Finite Group Databasebeta

← Group #150778

Character table — Group #150778

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222244444444424444444424444888888888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111-1-1-1-1111-1-1-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111-1-1-1-1111-1-1-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-1-1111111-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-111-1-11-1
χ10111111-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-111-1-111-1-111-1-1111-1
χ11111111-1-1-1111111-1-1-1-1-1-1-111-1-111111-1-111-1-1-1-111-1-111-11
χ12111111-1-1-1111111-1-1-1-1-1-1-111-1-1111-1-111-1-11111-1-111-1-1-11
χ13111111-1-1-111-1-1-1-1-1-1-11111-1-1111-1-1ii−i−i−i−iiiii−i−i−i−iii-11
χ14111111-1-1-111-1-1-1-1-1-1-11111-1-1111-1-1−i−iiiii−i−i−i−iiiii−i−i-11
χ15111111-1-1-111-1-1-1-1-1-1-11111-1-1-1-1111ii−i−i−i−iii−i−iiiii−i−i1-1
χ16111111-1-1-111-1-1-1-1-1-1-11111-1-1-1-1111−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222222222-2-2-2-222-2-200-200000000000000000000
χ1822222222222-2-2-2-22-2-222-2-22200-200000000000000000000
χ19222222-2-2-2222222-22222-2-2-2-200-200000000000000000000
χ20222222-2-2-222-2-2-2-2-222-2-2222200-200000000000000000000
χ2122-2-2-220002-222-2-202i−2i2i−2i000000000000000002−2i2−i22−2i2−i200
χ2222-2-2-220002-222-2-202i−2i2i−2i00000000000000000−22−i2i2−22−i2i200
χ2322-2-2-220002-222-2-20−2i2i−2i2i000000000000000002−2−i2i22−2−i2i200
χ2422-2-2-220002-222-2-20−2i2i−2i2i00000000000000000−22i2−i2−22i2−i200
χ2522-2-2-220002-2-2-22202i−2i−2i2i00000000000000000i2−i2−22−i2i22−200
χ2622-2-2-220002-2-2-22202i−2i−2i2i00000000000000000−i2i22−2i2−i2−2200
χ2722-2-2-220002-2-2-2220−2i2i2i−2i00000000000000000i2−i22−2−i2i2−2200
χ2822-2-2-220002-2-2-2220−2i2i2i−2i00000000000000000−i2i2−22i2−i22−200
χ29444444444-4-40000-40000000000000000000000000000000
χ30444444-4-4-4-4-4000040000000000000000000000000000000
χ314444-4-444-40000000000000002-202-2000000000000000000
χ324444-4-444-4000000000000000-220-22000000000000000000
χ334444-4-4-4-440000000000000002-20-22000000000000000000
χ344444-4-4-4-44000000000000000-2202-2000000000000000000
χ3544-4-4-44000-44000000000004i−4i00000000000000000000000
χ3644-4-4-44000-4400000000000−4i4i00000000000000000000000
χ374-44-4004i−4i0002i−2i2i−2i000002-200000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000
χ384-44-4004i−4i0002i−2i2i−2i000002-20000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000
χ394-44-4004i−4i000−2i2i−2i2i00000-2200000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000
χ404-44-4004i−4i000−2i2i−2i2i00000-220000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000
χ414-44-400−4i4i0002i−2i2i−2i00000-2200000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000
χ424-44-400−4i4i0002i−2i2i−2i00000-220000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000
χ434-44-400−4i4i000−2i2i−2i2i000002-200000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000
χ444-44-400−4i4i000−2i2i−2i2i000002-20000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000
χ4588-8-88-800000000000000000000000000000000000000000
χ468-8-8800000004i−4i−4i4i00000000000000000000000000000000
χ478-8-880000000−4i4i4i−4i00000000000000000000000000000000

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