Finite Group Databasebeta

← Group #150189

Character table — Group #150189

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444224488888888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-11111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111-1-1-1-1-11111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111-1-1-1-1-11111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-1-11111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111-1-1-1-111-1-111111-111-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111-1-1-1-111-1-111111-111-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111-1-1-1-111-1-111111-111-1-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111-1-1-1-111-1-111111-111-1-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111-1-1-1-111-1-11-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1411111-1-1-1-111-1-11-1-1-1-1111-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111-1-1-1-111-1-11-1-1-1-1111-1-1111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ1611111-1-1-1-111-1-11-1-1-1-1111-1-1111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-222-2000000000000000000000000
χ1822222222222222-2-2222-2-2-2-2-2-22000000000000000000000000
χ1922222-2-2-2-222-2-2222-2-22-2-222-2-22000000000000000000000000
χ2022222-2-2-2-222-2-22-2-222-2-2-22222-2000000000000000000000000
χ212-2-22222-2-2-222-2-22i−2i00000002i−2i000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ222-2-22222-2-2-222-2-22i−2i00000002i−2i00000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ232-2-22222-2-2-222-2-2−2i2i0000000−2i2i000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ242-2-22222-2-2-222-2-2−2i2i0000000−2i2i00000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ252-2-22222-2-2-2-2-222002-22000000-200000000i2−i2i2−i2i2−i2i2−i200000000
χ262-2-22222-2-2-2-2-222002-22000000-200000000−i2i2−i2i2−i2i2−i2i200000000
χ272-2-22222-2-2-2-2-22200-22-20000002000000002−22−2−22−2200000000
χ282-2-22222-2-2-2-2-22200-22-2000000200000000−22−222−22−200000000
χ292-2-222-2-222-22-22-22i−2i0000000−2i2i000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ302-2-222-2-222-22-22-22i−2i0000000−2i2i00000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ312-2-222-2-222-22-22-2−2i2i00000002i−2i000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ322-2-222-2-222-22-22-2−2i2i00000002i−2i00000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ332-2-222-2-222-2-22-22002-2-20000002000000002−2−222−2−2200000000
χ342-2-222-2-222-2-22-22002-2-2000000200000000−222−2−222−200000000
χ352-2-222-2-222-2-22-2200-222000000-200000000i2−i2−i2i2−i2i2i2−i200000000
χ362-2-222-2-222-2-22-2200-222000000-200000000−i2i2i2−i2i2−i2−i2i200000000
χ374444444444-4-4-4-4000000000000000000000000000000000000
χ3844444-4-4-4-44-444-4000000000000000000000000000000000000
χ394444-44-44-4-4000000000000000000002-22-20000000000000000
χ404444-44-44-4-400000000000000000000-22-220000000000000000
χ414444-4-44-44-4000000000000000000002-2-220000000000000000
χ424444-4-44-44-400000000000000000000-222-20000000000000000
χ434-4-44-44-4-44400000000000000002-22-200000000000000000000
χ444-4-44-44-4-4440000000000000000-22-2200000000000000000000
χ454-4-44-4-444-4400000000000000002-2-2200000000000000000000
χ464-4-44-4-444-440000000000000000-222-200000000000000000000
χ4788-8-80000000000000004-400000000000000000000000000000
χ4888-8-8000000000000000-4400000000000000000000000000000
χ498-88-8000000000000000004i−4i000000000000000000000000000
χ508-88-800000000000000000−4i4i000000000000000000000000000

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