Finite Group Databasebeta

← Group #150367

Character table — Group #150367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11112244444488888888161616161616161616161616161616161616161616163232
order12222244444444444444448888888888888888888844
χ111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ6111111111111-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ7111111111111-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ8111111111111-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-1-1-1111111-1-1-1-11-111-1-1ii−i−iii−i−iii−i−iii−i−i1-1
χ10111111-1-1-1-1111111-1-1-1-11-111-1-1−i−iii−i−iii−i−iii−i−iii1-1
χ11111111-1-1-1-1111111-1-1-1-11-1-1-111ii−i−iii−i−i−i−iii−i−iii-11
χ12111111-1-1-1-1111111-1-1-1-11-1-1-111−i−iii−i−iiiii−i−iii−i−i-11
χ13111111-1-1-1-111-1-1-1-111111-111-1-111-1-1-1-11111-1-1-1-111-11
χ14111111-1-1-1-111-1-1-1-111111-111-1-1-1-11111-1-1-1-11111-1-1-11
χ15111111-1-1-1-111-1-1-1-111111-1-1-11111-1-1-1-111-1-11111-1-11-1
χ16111111-1-1-1-111-1-1-1-111111-1-1-111-1-11111-1-111-1-1-1-1111-1
χ1722222222222222-2-222-2-2-2-20000000000000000000000
χ18222222222222-2-222-2-222-2-20000000000000000000000
χ19222222-2-2-2-22222-2-2-2-222-220000000000000000000000
χ20222222-2-2-2-222-2-22222-2-2-220000000000000000000000
χ212-22-2-222i−2i2i−2i2-2002-2002i−2i0000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000
χ222-22-2-222i−2i2i−2i2-2002-2002i−2i000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000
χ232-22-2-222i−2i2i−2i2-200-2200−2i2i0000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000000000
χ242-22-2-222i−2i2i−2i2-200-2200−2i2i000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000000000
χ252-22-2-222i−2i−2i2i-222i−2i002-200000000000000002−2i2−i2i2−i22−200
χ262-22-2-222i−2i−2i2i-222i−2i002-20000000000000000−22−i2i2−i2i2−2200
χ272-22-2-222i−2i−2i2i-22−2i2i00-220000000000000000i2−i2−222−2−i2i200
χ282-22-2-222i−2i−2i2i-22−2i2i00-220000000000000000−i2i22−2−22i2−i200
χ292-22-2-22−2i2i2i−2i-222i−2i00-220000000000000000i2−i22−2−22−i2i200
χ302-22-2-22−2i2i2i−2i-222i−2i00-220000000000000000−i2i2−222−2i2−i200
χ312-22-2-22−2i2i2i−2i-22−2i2i002-200000000000000002−2−i2i2−i2i22−200
χ322-22-2-22−2i2i2i−2i-22−2i2i002-20000000000000000−22i2−i2i2−i2−2200
χ332-22-2-22−2i2i−2i2i2-2002-200−2i2i0000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000
χ342-22-2-22−2i2i−2i2i2-2002-200−2i2i000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000
χ352-22-2-22−2i2i−2i2i2-200-22002i−2i0000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000000000
χ362-22-2-22−2i2i−2i2i2-200-22002i−2i000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000000000
χ3744444444-4-4-4-400000000000000000000000000000000
χ38444444-4-444-4-400000000000000000000000000000000
χ398888-8-800000000000000000000000000000000000000
χ4088-8-80000000000000000000022−22000000000000000000
χ4188-8-800000000000000000000−2222000000000000000000
χ428-88-88-800000000000000000000000000000000000000
χ438-8-880000000000000000002i2−2i200000000000000000000
χ448-8-88000000000000000000−2i22i200000000000000000000

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