Finite Group Databasebeta

← Group #11789686

Character table — Group #11789686

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order122244888833666666121212122424242424242424121224242424444488881212121212121212242424242424242422442244886612128888
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
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1
χ91-11-11-1ii−i−i11-111-1-1-1-1-111iiii−i−i−i−i1-1ii−i−ii−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-11-11-11-1i−ii−i1-1i−ii−i1-1
χ101-11-11-1ii−i−i11-111-1-1-1-1-111iiii−i−i−i−i1-1ii−i−ii−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-11-11-1-11−iii−i-11−ii−ii-11
χ111-11-11-1ii−i−i11-111-1-1-1-1-111iiii−i−i−i−i1-1ii−i−i−ii−ii-1-111−i−i−i−iiiii-1-1-1-111111-11-11-1i−ii−i1-1i−i−ii-11
χ121-11-11-1ii−i−i11-111-1-1-1-1-111iiii−i−i−i−i1-1ii−i−i−ii−ii-1-111−i−i−i−iiiii-1-1-1-111111-11-1-11−iii−i-11−iii−i1-1
χ131-11-11-1−i−iii11-111-1-1-1-1-111−i−i−i−iiiii1-1−i−iiii−ii−i-1-111iiii−i−i−i−i-1-1-1-111111-11-11-1−ii−ii1-1−iii−i-11
χ141-11-11-1−i−iii11-111-1-1-1-1-111−i−i−i−iiiii1-1−i−iiii−ii−i-1-111iiii−i−i−i−i-1-1-1-111111-11-1-11i−i−ii-11i−i−ii1-1
χ151-11-11-1−i−iii11-111-1-1-1-1-111−i−i−i−iiiii1-1−i−iii−ii−ii11-1-1−i−i−i−iiiii1111-1-1-1-11-11-11-1−ii−ii1-1−ii−ii1-1
χ161-11-11-1−i−iii11-111-1-1-1-1-111−i−i−i−iiiii1-1−i−iii−ii−ii11-1-1−i−i−i−iiiii1111-1-1-1-11-11-1-11i−i−ii-11i−ii−i-11
χ17222222222222222222222222222222222222000000000000000000000000-2-2-2-20000-2-200000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2-2-200002200000000
χ192222-2-2000022222222-2-2-2-200000000-2-2000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i22-2-200000000000000
χ202222-2-2000022222222-2-2-2-200000000-2-200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i22-2-200000000000000
χ212222-2-2000022222222-2-2-2-200000000-2-2000022-2-2000022-2-222-2-200000000-2-22200000000000000
χ222222-2-2000022222222-2-2-2-200000000-2-20000-2-2220000-2-222-2-22200000000-2-22200000000000000
χ232-22-22-22i2i−2i−2i22-222-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i2-22i2i−2i−2i000000000000000000000000-22-220000−2i2i00000000
χ242-22-22-2−2i−2i2i2i22-222-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2-2−2i−2i2i2i000000000000000000000000-22-2200002i−2i00000000
χ252-22-2-22000022-222-2-2-222-2-200000000-22000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i2-2-2200000000000000
χ262-22-2-22000022-222-2-2-222-2-200000000-2200000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i2-2-2200000000000000
χ272-22-2-22000022-222-2-2-222-2-200000000-2200002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000-222-200000000000000
χ282-22-2-22000022-222-2-2-222-2-200000000-220000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000-222-200000000000000
χ2944444444441-2-21-211-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-2-21-211-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ314444444444-211-21-2-21-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ324444444444-211-21-2-21-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ33444444-4-4-4-41-2-21-211-21111-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000
χ34444444-4-4-4-41-2-21-211-21111-1-1-1-1-1-1-1-1-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000
χ35444444-4-4-4-4-211-21-2-21-2-2-2-22222222211-1-1-1-1000000000000000000000000000022-2-200-1-1110000
χ36444444-4-4-4-4-211-21-2-21-2-2-2-22222222211-1-1-1-10000000000000000000000000000-2-2220011-1-10000
χ374444-4-400001-2-21-211-2-1-1-1-13i3i−3i−3i3i3i−3i−3i22000022-2-22i−2i2i−2i-1-111-1-111−i−iii−i−iii000000000000000000
χ384444-4-400001-2-21-211-2-1-1-1-13i3i−3i−3i3i3i−3i−3i220000-2-222−2i2i−2i2i11-1-111-1-1ii−i−iii−i−i000000000000000000
χ394444-4-400001-2-21-211-2-1-1-1-1−3i−3i3i3i−3i−3i3i3i22000022-2-2−2i2i−2i2i-1-111-1-111ii−i−iii−i−i000000000000000000
χ404444-4-400001-2-21-211-2-1-1-1-1−3i−3i3i3i−3i−3i3i3i220000-2-2222i−2i2i−2i11-1-111-1-1−i−iii−i−iii000000000000000000
χ4144-4-400−2i22i2−2i22i21-2-2-121-123i−3i3i−3i−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ2300−i2i2−i2i200000000−i3i33−3−i3i33−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ4244-4-400−2i22i2−2i22i21-2-2-121-123i−3i3i−3i−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ2300−i2i2−i2i200000000i3−i3−33i3−i3−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ4344-4-400−2i22i2−2i22i21-2-2-121-12−3i3i−3i3i2ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ2300−i2i2−i2i200000000−i3i3−33−i3i3−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ4444-4-400−2i22i2−2i22i21-2-2-121-12−3i3i−3i3i2ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ2300−i2i2−i2i200000000i3−i33−3i3−i33−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ4544-4-400−2i22i2−2i22i2444-4-44-4-400002i2−2i2−2i22i22i2−2i2−2i22i2002i2−2i22i2−2i2000000000000000000000000000000000000000000
