Finite Group Databasebeta

← Group #233003

Character table — Group #233003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888224488888888888844442222222244444444448888888822448888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ92222222222-2-2-222-2-2-20000000022-2-200000000000000002222222222-2-2-222-2-2-20000000022-2-20000000000000000
χ102222222222-2-2-222-2-2-200000000-2-22200000000000000002222222222-2-2-222-2-2-200000000-2-2220000000000000000
χ1122222222-2-2222-2-22-2-22222-2-2-2-20000000000000000000022222222-2-2222-2-22-2-22222-2-2-2-200000000000000000000
χ1222222222-2-2222-2-22-2-2-2-2-2-222220000000000000000000022222222-2-2222-2-22-2-2-2-2-2-2222200000000000000000000
χ1322222222-2-2-2-2-2-2-2-2220000000000002i2i−2i−2i00000000000022222222-2-2-2-2-2-2-2-2220000000000002i2i−2i−2i000000000000
χ1422222222-2-2-2-2-2-2-2-222000000000000−2i−2i2i2i00000000000022222222-2-2-2-2-2-2-2-222000000000000−2i−2i2i2i000000000000
χ15222-2-22-2-222000-2-200022−2−222−2−22-2002−22−2000000000000222-2-22-2-222000-2-200022−2−222−2−22-2002−22−2000000000000
χ16222-2-22-2-222000-2-200022−2−222−2−2-2200−22−22000000000000222-2-22-2-222000-2-200022−2−222−2−2-2200−22−22000000000000
χ17222-2-22-2-222000-2-2000−2−222−2−2222-200−22−22000000000000222-2-22-2-222000-2-2000−2−222−2−2222-200−22−22000000000000
χ18222-2-22-2-222000-2-2000−2−222−2−222-22002−22−2000000000000222-2-22-2-222000-2-2000−2−222−2−222-22002−22−2000000000000
χ19222-2-22-2-2-2-20002200022−2−2−2−222002i−2ii2−i2−i2i2000000000000222-2-22-2-2-2-20002200022−2−2−2−222002i−2ii2−i2−i2i2000000000000
χ20222-2-22-2-2-2-20002200022−2−2−2−22200−2i2i−i2i2i2−i2000000000000222-2-22-2-2-2-20002200022−2−2−2−22200−2i2i−i2i2i2−i2000000000000
χ21222-2-22-2-2-2-200022000−2−22222−2−2002i−2i−i2i2i2−i2000000000000222-2-22-2-2-2-200022000−2−22222−2−2002i−2i−i2i2i2−i2000000000000
χ22222-2-22-2-2-2-200022000−2−22222−2−200−2i2ii2−i2−i2i2000000000000222-2-22-2-2-2-200022000−2−22222−2−200−2i2ii2−i2−i2i2000000000000
χ2322-22-2-2-2200-22-20020000002-22-20000000022−2−222−2−2000022-22-2-2-2200-22-20020000002-22-20000000022−2−222−2−20000
χ2422-22-2-2-2200-22-20020000002-22-200000000−2−222−2−222000022-22-2-2-2200-22-20020000002-22-200000000−2−222−2−2220000
χ2522-22-2-2-2200-22-2002000000-22-220000000022−2−2−2−222000022-22-2-2-2200-22-2002000000-22-220000000022−2−2−2−2220000
χ2622-22-2-2-2200-22-2002000000-22-2200000000−2−22222−2−2000022-22-2-2-2200-22-2002000000-22-2200000000−2−22222−2−20000
χ272-22-22-2-2200-2-22002002-22-20000000000002−22−22−22−200002-22-22-2-2200-2-22002002-22-20000000000002−22−22−22−20000
χ282-22-22-2-2200-2-22002002-22-2000000000000−22−22−22−2200002-22-22-2-2200-2-22002002-22-2000000000000−22−22−22−220000
χ292-22-22-2-2200-2-2200200-22-220000000000002−22−2−22−2200002-22-22-2-2200-2-2200200-22-220000000000002−22−2−22−220000
χ302-22-22-2-2200-2-2200200-22-22000000000000−22−222−22−200002-22-22-2-2200-2-2200200-22-22000000000000−22−222−22−20000
χ312-2-2-2-22222-22-2-22-222-2000000000000000000002-2-2200002-2-2-2-22222-22-2-22-222-2000000000000000000002-2-220000
χ322-2-2-2-22222-22-2-22-222-200000000000000000000-222-200002-2-2-2-22222-22-2-22-222-200000000000000000000-222-20000
χ332-2-2-2-22222-2-2222-2-2-22000000000000000000000000002-22-2-2-2-22222-2-2222-2-2-22000000000000000000000000002-2
