Finite Group Databasebeta

← Group #254225

Character table — Group #254225

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222224444444888888888888888888881616161616161616161616161616163232
order12222244444444444444444444444448888888824444444444888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-11-1-111-11111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-1-1-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-1-1-11111111111111-111-1-1111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-11-1-1-111-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1111111-1-1
χ91111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-1-11111-1-11-1
χ101111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11-11-11-1-111-1-111-11
χ111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111-1-111-1-1-11
χ121111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-111-1-1-1-1111-1
χ131111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-11-11-1-1-1-1-1-1-111-11
χ141111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-111-1-111-1-1-1-111-1-11-1
χ151111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-1-111111-1-1111-1
χ161111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-1-1-1111111-1-1-11
χ1722222222-2-222-22222-2-2-2-22222-2-20000000000000000-2000000000000
χ1822222222-2-222-22222-2-2-2-2-2-2-2-22200000000000000002000000000000
χ1922222222-2-222-2-2-2-2-2-2-22222-2-2220000000000000000-2000000000000
χ2022222222-2-222-2-2-2-2-2-2-222-2-222-2-200000000000000002000000000000
χ21222222-2-222-2-2222-2-2-2-22-200000022-2-20000000000000002-200000000
χ22222222-2-222-2-2222-2-2-2-22-2000000-2-222000000000000000-2200000000
χ23222222-2-222-2-22-2-222-2-2-2200000022-2-2000000000000000-2200000000
χ24222222-2-222-2-22-2-222-2-2-22000000-2-2220000000000000002-200000000
χ25222222-2-2-2-2-2-2-222-2-222-2200000000000000000002000-20002-2000000
χ26222222-2-2-2-2-2-2-222-2-222-220000000000000000000-20002000-22000000
χ27222222-2-2-2-2-2-2-2-2-222222-200000000000000000002000-2000-22000000
χ28222222-2-2-2-2-2-2-2-2-222222-20000000000000000000-200020002-2000000
χ292222-2-22-2-2-22-2200002-2000000002i−2i2i−2i00002i2i−2i−2i002000-20000000000
χ302222-2-22-2-2-22-2200002-2000000002i−2i2i−2i0000−2i−2i2i2i00-200020000000000
χ312222-2-22-2-2-22-2200002-200000000−2i2i−2i2i00002i2i−2i−2i00-200020000000000
χ322222-2-22-2-2-22-2200002-200000000−2i2i−2i2i0000−2i−2i2i2i002000-20000000000
χ332222-2-2-22-2-2-2220000-22000000002i−2i−2i2i2i2i−2i−2i0000200-20000000000000
χ342222-2-2-22-2-2-2220000-22000000002i−2i−2i2i−2i−2i2i2i0000-20020000000000000
χ352222-2-2-22-2-2-2220000-2200000000−2i2i2i−2i2i2i−2i−2i0000-20020000000000000
χ362222-2-2-22-2-2-2220000-2200000000−2i2i2i−2i−2i−2i2i2i0000200-20000000000000
χ372-22-2-222-200-2202i−2i2i−2i00002-22i−2i0000002−22−2i2−i2i2−i2000000000002−2i2−i200
χ382-22-2-222-200-2202i−2i2i−2i00002-22i−2i000000−22−22−i2i2−i2i200000000000−22−i2i200
χ392-22-2-222-200-2202i−2i2i−2i0000-22−2i2i0000002−22−2i2−i2i2−i200000000000−22−i2i200
χ402-22-2-222-200-2202i−2i2i−2i0000-22−2i2i000000−22−22−i2i2−i2i2000000000002−2i2−i200
χ412-22-2-222-200-220−2i2i−2i2i00002-2−2i2i0000002−22−2−i2i2−i2i2000000000002−2−i2i200
χ422-22-2-222-200-220−2i2i−2i2i00002-2−2i2i000000−22−22i2−i2i2−i200000000000−22i2−i200
χ432-22-2-222-200-220−2i2i−2i2i0000-222i−2i0000002−22−2−i2i2−i2i200000000000−22i2−i200
χ442-22-2-222-200-220−2i2i−2i2i0000-222i−2i000000−22−22i2−i2i2−i2000000000002−2−i2i200
χ454444-4-44-4444-4-40000-440000000000000000000000000000000000000
χ464444-4-4-4444-44-400004-40000000000000000000000000000000000000
χ474-44-44-44400-4-40000000000000000000000022−22−222200000000000000000
χ484-44-44-44400-4-400000000000000000000000−222222−2200000000000000000
χ494-44-44-4-4-4004400000000000000000002i2−2i2−2i22i2000000000000000000000
χ504-44-44-4-4-400440000000000000000000−2i22i22i2−2i2000000000000000000000
χ514-44-4-44-44004-404i−4i−4i4i000000000000000000000000000000000000000
χ524-44-4-44-44004-40−4i4i4i−4i000000000000000000000000000000000000000
χ5388-8-80000000000000000000004-400000000000000000000000000000
χ5488-8-8000000000000000000000-4400000000000000000000000000000
χ558-8-8800008i−8i0000000000000000000000000000000000000000000000
χ568-8-880000−8i8i0000000000000000000000000000000000000000000000

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