Finite Group Databasebeta

← Group #150470

Character table — Group #150470

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222244444444444444444422444888888888888888888
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
χ51111111111-1-11-1-11-1-111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111-1-11-1-11-1-111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111-1-11-1-11-1-111-1-1-1-1-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111-1-11-1-11-1-111-1-1-1-1-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-1-1111111-1-1-1-1-1-1-1111-111-111-1-111-1-111-1-111-1-11-1
χ10111111-1-1-1111111-1-1-1-1-1-1-1111-111-1-1-111-1-111-1-111-1-1111-1
χ11111111-1-1-1111111-1-1-1-1-1-1-111-111-1111-1-111-1-1-1-111-1-111-11
χ12111111-1-1-1111111-1-1-1-1-1-1-111-111-11-1-111-1-11111-1-111-1-1-11
χ13111111-1-1-11-1-11-1-1-111-1-111-1-11-111-1ii−i−i−i−iiiii−i−i−i−iii-11
χ14111111-1-1-11-1-11-1-1-111-1-111-1-11-111-1−i−iiiii−i−i−i−iiiii−i−i-11
χ15111111-1-1-11-1-11-1-1-111-1-111-1-1-111-11ii−i−i−i−iii−i−iiiii−i−i1-1
χ16111111-1-1-11-1-11-1-1-111-1-111-1-1-111-11−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222222222-2-2-2-222-2-200-200000000000000000000
χ182222222222-2-22-2-2222-2-2-2-22200-200000000000000000000
χ19222222-2-2-2222222-22222-2-2-2-200-200000000000000000000
χ20222222-2-2-22-2-22-2-2-2-2-222222200-200000000000000000000
χ212-2-222-200022i−2i-22i−2i02i−2i2-2000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00
χ222-2-222-200022i−2i-22i−2i02i−2i2-200000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00
χ232-2-222-200022i−2i-22i−2i0−2i2i-22000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00
χ242-2-222-200022i−2i-22i−2i0−2i2i-2200000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00
χ252-2-222-20002−2i2i-2−2i2i02i−2i-22000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00
χ262-2-222-20002−2i2i-2−2i2i02i−2i-2200000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00
χ272-2-222-20002−2i2i-2−2i2i0−2i2i2-2000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00
χ282-2-222-20002−2i2i-2−2i2i0−2i2i2-200000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00
χ29444444444-400-400-40000000000000000000000000000000
χ30444444-4-4-4-400-40040000000000000000000000000000000
χ314444-4-444-4000000000000000220-2-2000000000000000000
χ324444-4-444-4000000000000000-2-2022000000000000000000
χ334444-4-4-4-440000000000000002-20-22000000000000000000
χ344444-4-4-4-44000000000000000-2202-2000000000000000000
χ3544-4-4004-400220-2-2000002-200000002−22−22−22−20000000000
χ3644-4-4004-400220-2-2000002-20000000−22−22−22−220000000000
χ3744-4-4004-400-2-202200000-220000000i2−i2i2−i2−i2i2−i2i20000000000
χ3844-4-4004-400-2-202200000-220000000−i2i2−i2i2i2−i2i2−i20000000000
χ3944-4-400-4400220-2-200000-2200000002−2−222−2−220000000000
χ4044-4-400-4400220-2-200000-220000000−222−2−222−20000000000
χ4144-4-400-4400-2-2022000002-20000000i2−i2−i2i2−i2i2i2−i20000000000
χ4244-4-400-4400-2-2022000002-20000000−i2i2i2−i2i2−i2−i2i20000000000
χ434-4-444-4000-40040000000004-400000000000000000000000
χ444-4-444-4000-4004000000000-4400000000000000000000000
χ458-88-80000004i−4i0−4i4i00000000000000000000000000000000
χ468-88-8000000−4i4i04i−4i00000000000000000000000000000000
χ478-8-88-8800000000000000000000000000000000000000000

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