χ342-2-2-2-22222-2-2222-2-2-2200000000000000000000000000-222-2-2-2-22222-2-2222-2-2-2200000000000000000000000000-22
χ352-2-2-2-2222-222-2-2-222-2200000000000000002-2-22000000002-2-2-2-2222-222-2-2-222-2200000000000000002-2-2200000000
χ362-2-2-2-2222-222-2-2-222-220000000000000000-222-2000000002-2-2-2-2222-222-2-2-222-220000000000000000-222-200000000
χ372-2-2-2-2222-22-222-22-22-20000000000000000000000002-2002-2-2-2-2222-22-222-22-22-20000000000000000000000002-200
χ382-2-2-2-2222-22-222-22-22-2000000000000000000000000-22002-2-2-2-2222-22-222-22-22-2000000000000000000000000-2200
χ3944-44-4-4-44004-4400-400000000000000000000000000000044-44-4-4-44004-4400-4000000000000000000000000000000
χ4044-4-44-44-40000000000000022−22−22220000000000000000000044-4-44-44-40000000000000022−22−222200000000000000000000
χ4144-4-44-44-400000000000000−222222−220000000000000000000044-4-44-44-400000000000000−222222−2200000000000000000000
χ424-444-4-44-4000000000022−22−22220000000000000000000000004-444-4-44-4000000000022−22−2222000000000000000000000000
χ434-444-4-44-40000000000−222222−220000000000000000000000004-444-4-44-40000000000−222222−22000000000000000000000000
χ444-44-44-4-440044-400-40000000000000000000000000000004-44-44-4-440044-400-4000000000000000000000000000000
χ454-4-4444-4-44-4000-4400000000000000000000000000000004-4-4444-4-44-4000-440000000000000000000000000000000
χ464-4-4444-4-4-440004-400000000000000000000000000000004-4-4444-4-4-440004-40000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ481111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4911111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ51111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111
χ52111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ53111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
χ54111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111
χ552222222222-2-2-222-2-2-20000000022-2-20000000000000000-2-2-2-2-2-2-2-2-2-2222-2-222200000000-2-2220000000000000000
χ562222222222-2-2-222-2-2-200000000-2-2220000000000000000-2-2-2-2-2-2-2-2-2-2222-2-22220000000022-2-20000000000000000
χ5722222222-2-2222-2-22-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-222-2-2-222-222-2-2-2-2222200000000000000000000
χ5822222222-2-2222-2-22-2-2-2-2-2-2222200000000000000000000-2-2-2-2-2-2-2-222-2-2-222-2222222-2-2-2-200000000000000000000
χ5922222222-2-2-2-2-2-2-2-2220000000000002i2i−2i−2i000000000000-2-2-2-2-2-2-2-222222222-2-2000000000000−2i−2i2i2i000000000000
χ6022222222-2-2-2-2-2-2-2-222000000000000−2i−2i2i2i000000000000-2-2-2-2-2-2-2-222222222-2-20000000000002i2i−2i−2i000000000000
χ61222-2-22-2-222000-2-200022−2−222−2−22-2002−22−2000000000000-2-2-222-222-2-200022000−2−222−2−222-2200−22−22000000000000
χ62222-2-22-2-222000-2-200022−2−222−2−2-2200−22−22000000000000-2-2-222-222-2-200022000−2−222−2−2222-2002−22−2000000000000
χ63222-2-22-2-222000-2-2000−2−222−2−2222-200−22−22000000000000-2-2-222-222-2-20002200022−2−222−2−2-22002−22−2000000000000
χ64222-2-22-2-222000-2-2000−2−222−2−222-22002−22−2000000000000-2-2-222-222-2-20002200022−2−222−2−22-200−22−22000000000000
χ65222-2-22-2-2-2-20002200022−2−2−2−222002i−2ii2−i2−i2i2000000000000-2-2-222-22222000-2-2000−2−22222−2−200−2i2i−i2i2i2−i2000000000000
