Finite Group Databasebeta

← Group #152918

Character table — Group #152918

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
χ9111111-1-1-1111111-1-1-111-1-1111-1-11-111-1-111-1-111-1-111-1-11-1
χ10111111-1-1-1111111-1-1-111-1-1111-1-11-1-1-111-1-111-1-111-1-1111-1
χ11111111-1-1-1111111-1-1-111-1-111-11-1-1111-1-111-1-1-1-111-1-111-11
χ12111111-1-1-1111111-1-1-111-1-111-11-1-11-1-111-1-11111-1-111-1-1-11
χ13111111-1-1-11-1-11-1-1-1111111-1-11-1-11-1ii−i−i−i−iiiii−i−i−i−iii-11
χ14111111-1-1-11-1-11-1-1-1111111-1-11-1-11-1−i−iiiii−i−i−i−iiiii−i−i-11
χ15111111-1-1-11-1-11-1-1-1111111-1-1-11-1-11ii−i−i−i−iii−i−iiiii−i−i1-1
χ16111111-1-1-11-1-11-1-1-1111111-1-1-11-1-11−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
χ19222222-2-2-2222222-222-2-2-2-2-2-200200000000000000000000
χ20222222-2-2-22-2-22-2-2-2-2-2-2-2222200200000000000000000000
χ212-2-222-2000-2222-2-20002-2002-20000000000000002i−2i002i−2i00
χ222-2-222-2000-2222-2-20002-2002-2000000000000000−2i2i00−2i2i00
χ232-2-222-2000-2222-2-2000-2200-2200000000000002i−2i002i−2i0000
χ242-2-222-2000-2222-2-2000-2200-220000000000000−2i2i00−2i2i0000
χ252-2-222-2000-2-2-22220002-200-220000000000000002-200-2200
χ262-2-222-2000-2-2-22220002-200-22000000000000000-22002-200
χ272-2-222-2000-2-2-2222000-22002-200000000000002-200-220000
χ282-2-222-2000-2-2-2222000-22002-20000000000000-22002-20000
χ29444444444-400-400-40000000000000000000000000000000
χ30444444-4-4-4-400-40040000000000000000000000000000000
χ314444-4-444-40000000000000002-20-22000000000000000000
χ324444-4-444-4000000000000000-2202-2000000000000000000
χ334444-4-4-4-44000000000000000220-2-2000000000000000000
χ344444-4-4-4-44000000000000000-2-2022000000000000000000
χ354-44-4004i−4i002-202-2000002i−2i0000000i2−i22−2i2−i22−20000000000
χ364-44-4004i−4i002-202-2000002i−2i0000000−i2i2−22−i2i2−220000000000
χ374-44-4004i−4i00-220-2200000−2i2i00000002−2−i2i2−22i2−i20000000000
χ384-44-4004i−4i00-220-2200000−2i2i0000000−22i2−i22−2−i2i20000000000
χ394-44-400−4i4i002-202-200000−2i2i0000000i2−i2−22i2−i2−220000000000
χ404-44-400−4i4i002-202-200000−2i2i0000000−i2i22−2−i2i22−20000000000
χ414-44-400−4i4i00-220-22000002i−2i00000002−2i2−i2−22−i2i20000000000
χ424-44-400−4i4i00-220-22000002i−2i0000000−22−i2i22−2i2−i20000000000
χ434-4-444-4000400-40004i−4i00000000000000000000000000000
χ444-4-444-4000400-4000−4i4i00000000000000000000000000000
χ4588-8-80000004-40-4400000000000000000000000000000000
χ4688-8-8000000-4404-400000000000000000000000000000000
χ478-8-88-8800000000000000000000000000000000000000000

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