Finite Group Databasebeta

← Group #150409

Character table — Group #150409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222244444444422244444424444888888888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-11-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111-1-1-1-11-1-111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111-1-1-1-11-1-111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111-1-1-1-11-1-111-1-1-1-1-11-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111-1-1-1-11-1-111-1-1-1-1-11-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-1-1111111-1-1-1-1-11-1-1111-1-1111-1-111-1-111-1-111-1-11-1
χ10111111-1-1-1111111-1-1-1-1-11-1-1111-1-11-1-111-1-111-1-111-1-1111-1
χ11111111-1-1-1111111-1-1-1-1-11-1-11-1111-111-1-111-1-1-1-111-1-111-11
χ12111111-1-1-1111111-1-1-1-1-11-1-11-1111-1-1-111-1-11111-1-111-1-1-11
χ13111111-1-1-111-1-1-1-1-111-1-1-111-111-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ14111111-1-1-111-1-1-1-1-111-1-1-111-111-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ15111111-1-1-111-1-1-1-1-111-1-1-111-1-1111-1ii−i−i−i−iii−i−iiiii−i−i1-1
χ16111111-1-1-111-1-1-1-1-111-1-1-111-1-1111-1−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222222222-2-2-2-2-222-20-2000000000000000000000
χ1822222222222-2-2-2-2222-2-22-2-220-2000000000000000000000
χ19222222-2-2-2222222-22222-2-2-2-20-2000000000000000000000
χ20222222-2-2-222-2-2-2-2-2-2-22222220-2000000000000000000000
χ212-2-222-20002-22i2i−2i−2i02-22i−2i000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00
χ222-2-222-20002-22i2i−2i−2i02-22i−2i00000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00
χ232-2-222-20002-22i2i−2i−2i0-22−2i2i000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00
χ242-2-222-20002-22i2i−2i−2i0-22−2i2i00000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00
χ252-2-222-20002-2−2i−2i2i2i02-2−2i2i000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00
χ262-2-222-20002-2−2i−2i2i2i02-2−2i2i00000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00
χ272-2-222-20002-2−2i−2i2i2i0-222i−2i000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00
χ282-2-222-20002-2−2i−2i2i2i0-222i−2i00000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00
χ29444444444-4-40000-40000000000000000000000000000000
χ30444444-4-4-4-4-4000040000000000000000000000000000000
χ314444-4-444-4000000000000000202-2-2000000000000000000
χ324444-4-444-4000000000000000-20-222000000000000000000
χ334444-4-4-4-4400000000000000020-22-2000000000000000000
χ344444-4-4-4-44000000000000000-202-22000000000000000000
χ3544-4-4004i−4i0002-22-20000002i−2i000000i2−i22−2i2−i22−20000000000
χ3644-4-4004i−4i0002-22-20000002i−2i000000−i2i2−22−i2i2−220000000000
χ3744-4-4004i−4i000-22-22000000−2i2i0000002−2−i2i2−22i2−i20000000000
χ3844-4-4004i−4i000-22-22000000−2i2i000000−22i2−i22−2−i2i20000000000
χ3944-4-400−4i4i0002-22-2000000−2i2i000000i2−i2−22i2−i2−220000000000
χ4044-4-400−4i4i0002-22-2000000−2i2i000000−i2i22−2−i2i22−20000000000
χ4144-4-400−4i4i000-22-220000002i−2i0000002−2i2−i2−22−i2i20000000000
χ4244-4-400−4i4i000-22-220000002i−2i000000−22−i2i22−2i2−i20000000000
χ434-4-444-4000-44000000000400-400000000000000000000000
χ444-4-444-4000-44000000000-400400000000000000000000000
χ458-88-800000004i−4i−4i4i00000000000000000000000000000000
χ468-88-80000000−4i4i4i−4i00000000000000000000000000000000
χ478-8-88-8800000000000000000000000000000000000000000

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