Finite Group Databasebeta

← Group #235227

Character table — Group #235227

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222244444444444422444444224444448888888824444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111-1-1111-1-1-1-1111-1-11-11-1-1111-1-111-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-1
χ10111111-1-1111-1-1-1-1111-1-11-11-1-1111-1-111-1-11111-1-1-1-11-11-1-1-111-1-111-1-111-1-111
χ11111111-1-1111-1-1-1-1111-1-11-11-1-1111-1-111-1-1-1-1-1-11111-11-1111-1-111-1-1-1-111-1-111
χ12111111-1-1111-1-1-1-1111-1-11-11-1-1111-1-111-1-1-1-1-1-11111-11-11-1-111-1-11111-1-111-1-1
χ13111111-1-1111-1-1-1-1111-1-11-11-1-11-1-111-1-1111111-1-1-1-1-11-1111-1-1-1-11111-1-1-1-111
χ14111111-1-1111-1-1-1-1111-1-11-11-1-11-1-111-1-1111111-1-1-1-1-11-11-1-11111-1-1-1-11111-1-1
χ15111111-1-1111-1-1-1-1111-1-11-11-1-11-1-111-1-111-1-1-1-111111-11-111-1-1-1-111-1-11111-1-1
χ16111111-1-1111-1-1-1-1111-1-11-11-1-11-1-111-1-111-1-1-1-111111-11-1-1-11111-1-111-1-1-1-111
χ172222222222222-2-2-2-22-2-2-22-22-2-2000000000000000000002-22-2000000000000
χ182222222222222-2-2-2-22-2-2-22-22-2-200000000000000000000-22-22000000000000
χ1922222222-2-2-2-2-222-2-2-2-2-2-222-2222222-2-2-2-20000000000000000000000000000
χ2022222222-2-2-2-2-222-2-2-2-2-2-222-222-2-2-2-222220000000000000000000000000000
χ2122222222-2-2-2-2-2-2-222-22222-2-2-2-20000000000000000000000002-22-200000000
χ2222222222-2-2-2-2-2-2-222-22222-2-2-2-2000000000000000000000000-22-2200000000
χ23222222-2-2222-2-222-2-2222-2-2-2-22-2000000000000000000002-2-22000000000000
χ24222222-2-2222-2-222-2-2222-2-2-2-22-200000000000000000000-222-2000000000000
χ25222222-2-2-2-2-2222222-2-2-22-2-222-20000000000000000000000002-2-2200000000
χ26222222-2-2-2-2-2222222-2-2-22-2-222-2000000000000000000000000-222-200000000
χ27222222-2-2-2-2-222-2-2-2-2-222-2-222-2222-2-2-2-2220000000000000000000000000000
χ28222222-2-2-2-2-222-2-2-2-2-222-2-222-22-2-22222-2-20000000000000000000000000000
χ292222-2-22222-2222222-22-2-2-2-2-2-220000000022-2-222-2-200000000000000000000
χ302222-2-22222-2222222-22-2-2-2-2-2-2200000000-2-222-2-22200000000000000000000
χ312222-2-22222-222-2-2-2-2-2-222-22-22-200000000000000000000000000002i−2i2i−2i0000
χ322222-2-22222-222-2-2-2-2-2-222-22-22-20000000000000000000000000000−2i2i−2i2i0000
χ332222-2-222-2-22-2-222-2-22-222-2-22-22000000000000000022-2-20000000000000000
χ342222-2-222-2-22-2-222-2-22-222-2-22-220000000000000000-2-2220000000000000000
χ352222-2-222-2-22-2-2-2-22222-2-2-2222-2000000000000000000000000000000002-22-2
χ362222-2-222-2-22-2-2-2-22222-2-2-2222-200000000000000000000000000000000-22-22
χ372222-2-2-2-222-2-2-222-2-2-22-22222-2-200000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-222-2-2-222-2-2-22-22222-2-20000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-222-2-2-2-2-222-2-22-22-22220000000022-2-2-2-22200000000000000000000
χ402222-2-2-2-222-2-2-2-2-222-2-22-22-222200000000-2-22222-2-200000000000000000000
χ412222-2-2-2-2-2-222222222-22-222-2-2-2000000000000000000000000000000002-2-22
χ422222-2-2-2-2-2-222222222-22-222-2-2-200000000000000000000000000000000-222-2
χ432222-2-2-2-2-2-2222-2-2-2-222-222-2-22200000000000000002-2-220000000000000000
χ442222-2-2-2-2-2-2222-2-2-2-222-222-2-2220000000000000000-222-20000000000000000
χ454-44-400000004-44i−4i4i−4i0000000002-22i−2i2i−2i2-20000000000000000000000000000
χ464-44-400000004-44i−4i4i−4i000000000-22−2i2i−2i2i-220000000000000000000000000000
χ474-44-400000004-4−4i4i−4i4i0000000002-2−2i2i−2i2i2-20000000000000000000000000000
χ484-44-400000004-4−4i4i−4i4i000000000-222i−2i2i−2i-220000000000000000000000000000
χ494-44-40000000-444i−4i−4i4i0000000002-22i−2i−2i2i-220000000000000000000000000000
χ504-44-40000000-444i−4i−4i4i000000000-22−2i2i2i−2i2-20000000000000000000000000000
χ514-44-40000000-44−4i4i4i−4i0000000002-2−2i2i2i−2i-220000000000000000000000000000
χ524-44-40000000-44−4i4i4i−4i000000000-222i−2i−2i2i2-20000000000000000000000000000
χ534-4-444-4004-44000000-4000000000000000022−2222−22000000000000000000000000
χ544-4-444-4004-44000000-40000000000000000−2222−2222000000000000000000000000
χ554-4-444-400-44-40000004000000000000000000002i2−2i22i2−2i200000000000000000000
χ564-4-444-400-44-4000000400000000000000000000−2i22i2−2i22i200000000000000000000
χ574-4-44-44004-4-40000004000000000000000022−22−2222000000000000000000000000
χ584-4-44-44004-4-400000040000000000000000−222222−22000000000000000000000000
χ594-4-44-4400-444000000-4000000000000000000002i2−2i2−2i22i200000000000000000000
χ604-4-44-4400-444000000-400000000000000000000−2i22i22i2−2i200000000000000000000
χ6188-8-8008-8000000000000000000000000000000000000000000000000000000
χ6288-8-800-88000000000000000000000000000000000000000000000000000000

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