Finite Group Databasebeta

← Group #7622994

Character table — Group #7622994

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112222222222222222222224444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order122222222444444448816161616222244448888888888888881616161616161616161616161616161616161616161616161616161616162222444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-11111-1-1-1-1
χ61111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-11-1-1-1-1-1-1-11111
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-11-11111111-1-1-1-1
χ911111-1-1-1-111-1-1-1-11111111111-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-111-1-111-1-1
χ1011111-1-1-1-111-1-1-1-11111111111-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-111
χ1111111-1-1-1-111-1-1-1-111111111-1-111-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-111-1-111
χ1211111-1-1-1-111-1-1-1-111111111-1-111-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1111-1-111-1-1
χ1311111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-11-1-1-1111-1-1-1-111
χ1411111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11-1111-1-1-11111-1-1
χ1511111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-11-1-1-11-1-11111-1-1
χ1611111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1111-111-1-1-1-111
χ17111-1-111-1-1-1-111-1-1111111111-11-11-11-11-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-11-111-11-11-11-1
χ18111-1-111-1-1-1-111-1-1111111111-11-11-11-11-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-111-11-1-11-11-11-11
χ19111-1-111-1-1-1-111-1-111111111-11-11-11-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-11-11-11-11-11
χ20111-1-111-1-1-1-111-1-111111111-11-11-11-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-11-11-11-11-11-1
χ21111-1-111-1-1-1-111-1-11111-1-1-1-11-11-11-11-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-11-11-1-11-11
χ22111-1-111-1-1-1-111-1-11111-1-1-1-11-11-11-11-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1-111-11-11-111-11-1
χ23111-1-111-1-1-1-111-1-11111-1-1-1-1-11-11-11-111-1-111-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-111-1-11-1-11-111-11-1
χ24111-1-111-1-1-1-111-1-11111-1-1-1-1-11-11-11-111-1-111-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-111-11-1-11-11
χ25111-1-1-1-111-1-1-1-111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-11-1-111-1-11
χ26111-1-1-1-111-1-1-1-111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-111-111-1-111-1
χ27111-1-1-1-111-1-1-1-11111111111-111-1-111-11-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1-111-1-111-1
χ28111-1-1-1-111-1-1-1-11111111111-111-1-111-11-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1111-1-111-1-11
χ29111-1-1-1-111-1-1-1-1111111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-11-1111-1-11-111-1
χ30111-1-1-1-111-1-1-1-1111111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-11-1-1-111-11-1-11
χ31111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-111-11-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-11-111-111-11-1-11
χ32111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-111-11-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-11-1-11-1-11-111-1
χ3322222222222222222-2-2000022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000
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χ362222222-2-2-2-2-2-222-2-20022−2−2000000000000000−2i2i−2i2i−2i2i−2i2i2−222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ372222222-2-2-2-2-2-222-2-200−2−2220000000000000002i−2i2i−2i2i−2i2i−2i−22−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ382222222-2-2-2-2-2-222-2-200−2−222000000000000000−2i2i−2i2i−2i2i−2i2i−22−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3922222-2-222-2-222-2-2-2-20022−2−20000000000000002i−2i2i−2i−2i2i−2i2i2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4022222-2-222-2-222-2-2-2-20022−2−2000000000000000−2i2i−2i2i2i−2i2i−2i2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4122222-2-222-2-222-2-2-2-200−2−2220000000000000002i−2i2i−2i−2i2i−2i2i−22−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ4222222-2-222-2-222-2-2-2-200−2−222000000000000000−2i2i−2i2i2i−2i2i−2i−22−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4322222-2-2-2-222-2-2-2-222-2-2000022-2-222-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000000000
χ4422222-2-2-2-222-2-2-2-222-2-20000-2-222-2-222-2-2-222222222-2-2-2-20000000000000000000000000000000000000000000000
χ45222-2-2222222-2-2-2-2-2-20022−2−20000000000000002i−2i−2i2i2i−2i−2i2i2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ46222-2-2222222-2-2-2-2-2-20022−2−2000000000000000−2i2i2i−2i−2i2i2i−2i2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ47222-2-2222222-2-2-2-2-2-200−2−2220000000000000002i−2i−2i2i2i−2i−2i2i−2222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ48222-2-2222222-2-2-2-2-2-200−2−222000000000000000−2i2i2i−2i−2i2i2i−2i−2222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ49222-2-222-2-2-2-222-2-222-2-200002-22-22-22-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000000
χ50222-2-222-2-2-2-222-2-222-2-20000-22-22-22-22-222-2-22222-2-222-2-20000000000000000000000000000000000000000000000