χ4644-4-4002i2−2i22i2−2i21-2-2-121-123i−3i3i−3iζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ2300i2−i2i2−i200000000−i3i33−3−i3i33−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ4744-4-4002i2−2i22i2−2i21-2-2-121-123i−3i3i−3iζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ2300i2−i2i2−i200000000i3−i3−33i3−i3−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ4844-4-4002i2−2i22i2−2i21-2-2-121-12−3i3i−3i3i−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ2300i2−i2i2−i200000000−i3i3−33−i3i3−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ4944-4-4002i2−2i22i2−2i21-2-2-121-12−3i3i−3i3i−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ2300i2−i2i2−i200000000i3−i33−3i3−i33−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ5044-4-4002i2−2i22i2−2i2444-4-44-4-40000−2i22i22i2−2i2−2i22i22i2−2i200−2i22i2−2i22i2000000000000000000000000000000000000000000
χ514-44-44-44i4i−4i−4i1-221-2-1-12-1-111iiii−i−i−i−i-22−2i−2i2i2i2i−2i2i−2i22-2-2−i−i−i−iiiii-1-1-1-11111000000000000000000
χ524-44-44-44i4i−4i−4i1-221-2-1-12-1-111iiii−i−i−i−i-22−2i−2i2i2i−2i2i−2i2i-2-222iiii−i−i−i−i1111-1-1-1-1000000000000000000
χ534-44-44-44i4i−4i−4i-21-1-2122-122-2-2−2i−2i−2i−2i2i2i2i2i1-1ii−i−i00000000000000000000000000002-22i−2i00-11−ii0000
χ544-44-44-44i4i−4i−4i-21-1-2122-122-2-2−2i−2i−2i−2i2i2i2i2i1-1ii−i−i0000000000000000000000000000-22−2i2i001-1i−i0000
χ554-44-44-4−4i−4i4i4i1-221-2-1-12-1-111−i−i−i−iiiii-222i2i−2i−2i2i−2i2i−2i-2-222−i−i−i−iiiii1111-1-1-1-1000000000000000000
χ564-44-44-4−4i−4i4i4i1-221-2-1-12-1-111−i−i−i−iiiii-222i2i−2i−2i−2i2i−2i2i22-2-2iiii−i−i−i−i-1-1-1-11111000000000000000000
χ574-44-44-4−4i−4i4i4i-21-1-2122-122-2-22i2i2i2i−2i−2i−2i−2i1-1−i−iii00000000000000000000000000002-2−2i2i00-11i−i0000
χ584-44-44-4−4i−4i4i4i-21-1-2122-122-2-22i2i2i2i−2i−2i−2i−2i1-1−i−iii0000000000000000000000000000-222i−2i001-1−ii0000
χ594-44-4-4400001-221-2-1-1211-1-133-3-3-3-3332-200002i−2i−2i2i−2i2i2i−2i−i−iiiii−i−iii−i−i−i−iii000000000000000000
χ604-44-4-4400001-221-2-1-1211-1-133-3-3-3-3332-20000−2i2i2i−2i2i−2i−2i2iii−i−i−i−iii−i−iiiii−i−i000000000000000000
χ614-44-4-4400001-221-2-1-1211-1-1-3-33333-3-32-200002i−2i−2i2i2i−2i−2i2i−i−iiiii−i−i−i−iiiii−i−i000000000000000000
χ624-44-4-4400001-221-2-1-1211-1-1-3-33333-3-32-20000−2i2i2i−2i−2i2i2i−2iii−i−i−i−iiiii−i−i−i−iii000000000000000000
χ634-4-440022−22−22221-22-12-11-23i−3i−3i3i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23002−2−22000000003−3−i3i3−33i3−i3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ644-4-440022−22−22221-22-12-11-23i−3i−3i3i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23002−2−2200000000−33i3−i33−3−i3i3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ654-4-440022−22−22221-22-12-11-2−3i3i3i−3i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23002−2−22000000003−3i3−i3−33−i3i3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ664-4-440022−22−22221-22-12-11-2−3i3i3i−3i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23002−2−2200000000−33−i3i33−3i3−i3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ674-4-440022−22−222244-4-4-4-4440000−222222−2222−22−222200−222222−22000000000000000000000000000000000000000000
χ684-4-4400−222222−221-22-12-11-23i−3i−3i3iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ2300−222−2000000003−3−i3i3−33i3−i3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ694-4-4400−222222−221-22-12-11-23i−3i−3i3iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ2300−222−200000000−33i3−i33−3−i3i3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ704-4-4400−222222−221-22-12-11-2−3i3i3i−3i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ2300−222−2000000003−3i3−i3−33−i3i3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ714-4-4400−222222−221-22-12-11-2−3i3i3i−3i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ2300−222−200000000−33−i3i33−3i3−i3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ724-4-4400−222222−2244-4-4-4-444000022−22−2222−222222−220022−22−2222000000000000000000000000000000000000000000
χ738888-8-80000-422-42-4-42444400000000-2-20000000000000000000000000000000000000000000000
χ7488-8-800−4i24i2−4i24i2-4224-2-44-20000−2i22i22i2−2i2−2i22i22i2−2i200i2−i2i2−i2000000000000000000000000000000000000000000
χ7588-8-8004i2−4i24i2−4i2-4224-2-44-200002i2−2i2−2i22i22i2−2i2−2i22i200−i2i2−i2i2000000000000000000000000000000000000000000
χ768-88-8-880000-42-2-4244-2-4-44400000000-220000000000000000000000000000000000000000000000
χ778-8-880042−42−4242-42-24-24-42000022−22−2222−222222−2200−222−2000000000000000000000000000000000000000000
χ788-8-8800−424242−42-42-24-24-420000−222222−2222−22−2222002−2−22000000000000000000000000000000000000000000

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