Finite Group Databasebeta

← Group #11790509

Character table — Group #11790509

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order12224488883366666612121212242424242424242412122424242444448888121212121212121224242424242424242244444488121212128888
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
χ91-11-1-1111-1-111-111-1-1-111-1-11111-1-1-1-1-1111-1-1i−ii−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-11i−ii−i1-1i−ii−i1-11-1
χ101-11-1-1111-1-111-111-1-1-111-1-11111-1-1-1-1-1111-1-1i−ii−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-11−ii−ii1-1−ii−ii-11-11
χ111-11-1-1111-1-111-111-1-1-111-1-11111-1-1-1-1-1111-1-1−ii−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1-11i−ii−i1-1i−ii−i-11-11
χ121-11-1-1111-1-111-111-1-1-111-1-11111-1-1-1-1-1111-1-1−ii−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1-11−ii−ii1-1−ii−ii1-11-1
χ131-11-1-11-1-11111-111-1-1-111-1-1-1-1-1-11111-11-1-111i−ii−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii-11i−i−ii1-1-11
χ141-11-1-11-1-11111-111-1-1-111-1-1-1-1-1-11111-11-1-111i−ii−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i-11−iii−i-111-1
χ151-11-1-11-1-11111-111-1-1-111-1-1-1-1-1-11111-11-1-111−ii−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii-11i−i−ii-111-1
χ161-11-1-11-1-11111-111-1-1-111-1-1-1-1-1-11111-11-1-111−ii−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i-11−iii−i1-1-11
χ17222222222222222222222222222222222222000000000000000000000000-2-2-2-20000-2-200000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2-2-200002200000000
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
χ232-22-22-2000022-222-2-2-2-2-222000000002-2000000002-2-220000000022-2-2-2-2222-22-200000000000000
χ242-22-22-2000022-222-2-2-2-2-222000000002-200000000-222-200000000-2-22222-2-22-22-200000000000000
χ252-22-22-2000022-222-2-2-2-2-222000000002-200002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000-22-2200000000000000
χ262-22-22-2000022-222-2-2-2-2-222000000002-20000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000-22-2200000000000000
χ272-22-2-2222-2-222-222-2-2-222-2-22222-2-2-2-2-2222-2-2000000000000000000000000-222-20000-2200000000
χ282-22-2-22-2-22222-222-2-2-222-2-2-2-2-2-22222-22-2-222000000000000000000000000-222-200002-200000000
χ2944444444441-211-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ3044444444441-211-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ314444444444-21-2-2111-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ324444444444-21-2-2111-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ33444444-4-4-4-41-211-2-2-21-2-2-2-22222222211-1-1-1-1000000000000000000000000000022-2-200-1-1110000
χ34444444-4-4-4-41-211-2-2-21-2-2-2-22222222211-1-1-1-10000000000000000000000000000-2-2220011-1-10000
χ35444444-4-4-4-4-21-2-2111-21111-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000
χ36444444-4-4-4-4-21-2-2111-21111-1-1-1-1-1-1-1-1-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000
χ374444-4-40000-21-2-2111-2-1-1-1-13i3i−3i−3i3i3i−3i−3i22000022-2-22i−2i2i−2i-1-111-1-111−i−iii−i−iii000000000000000000
χ384444-4-40000-21-2-2111-2-1-1-1-13i3i−3i−3i3i3i−3i−3i220000-2-222−2i2i−2i2i11-1-111-1-1ii−i−iii−i−i000000000000000000
χ394444-4-40000-21-2-2111-2-1-1-1-1−3i−3i3i3i−3i−3i3i3i22000022-2-2−2i2i−2i2i-1-111-1-111ii−i−iii−i−i000000000000000000
χ404444-4-40000-21-2-2111-2-1-1-1-1−3i−3i3i3i−3i−3i3i3i220000-2-2222i−2i2i−2i11-1-111-1-1−i−iii−i−iii000000000000000000
χ4144-4-40022−2222−22444-4-44-4-4000022−2222−2222−2222−220022−2222−22000000000000000000000000000000000000000000
χ4244-4-40022−2222−22-21-22-11-123i−3i3i−3i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ2300−22−2200000000−i3i33−3−i3i33−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ4344-4-40022−2222−22-21-22-11-123i−3i3i−3i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ2300−22−2200000000i3−i3−33i3−i3−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ4444-4-40022−2222−22-21-22-11-12−3i3i−3i3iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ2300−22−2200000000−i3i3−33−i3i3−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ4544-4-40022−2222−22-21-22-11-12−3i3i−3i3iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ2300−22−2200000000i3−i33−3i3−i33−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ4644-4-400−2222−2222444-4-44-4-40000−2222−2222−2222−222200−2222−2222000000000000000000000000000000000000000000
