ36444444-4-4-4-4-21-21-2-211-2-2-2-22222222211-1-1-1-10000000000000000000000000000-2-2220011-1-10000
χ374444-4-444-4-41-21-211-2-2-1-1-1-11111-1-1-1-12222-2-22i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ384444-4-444-4-41-21-211-2-2-1-1-1-11111-1-1-1-12222-2-2−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ394444-4-444-4-4-21-21-2-2112222-2-2-2-22222-1-1-1-11100000000000000000000000000002-22-200-11-110000
χ404444-4-444-4-4-21-21-2-2112222-2-2-2-22222-1-1-1-1110000000000000000000000000000-22-22001-11-10000
χ414444-4-4-4-4441-21-211-2-2-1-1-1-1-1-1-1-1111122-2-22222-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000
χ424444-4-4-4-4441-21-211-2-2-1-1-1-1-1-1-1-1111122-2-222-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000
χ434444-4-4-4-444-21-21-2-21122222222-2-2-2-2-1-111-1-100000000000000000000000000002-2-2200-111-10000
χ444444-4-4-4-444-21-21-2-21122222222-2-2-2-2-1-111-1-10000000000000000000000000000-222-2001-1-110000
χ4544-4-400004-41-21-2-1-1223i3i−3i−3i3i3i−3i−3i11-1-100-22002-22i−2i2i−2i2-2-1-111−i−iii−i−iii-1-111000000000000000000
χ4644-4-400004-41-21-2-1-1223i3i−3i−3i3i3i−3i−3i11-1-100-2200-22−2i2i−2i2i-2211-1-1ii−i−iii−i−i11-1-1000000000000000000
χ4744-4-400004-41-21-2-1-122−3i−3i3i3i−3i−3i3i3i11-1-100-22002-2−2i2i−2i2i2-2-1-111ii−i−iii−i−i-1-111000000000000000000
χ4844-4-400004-41-21-2-1-122−3i−3i3i3i−3i−3i3i3i11-1-100-2200-222i−2i2i−2i-2211-1-1−i−iii−i−iii11-1-1000000000000000000
χ4944-4-40000-441-21-2-1-1223i3i−3i−3i−3i−3i3i3i-1-111002-2002i−2i-222-2−2i2i−i−iii11-1-1-1-111ii−i−i000000000000000000
χ5044-4-40000-441-21-2-1-1223i3i−3i−3i−3i−3i3i3i-1-111002-200−2i2i2-2-222i−2iii−i−i-1-11111-1-1−i−iii000000000000000000
χ5144-4-40000-441-21-2-1-122−3i−3i3i3i3i3i−3i−3i-1-111002-2002i−2i2-2-22−2i2i−i−iii-1-11111-1-1ii−i−i000000000000000000
χ5244-4-40000-441-21-2-1-122−3i−3i3i3i3i3i−3i−3i-1-111002-200−2i2i-222-22i−2iii−i−i11-1-1-1-111−i−iii000000000000000000
χ534-44-44-400001-2-121-1-221-11-13i−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
χ544-44-44-400001-2-121-1-221-11-13i−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
χ554-44-44-400001-2-121-1-221-11-1−3i3i−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
χ564-44-44-400001-2-121-1-221-11-1−3i3i−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
χ574-44-44-4000044-4-44-44-44-44-400000000-440000000000000000000000000000000000000000000000
χ584-44-4-4400001-2-121-1-22-11-113i−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
χ594-44-4-4400001-2-121-1-22-11-113i−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
χ604-44-4-4400001-2-121-1-22-11-11−3i3i−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
χ614-44-4-4400001-2-121-1-22-11-11−3i3i−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
χ624-44-4-44000044-4-44-44-4-44-44000000004-40000000000000000000000000000000000000000000000
χ634-4-44004-4001-2-12-112-23i−3i−3i3i1-1-11−3i3i3i−3i00002-200000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ644-4-44004-4001-2-12-112-23i−3i−3i3i1-1-11−3i3i3i−3i00002-200000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ654-4-44004-4001-2-12-112-2−3i3i3i−3i1-1-113i−3i−3i3i00002-200000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ664-4-44004-4001-2-12-112-2−3i3i3i−3i1-1-113i−3i−3i3i00002-200000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ674-4-44004-40044-4-4-44-4400004-4-4400000000-44000000000000000000000000000000000000000000
χ684-4-4400-44001-2-12-112-23i−3i−3i3i-111-13i−3i−3i3i0000-2200000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ694-4-4400-44001-2-12-112-23i−3i−3i3i-111-13i−3i−3i3i0000-2200000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ704-4-4400-44001-2-12-112-2−3i3i3i−3i-111-1−3i3i3i−3i0000-2200000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ714-4-4400-44001-2-12-112-2−3i3i3i−3i-111-1−3i3i3i−3i0000-2200000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ724-4-4400-440044-4-4-44-440000-444-4000000004-4000000000000000000000000000000000000000000
χ7388-8-800008-8-42-4244-2-200000000-4-444002-200000000000000000000000000000000000000000000
χ7488-8-80000-88-42-4244-2-20000000044-4-400-2200000000000000000000000000000000000000000000
χ758-88-88-80000-424-2-442-2-44-4400000000-220000000000000000000000000000000000000000000000
χ768-88-8-880000-424-2-442-24-44-4000000002-20000000000000000000000000000000000000000000000
χ778-8-88008-800-424-24-4-220000-444-400000000-22000000000000000000000000000000000000000000
χ788-8-8800-8800-424-24-4-2200004-4-44000000002-2000000000000000000000000000000000000000000

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