Finite Group Databasebeta

← Group #152697

Character table — Group #152697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222244444444422244444422444888888888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111-1-111-1-11-1-111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ6111111111-1-111-1-11-1-111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ7111111111-1-111-1-11-1-111-1-1-1-11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ8111111111-1-111-1-11-1-111-1-1-1-11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-1-1111111-1-1-1111-1-11-11-1-1111-1-111-1-111-1-111-1-11-1
χ10111111-1-1-1111111-1-1-1111-1-11-11-1-11-1-111-1-111-1-111-1-1111-1
χ11111111-1-1-1111111-1-1-1111-1-11-1-111-111-1-111-1-1-1-111-1-111-11
χ12111111-1-1-1111111-1-1-1111-1-11-1-111-1-1-111-1-11111-1-111-1-1-11
χ13111111-1-1-1-1-111-1-1-11111-111-1-11-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ14111111-1-1-1-1-111-1-1-11111-111-1-11-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ15111111-1-1-1-1-111-1-1-11111-111-1-1-111-1ii−i−i−i−iii−i−iiiii−i−i1-1
χ16111111-1-1-1-1-111-1-1-11111-111-1-1-111-1−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222222222-2-2-2-2-222-2-20000000000000000000000
χ18222222222-2-222-2-2222-2-22-2-22-20000000000000000000000
χ19222222-2-2-2222222-222-2-2-2-2-2-220000000000000000000000
χ20222222-2-2-2-2-222-2-2-2-2-2-2-2222220000000000000000000000
χ212-2-22-220002-22-22-20002-2200-20000000000000002i−2i002i−2i00
χ222-2-22-220002-22-22-20002-2200-2000000000000000−2i2i00−2i2i00
χ232-2-22-220002-22-22-2000-22-200200000000000002-2002-20000
χ242-2-22-220002-22-22-2000-22-20020000000000000-2200-220000
χ252-2-22-22000-222-2-220002-2-20020000000000000002-200-2200
χ262-2-22-22000-222-2-220002-2-2002000000000000000-22002-200
χ272-2-22-22000-222-2-22000-22200-200000000000002i−2i00−2i2i0000
χ282-2-22-22000-222-2-22000-22200-20000000000000−2i2i002i−2i0000
χ2944444444400-4-400-40000000000000000000000000000000
χ30444444-4-4-400-4-40040000000000000000000000000000000
χ314444-4-444-4000000000000000022-2-2000000000000000000
χ324444-4-444-40000000000000000-2-222000000000000000000
χ334444-4-4-4-4400000000000000002-22-2000000000000000000
χ344444-4-4-4-440000000000000000-22-22000000000000000000
χ3544-4-4004i−4i02-200-220000002i−2i0000002−2i2−i22−2i2−i20000000000
χ3644-4-4004i−4i02-200-220000002i−2i000000−22−i2i2−22−i2i20000000000
χ3744-4-4004i−4i0-22002-2000000−2i2i000000i2−i2−22−i2i22−20000000000
χ3844-4-4004i−4i0-22002-2000000−2i2i000000−i2i22−2i2−i2−220000000000
χ3944-4-400−4i4i02-200-22000000−2i2i0000002−2−i2i22−2−i2i20000000000
χ4044-4-400−4i4i02-200-22000000−2i2i000000−22i2−i2−22i2−i20000000000
χ4144-4-400−4i4i0-22002-20000002i−2i000000i2−i22−2−i2i2−220000000000
χ4244-4-400−4i4i0-22002-20000002i−2i000000−i2i2−22i2−i22−20000000000
χ434-4-44-4400000-440004-400000000000000000000000000000
χ444-4-44-4400000-44000-4400000000000000000000000000000
χ458-88-8000004400-4-400000000000000000000000000000000
χ468-88-800000-4-4004400000000000000000000000000000000
χ478-8-888-800000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).