Finite Group Databasebeta

← Group #268125

Character table — Group #268125

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888881616161616161616161616161616161616161616161632
order12222244444444444444444888822444444888888888888882
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1
χ311111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-11-1-11-1-111-1-1-1-11111-1-1-1-1-1-11
χ5111111111111-1-1111111-1-1-11111-111-11111-1-1-1-1-1-1-1-111-1-1-1-11
χ6111111111111-1-1111111-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1
χ7111111111111-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-11111-1
χ8111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ911111111-1-11111111-1-1-111111-1-1-11-1-11-1111-11-1-1-1111-111-1-1-1
χ1011111111-1-11111111-1-1-111111-1-1-1-11-1-11-1-1-11-1111-1-11-111-1-11
χ1111111111-1-11111111-1-1-1111-1-111-11-1-11-1-1-11-11-111-1-1-11-1-1111
χ1211111111-1-11111111-1-1-1111-1-111-1-11-1-1111-11-11-1-111-11-1-111-1
χ1311111111-1-111-1-1111-1-1-1-1-1-111-1-111-111-111-11-1111-1-11-1-1-111-1
χ1411111111-1-111-1-1111-1-1-1-1-1-111-1-11-111-11-1-11-11-1-1-1111-1-1-1111
χ1511111111-1-111-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-11-11-1-111-1111-1-11
χ1611111111-1-111-1-1111-1-1-1-1-1-1-1-1111-111-11111-11-111-1-1-1111-1-1-1
χ172222222222-2-2222-2-2-22-22-2-20000-20020000000000000000000
χ182222222222-2-2-2-22-2-2-22-2-2220000200-20000000000000000000
χ1922222222-2-2-2-2222-2-22-222-2-20000200-20000000000000000000
χ2022222222-2-2-2-2-2-22-2-22-22-2220000-20020000000000000000000
χ21222222-2-2222200-2-2-22-2-200000000000000000000000002i−2i2i−2i0
χ22222222-2-2222200-2-2-22-2-20000000000000000000000000−2i2i−2i2i0
χ23222222-2-222-2-200-222-2-2200022220000000000000000-2-200000
χ24222222-2-222-2-200-222-2-22000-2-2-2-200000000000000002200000
χ25222222-2-2-2-22200-2-2-2-22200000000000000000000000002i−2i−2i2i0
χ26222222-2-2-2-22200-2-2-2-2220000000000000000000000000−2i2i2i−2i0
χ27222222-2-2-2-2-2-200-22222-200022-2-20000000000000000-2200000
χ28222222-2-2-2-2-2-200-22222-2000-2-22200000000000000002-200000
χ292222-2-222002-222-22-2000-22-2000000200-200020-200000000000
χ302222-2-222002-222-22-2000-22-2000000-2002000-20200000000000
χ312222-2-222002-2-2-2-22-20002-22000000200-2000-20200000000000
χ322222-2-222002-2-2-2-22-20002-22000000-200200020-200000000000
χ332222-2-22200-2222-2-22000-2-2200000200-2000-202000000000000
χ342222-2-22200-2222-2-22000-2-2200000-200200020-2000000000000
χ352222-2-22200-22-2-2-2-2200022-200000200-200020-2000000000000
χ362222-2-22200-22-2-2-2-2200022-200000-2002000-202000000000000
χ374444-4-4-4-4004-4004-44000000000000000000000000000000000
χ384444-4-4-4-400-440044-4000000000000000000000000000000000
χ394-44-4004-400004i−4i00000000000000000002i−2i0000002-20000000
χ404-44-4004-400004i−4i0000000000000000000−2i2i000000-220000000
χ414-44-4004-40000−4i4i00000000000000000002i−2i000000-220000000
χ424-44-4004-40000−4i4i0000000000000000000−2i2i0000002-20000000
χ434-4-444-4004i−4i00000000000002i2−2i222−2200000000000000000000000
χ444-4-444-4004i−4i0000000000000−2i22i2−222200000000000000000000000
χ454-4-444-400−4i4i00000000000002i2−2i2−222200000000000000000000000
χ464-4-444-400−4i4i0000000000000−2i22i222−2200000000000000000000000
χ4788-8-8000000000000000000000000000000000002i2−2i2000000000
χ4888-8-800000000000000000000000000000000000−2i22i2000000000
χ498-88-800-88000000000000000000000000000000000000000000
χ508-8-88-8800000000000000000000000000000000000000000000

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