Finite Group Databasebeta

← Group #307663

Character table — Group #307663

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888824444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-1-1-111
χ3111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-111111-1-1-1-1
χ51111111111111111111111-1-111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-11111-11111-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11-1-11111-11
χ11111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1111-1-111-1-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1111-1-1111-1
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1
χ14111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-1111-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-1-111-1-1-11111-11
χ1722222222222-2-2-2-22-2-22222220000000022-2-2000000000000-20000-200000000
χ1822222222222-2-2-2-22-2-22222-2-200000000-2-2-2-200000000000020000200000000
χ1922222222222-2-2-2-22-2-2-2-2-2-22200000000-2-22200000000000020000-200000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-2000000002222000000000000-20000200000000
χ2122222222-2-2-22222-2-2-20000002222-2-2-2-2000022-2-20000000000000000000000
χ2222222222-2-2-22222-2-2-200000022-2-2-2-2220000-2-2220000000000000000000000
χ2322222222-2-2-22222-2-2-2000000-2-22222-2-20000-2-2220000000000000000000000
χ2422222222-2-2-22222-2-2-2000000-2-2-2-22222000022-2-20000000000000000000000
χ25222-22-2-2-2-22-200002002i2i−2i−2i2-2000000002i−2i002−22−20000i2i2−i2−i20000002−2i2−i20000
χ26222-22-2-2-2-22-200002002i2i−2i−2i2-2000000002i−2i00−22−220000−i2−i2i2i2000000−22−i2i20000
χ27222-22-2-2-2-22-200002002i2i−2i−2i-2200000000−2i2i002−22−20000i2i2−i2−i2000000−22−i2i20000
χ28222-22-2-2-2-22-200002002i2i−2i−2i-2200000000−2i2i00−22−220000−i2−i2i2i20000002−2i2−i20000
χ29222-22-2-2-2-22-20000200−2i−2i2i2i2-200000000−2i2i002−22−20000−i2−i2i2i20000002−2−i2i20000
χ30222-22-2-2-2-22-20000200−2i−2i2i2i2-200000000−2i2i00−22−220000i2i2−i2−i2000000−22i2−i20000
χ31222-22-2-2-2-22-20000200−2i−2i2i2i-22000000002i−2i002−22−20000−i2−i2i2i2000000−22i2−i20000
χ32222-22-2-2-2-22-20000200−2i−2i2i2i-22000000002i−2i00−22−220000i2i2−i2−i20000002−2−i2i20000
χ332-222-2-2-222-2-222-2-222-2000000002i−2i002i−2i0000000022-2-22i−2i2i−2i00000000000000
χ342-222-2-2-222-2-222-2-222-2000000002i−2i002i−2i00000000-2-222−2i2i−2i2i00000000000000
χ352-222-2-2-222-2-222-2-222-200000000−2i2i00−2i2i0000000022-2-2−2i2i−2i2i00000000000000
χ362-222-2-2-222-2-222-2-222-200000000−2i2i00−2i2i00000000-2-2222i−2i2i−2i00000000000000
χ372-222-2-2-22-22222-2-2-2-222-22-200002i−2i00−2i2i002-200000000000000000000002i−2i00
χ382-222-2-2-22-22222-2-2-2-222-22-20000−2i2i002i−2i002-20000000000000000000000−2i2i00
χ392-222-2-2-22-22222-2-2-2-22-22-2200002i−2i00−2i2i00-220000000000000000000000−2i2i00
χ402-222-2-2-22-22222-2-2-2-22-22-220000−2i2i002i−2i00-2200000000000000000000002i−2i00
χ412-222-2-2-22-222-2-222-22-22-22-2000000000000-2200000000000002i−2i2i−2i000000000
χ422-222-2-2-22-222-2-222-22-22-22-2000000000000-220000000000000−2i2i−2i2i000000000
χ432-222-2-2-22-222-2-222-22-2-22-220000000000002-200000000000002i−2i−2i2i000000000
χ442-222-2-2-22-222-2-222-22-2-22-220000000000002-20000000000000−2i2i2i−2i000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-44-4-4-44-440000-40000000000000000000022−22−22220000000000000000000000
χ47444-44-4-4-44-440000-400000000000000000000−222222−220000000000000000000000
χ4844-4-4-4-4440004-44-4000000000000000000000000022−2222−22000000000000000000
χ4944-4-4-4-4440004-44-40000000000000000000000000−2222−2222000000000000000000
χ5044-4-4-4-444000-44-4400000000000004-400000000000000000000000000000000
χ5144-4-4-4-444000-44-440000000000000-4400000000000000000000000000000000
χ524-444-4-4-444-4-4-4-4444-4400000000000000000000000000000000000000000000
χ534-44-4-444-444-40000-4004i−4i−4i4i0000000000000000000000000000000000000000
χ544-44-4-444-444-40000-400−4i4i4i−4i0000000000000000000000000000000000000000
χ554-44-4-444-4-4-4400004000000000000000000000000000022−22−222200000000000000
χ564-44-4-444-4-4-44000040000000000000000000000000000−222222−2200000000000000
χ574-4-4-444-440004-4-44000000000000000000000000022−22−2222000000000000000000
χ584-4-4-444-440004-4-440000000000000000000000000−222222−22000000000000000000
χ594-4-4-444-44000-444-40000000004-4000000000000000000000000000000000000
χ604-4-4-444-44000-444-4000000000-44000000000000000000000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-88-8000000000000000000000000000000000000000000000000000000

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