Finite Group Databasebeta

← Group #150239

Character table — Group #150239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order12222244442244444444444422444488888888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111-1-1-11-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111-1-1-11-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-1-1-1-1-1111111-1-1-1-1111-11-11-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-1-1-1111111-1-1-1-1111-11-11-111-1-1-1-111-1-111-1-111-1-111
χ11111111-1-1-1-1-1-1111111-1-1-1-111-111-1-11-1-11111-1-111-1-1-1-111-1-111
χ12111111-1-1-1-1-1-1111111-1-1-1-111-111-1-11-1-111-1-111-1-11111-1-111-1-1
χ13111111-1-1-1-1-1-11-1-1-11-11111-1-11-11-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-1-1-1-11-1-1-11-11111-1-11-11-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-1-1-1-11-1-1-11-11111-1-1-111-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-1-1-11-1-1-11-11111-1-1-111-1-1111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-222-2-200-2-20000000000000000000000
χ182222222222222-2-2-22-222-2-22200-2-20000000000000000000000
χ19222222-2-2-2-2-2-222222222-2-2-2-200-220000000000000000000000
χ20222222-2-2-2-2-2-22-2-2-22-2-2-2222200-220000000000000000000000
χ212-2-22-2222-2-22-22000-202i−2i002i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ222-2-22-2222-2-22-22000-202i−2i002i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ232-2-22-2222-2-22-22000-20−2i2i00−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ242-2-22-2222-2-22-22000-20−2i2i00−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ252-2-22-2222-2-2-22-222-22-2002-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ262-2-22-2222-2-2-22-222-22-2002-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ272-2-22-2222-2-2-22-2-2-222200-22000000000000000000002−22−2−22−22
χ282-2-22-2222-2-2-22-2-2-222200-2200000000000000000000−22−222−22−2
χ292-2-22-22-2-2222-2-222-22-200-2200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ302-2-22-22-2-2222-2-222-22-200-2200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ312-2-22-22-2-2222-2-2-2-2222002-2000000000000000000002−2−22−222−2
χ322-2-22-22-2-2222-2-2-2-2222002-200000000000000000000−222−22−2−22
χ332-2-22-22-2-222-222000-202i−2i00−2i2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ342-2-22-22-2-222-222000-202i−2i00−2i2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ352-2-22-22-2-222-222000-20−2i2i002i−2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ362-2-22-22-2-222-222000-20−2i2i002i−2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ374444444444-4-4-4000-4000000000000000000000000000000000
χ38444444-4-4-4-444-4000-4000000000000000000000000000000000
χ394444-4-44-44-4000000000000002200-2-200000000000000000000
χ404444-4-44-44-400000000000000-2-2002200000000000000000000
χ414444-4-4-44-44000000000000002-200-2200000000000000000000
χ424444-4-4-44-4400000000000000-22002-200000000000000000000
χ434-4-444-44-4-44000000000000000000002i−2i2i−2i0000000000000000
χ444-4-444-44-4-4400000000000000000000−2i2i−2i2i0000000000000000
χ454-4-444-4-444-4000000000000000000002i−2i−2i2i0000000000000000
χ464-4-444-4-444-400000000000000000000−2i2i2i−2i0000000000000000
χ4788-8-80000000004-440-400000000000000000000000000000000
χ4888-8-8000000000-44-40400000000000000000000000000000000
χ498-88-80000000004-4-40400000000000000000000000000000000
χ508-88-8000000000-4440-400000000000000000000000000000000

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