χ66222-2-22-2-2-2-20002200022−2−2−2−22200−2i2i−i2i2i2−i2000000000000-2-2-222-22222000-2-2000−2−22222−2−2002i−2ii2−i2−i2i2000000000000
χ67222-2-22-2-2-2-200022000−2−22222−2−2002i−2i−i2i2i2−i2000000000000-2-2-222-22222000-2-200022−2−2−2−22200−2i2ii2−i2−i2i2000000000000
χ68222-2-22-2-2-2-200022000−2−22222−2−200−2i2ii2−i2−i2i2000000000000-2-2-222-22222000-2-200022−2−2−2−222002i−2i−i2i2i2−i2000000000000
χ6922-22-2-2-2200-22-20020000002-22-20000000022−2−222−2−20000-2-22-2222-2002-2200-2000000-22-2200000000−2−222−2−2220000
χ7022-22-2-2-2200-22-20020000002-22-200000000−2−222−2−2220000-2-22-2222-2002-2200-2000000-22-220000000022−2−222−2−20000
χ7122-22-2-2-2200-22-2002000000-22-220000000022−2−2−2−2220000-2-22-2222-2002-2200-20000002-22-200000000−2−22222−2−20000
χ7222-22-2-2-2200-22-2002000000-22-2200000000−2−22222−2−20000-2-22-2222-2002-2200-20000002-22-20000000022−2−2−2−2220000
χ732-22-22-2-2200-2-22002002-22-20000000000002−22−22−22−20000-22-22-222-20022-200-200-22-22000000000000−22−22−22−220000
χ742-22-22-2-2200-2-22002002-22-2000000000000−22−22−22−220000-22-22-222-20022-200-200-22-220000000000002−22−22−22−20000
χ752-22-22-2-2200-2-2200200-22-220000000000002−22−2−22−220000-22-22-222-20022-200-2002-22-2000000000000−22−222−22−20000
χ762-22-22-2-2200-2-2200200-22-22000000000000−22−222−22−20000-22-22-222-20022-200-2002-22-20000000000002−22−2−22−220000
χ772-2-2-2-22222-22-2-22-222-2000000000000000000002-2-220000-22222-2-2-2-22-222-22-2-2200000000000000000000-222-20000
χ782-2-2-2-22222-22-2-22-222-200000000000000000000-222-20000-22222-2-2-2-22-222-22-2-22000000000000000000002-2-220000
χ792-2-2-2-22222-2-2222-2-2-22000000000000000000000000002-2-22222-2-2-2-222-2-2-2222-200000000000000000000000000-22
χ802-2-2-2-22222-2-2222-2-2-2200000000000000000000000000-22-22222-2-2-2-222-2-2-2222-2000000000000000000000000002-2
χ812-2-2-2-2222-222-2-2-222-2200000000000000002-2-2200000000-22222-2-2-22-2-2222-2-22-20000000000000000-222-200000000
χ822-2-2-2-2222-222-2-2-222-220000000000000000-222-200000000-22222-2-2-22-2-2222-2-22-200000000000000002-2-2200000000
χ832-2-2-2-2222-22-222-22-22-20000000000000000000000002-200-22222-2-2-22-22-2-22-22-22000000000000000000000000-2200
χ842-2-2-2-2222-22-222-22-22-2000000000000000000000000-2200-22222-2-2-22-22-2-22-22-220000000000000000000000002-200
χ8544-44-4-4-44004-4400-4000000000000000000000000000000-4-44-4444-400-44-4004000000000000000000000000000000
χ8644-4-44-44-40000000000000022−22−222200000000000000000000-4-444-44-4400000000000000−222222−2200000000000000000000
χ8744-4-44-44-400000000000000−222222−2200000000000000000000-4-444-44-440000000000000022−22−222200000000000000000000
χ884-444-4-44-4000000000022−22−2222000000000000000000000000-44-4-444-440000000000−222222−22000000000000000000000000
χ894-444-4-44-40000000000−222222−22000000000000000000000000-44-4-444-44000000000022−22−2222000000000000000000000000
χ904-44-44-4-440044-400-4000000000000000000000000000000-44-44-444-400-4-44004000000000000000000000000000000
χ914-4-4444-4-44-4000-440000000000000000000000000000000-444-4-4-444-440004-40000000000000000000000000000000
χ924-4-4444-4-4-440004-40000000000000000000000000000000-444-4-4-4444-4000-440000000000000000000000000000000

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