χ4744-4-400−2222−2222-21-22-11-123i−3i3i−3i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23002−22−200000000−i3i33−3−i3i33−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ4844-4-400−2222−2222-21-22-11-123i−3i3i−3i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23002−22−200000000i3−i3−33i3−i3−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ4944-4-400−2222−2222-21-22-11-12−3i3i−3i3i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23002−22−200000000−i3i3−33−i3i3−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ5044-4-400−2222−2222-21-22-11-12−3i3i−3i3i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23002−22−200000000i3−i33−3i3−i33−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ514-44-44-40000-212-21-1-12-1-1113i3i−3i−3i−3i−3i3i3i-2200002i−2i−2i2i-222-2−i−iiiii−i−i11-1-1-1-111000000000000000000
χ524-44-44-40000-212-21-1-12-1-1113i3i−3i−3i−3i−3i3i3i-220000−2i2i2i−2i2-2-22ii−i−i−i−iii-1-11111-1-1000000000000000000
χ534-44-44-40000-212-21-1-12-1-111−3i−3i3i3i3i3i−3i−3i-2200002i−2i−2i2i2-2-22−i−iiiii−i−i-1-11111-1-1000000000000000000
χ544-44-44-40000-212-21-1-12-1-111−3i−3i3i3i3i3i−3i−3i-220000−2i2i2i−2i-222-2ii−i−i−i−iii11-1-1-1-111000000000000000000
χ554-44-4-4444-4-41-2-11-222-1-2-222-2-2-2-22222-1111-1-100000000000000000000000000002i−2i2i−2i00−ii−ii0000
χ564-44-4-4444-4-41-2-11-222-1-2-222-2-2-2-22222-1111-1-10000000000000000000000000000−2i2i−2i2i00i−ii−i0000
χ574-44-4-4444-4-4-212-21-1-1211-1-11111-1-1-1-12-2-2-2222i−2i2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ584-44-4-4444-4-4-212-21-1-1211-1-11111-1-1-1-12-2-2-222−2i2i−2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ594-44-4-44-4-4441-2-11-222-1-2-2222222-2-2-2-2-11-1-11100000000000000000000000000002i−2i−2i2i00−iii−i0000
χ604-44-4-44-4-4441-2-11-222-1-2-2222222-2-2-2-2-11-1-1110000000000000000000000000000−2i2i2i−2i00i−i−ii0000
χ614-44-4-44-4-444-212-21-1-1211-1-1-1-1-1-111112-222-2-22i−2i2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000
χ624-44-4-44-4-444-212-21-1-1211-1-1-1-1-1-111112-222-2-2−2i2i−2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000
χ634-4-440022−22−222244-4-4-4-444000022−2222−22−2222−22220022−22−2222000000000000000000000000000000000000000000
χ644-4-440022−22−2222-2122-1-11-23i−3i−3i3i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ2300−222−2000000003−3i3−i3−33−i3i3ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ654-4-440022−22−2222-2122-1-11-23i−3i−3i3i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ2300−222−200000000−33−i3i33−3i3−i3−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ664-4-440022−22−2222-2122-1-11-2−3i3i3i−3iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ2300−222−2000000003−3−i3i3−33i3−i3−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ674-4-440022−22−2222-2122-1-11-2−3i3i3i−3iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ2300−222−200000000−33i3−i33−3−i3i3ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ684-4-4400−222222−2244-4-4-4-4440000−2222−222222−2222−2200−222222−22000000000000000000000000000000000000000000
χ694-4-4400−222222−22-2122-1-11-23i−3i−3i3i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23002−2−22000000003−3i3−i3−33−i3i3−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ704-4-4400−222222−22-2122-1-11-23i−3i−3i3i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23002−2−2200000000−33−i3i33−3i3−i3ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ714-4-4400−222222−22-2122-1-11-2−3i3i3i−3i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23002−2−22000000003−3−i3i3−33i3−i3ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ724-4-4400−222222−22-2122-1-11-2−3i3i3i−3i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23002−2−2200000000−33i3−i33−3−i3i3−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ738888-8-800002-422-4-4-42444400000000-2-20000000000000000000000000000000000000000000000
χ7488-8-80042−4242−422-42-24-44-20000−2222−2222−2222−2222002−22−2000000000000000000000000000000000000000000
χ7588-8-800−4242−42422-42-24-44-2000022−2222−2222−2222−2200−22−22000000000000000000000000000000000000000000
χ768-88-88-800002-4-22-444-244-4-4000000002-20000000000000000000000000000000000000000000000
χ778-8-880042−42−42422-4-2-244-420000−2222−222222−2222−22002−2−22000000000000000000000000000000000000000000
χ788-8-8800−424242−422-4-2-244-42000022−2222−22−2222−222200−222−2000000000000000000000000000000000000000000

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