χ51222-2-2-2-222-2-2-2-22222-2-200002-2-222-2-22-22222-2-2-2-22222-2-20000000000000000000000000000000000000000000000
χ52222-2-2-2-222-2-2-2-22222-2-20000-222-2-222-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000000000
χ53222-2-2-2-2-2-2222222-2-20022−2−20000000000000002i−2i−2i2i−2i2i2i−2i2−2−2−222−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ54222-2-2-2-2-2-2222222-2-20022−2−2000000000000000−2i2i2i−2i2i−2i−2i2i2−2−2−222−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ55222-2-2-2-2-2-2222222-2-200−2−2220000000000000002i−2i−2i2i−2i2i2i−2i−2222−2−222−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ56222-2-2-2-2-2-2222222-2-200−2−222000000000000000−2i2i2i−2i2i−2i−2i2i−2222−2−222−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5722-22-22-22-22-22-22-22-222222200000000-22-22-22-200000000-2-22-22-22-22-22-22-200000000000000000000000000000000
χ5822-22-22-22-22-22-22-22-222-2-2-2-200000000-22-22-22-20000000022-22-22-22-22-22-2200000000000000000000000000000000
χ5922-22-22-22-22-22-22-22-2-2-20000000000002-22-22-2200000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000
χ6022-22-22-22-22-22-22-22-2-2-20000000000002-22-22-220000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000
χ6122-22-22-2-22-22-222-2-220022−2−2222-2-2-2-22000000000000000−222−2−222−2−222−2−222−2−222−2−222−2−222−2−220000000000000000
χ6222-22-22-2-22-22-222-2-220022−2−2-2-2-22222-2000000000000000−222−2−222−2−222−2−22−222−2−222−2−222−2−222−20000000000000000
χ6322-22-22-2-22-22-222-2-2200−2−222222-2-2-2-220000000000000002−2−222−2−222−2−222−2−222−2−222−2−222−2−222−20000000000000000
χ6422-22-22-2-22-22-222-2-2200−2−222-2-2-22222-20000000000000002−2−222−2−222−2−222−22−2−222−2−222−2−222−2−220000000000000000
χ6522-22-2-222-2-222-2-22-220022−2−222-22-2-22-2000000000000000−222−2−22−222−2−222−22−2−222−2−22−222−2−222−20000000000000000
χ6622-22-2-222-2-222-2-22-220022−2−2-2-22-222-22000000000000000−222−2−22−222−2−222−2−222−2−222−22−2−222−2−220000000000000000
χ6722-22-2-222-2-222-2-22-2200−2−22222-22-2-22-20000000000000002−2−222−22−2−222−2−22−222−2−222−22−2−222−2−220000000000000000
χ6822-22-2-222-2-222-2-22-2200−2−222-2-22-222-220000000000000002−2−222−22−2−222−2−222−2−222−2−22−222−2−222−20000000000000000
χ6922-22-2-22-222-2-22-222-222222200000000-22-2-22-2200000000-2-22-22-2-22-22-22-2200000000000000000000000000000000
χ7022-22-2-22-222-2-22-222-222-2-2-2-200000000-22-2-22-220000000022-22-222-22-22-22-200000000000000000000000000000000
χ7122-22-2-22-222-2-22-222-2-2-20000000000002-222-22-200000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000
χ7222-22-2-22-222-2-22-222-2-2-20000000000002-222-22-20000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000
χ7322-2-222-22-22-2-22-22-220022−2−22-222-22-2-2000000000000000−22−222−22−2−22−222−22−2−22−222−22−2−22−222−20000000000000000
χ7422-2-222-22-22-2-22-22-220022−2−2-22-2-22-222000000000000000−22−222−22−2−22−222−2−222−22−2−22−222−22−2−220000000000000000
χ7522-2-222-22-22-2-22-22-2200−2−2222-222-22-2-20000000000000002−22−2−22−222−22−2−22−222−22−2−22−222−22−2−220000000000000000
χ7622-2-222-22-22-2-22-22-2200−2−222-22-2-22-2220000000000000002−22−2−22−222−22−2−222−2−22−222−22−2−22−222−20000000000000000
χ7722-2-222-2-22-222-2-222-222222200000000-2-222-2-2200000000-2-2-22-222-22-2-22-2200000000000000000000000000000000
χ7822-2-222-2-22-222-2-222-222-2-2-2-200000000-2-222-2-2200000000222-22-2-22-222-22-200000000000000000000000000000000
χ7922-2-222-2-22-222-2-222-2-2-200000000000022-2-222-200000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000
χ8022-2-222-2-22-222-2-222-2-2-200000000000022-2-222-20000000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000
χ8122-2-22-222-2-22-222-22-222222200000000-2-22-222-200000000-2-2-22-22-22-222-22-200000000000000000000000000000000
χ8222-2-22-222-2-22-222-22-222-2-2-2-200000000-2-22-222-200000000222-22-22-22-2-22-2200000000000000000000000000000000
χ8322-2-22-222-2-22-222-22-2-2-200000000000022-22-2-2200000000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000
χ8422-2-22-222-2-22-222-22-2-2-200000000000022-22-2-220000000000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000
χ8522-2-22-22-222-22-22-2-220022−2−22-2-2-2-2222000000000000000−22−222−2−222−22−2−222−2−22−222−2−222−22−2−220000000000000000
χ8622-2-22-22-222-22-22-2-220022−2−2-22222-2-2-2000000000000000−22−222−2−222−22−2−22−222−22−2−222−2−22−222−20000000000000000
χ8722-2-22-22-222-22-22-2-2200−2−2222-2-2-2-22220000000000000002−22−2−222−2−22−222−2−222−22−2−222−2−22−222−20000000000000000
χ8822-2-22-22-222-22-22-2-2200−2−222-22222-2-2-20000000000000002−22−2−222−2−22−222−22−2−22−222−2−222−22−2−220000000000000000
χ898-800000000000000042−424ζ+4ζ7−4ζ−4ζ74ζ3+4ζ5−4ζ3−4ζ5000000000000000000000000000000000000000000000000000000000000000000000
χ908-800000000000000042−42−4ζ−4ζ74ζ+4ζ7−4ζ3−4ζ54ζ3+4ζ5000000000000000000000000000000000000000000000000000000000000000000000
χ918-8000000000000000−42424ζ3+4ζ5−4ζ3−4ζ5−4ζ−4ζ74ζ+4ζ7000000000000000000000000000000000000000000000000000000000000000000000
χ928-8000000000000000−4242−4ζ3−4ζ54ζ3+4ζ54ζ+4ζ7−4ζ−4ζ7000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.