Finite Group Databasebeta

← Group #150488

Character table — Group #150488

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222444444488888888888888888161616161616161616323232323232
order12222244444444422444444488888888244444444448888
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11-1-111-1-111111111-1iiii−i−i−i−i-1-1ii−i−i
χ6111111111111111-1-11-1-111-1-111111111-1−i−i−i−iiiii-1-1−i−iii
χ7111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-1-11-1-1-1-1111-1-1-111111111-1-1-1-1-111-1-111-1-11-11-11-1
χ10111111-1-1-11-1-1-1-1111-1-1-111111111-1-1-1-1-1-1-111-1-1111-1-11-11
χ11111111-1-1-11-1-1-1-1111-1-1-11111-1-1-1-11111-111-1-111-1-1-11-11-11
χ12111111-1-1-11-1-1-1-1111-1-1-11111-1-1-1-11111-1-1-111-1-111-111-11-1
χ13111111-1-1-11-1-1-1-11-1-1-11111-1-11111-1-1-1-11ii−i−i−i−iii-11i−i−ii
χ14111111-1-1-11-1-1-1-11-1-1-11111-1-11111-1-1-1-11−i−iiiii−i−i-11−iii−i
χ15111111-1-1-11-1-1-1-11-1-1-11111-1-1-1-1-1-111111ii−i−i−i−iii1-1−iii−i
χ16111111-1-1-11-1-1-1-11-1-1-11111-1-1-1-1-1-111111−i−iiiii−i−i1-1i−i−ii
χ172222222222-2-2-2-2222222-2-2-2-200000000-200000000000000
χ182222222222-2-2-2-22-2-22-2-2-2-22200000000200000000000000
χ19222222-2-2-222222222-2-2-2-2-2-2-200000000200000000000000
χ20222222-2-2-2222222-2-2-222-2-22200000000-200000000000000
χ212-2-222-2000222-2-2-20002i−2i002i−2i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ222-2-222-2000222-2-2-20002i−2i002i−2i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ232-2-222-2000222-2-2-2000−2i2i00−2i2i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ242-2-222-2000222-2-2-2000−2i2i00−2i2i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ252-2-222-20002-2-222-20002i−2i00−2i2i0000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000
χ262-2-222-20002-2-222-20002i−2i00−2i2i000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000
χ272-2-222-20002-2-222-2000−2i2i002i−2i0000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000
χ282-2-222-20002-2-222-2000−2i2i002i−2i000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000
χ29444444444-40000-400-400000000000000000000000000000
χ30444444-4-4-4-40000-400400000000000000000000000000000
χ314444-4-444-400000000000000022-2-222-2-2000000000000000
χ324444-4-444-4000000000000000-2-222-2-222000000000000000
χ334444-4-4-4-4400000000000000022-2-2-2-222000000000000000
χ344444-4-4-4-44000000000000000-2-22222-2-2000000000000000
χ354-44-4004-4002-22-20000002-200002i2−2i2002i2−2i2000000000000000
χ364-44-4004-4002-22-20000002-20000−2i22i200−2i22i2000000000000000
χ374-44-4004-400-22-22000000-22002i2−2i2002i2−2i200000000000000000
χ384-44-4004-400-22-22000000-2200−2i22i200−2i22i200000000000000000
χ394-44-400-44002-22-2000000-22002i2−2i200−2i22i200000000000000000
χ404-44-400-44002-22-2000000-2200−2i22i2002i2−2i200000000000000000
χ414-44-400-4400-22-220000002-200002i2−2i200−2i22i2000000000000000
χ424-44-400-4400-22-220000002-20000−2i22i2002i2−2i2000000000000000
χ434-4-444-4000-4000044-4000000000000000000000000000000
χ444-4-444-4000-400004-44000000000000000000000000000000
χ4588-8-80000004-4-44000000000000000000000000000000000
χ4688-8-8000000-444-4000000000000000000000000000000000
χ478-8-88-8800000000000000000000000000000000000000000

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