Finite Group Databasebeta

← Group #243154

Character table — Group #243154

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888444488888888888844442222222244444444448888888844448888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ92222222222-2-22-2-22-2-22222-2-2-2-2000000000000000000002222222222-2-22-2-22-2-22222-2-2-2-200000000000000000000
χ102222222222-2-22-2-22-2-2-2-2-2-22222000000000000000000002222222222-2-22-2-22-2-2-2-2-2-2222200000000000000000000
χ1122222222-2-222-222-2-2-20000000022-2-2000000000000000022222222-2-222-222-2-2-20000000022-2-20000000000000000
χ1222222222-2-222-222-2-2-200000000-2-222000000000000000022222222-2-222-222-2-2-200000000-2-2220000000000000000
χ1322222222-2-2-2-2-2-2-2-222000000000000000000002i2i−2i−2i000022222222-2-2-2-2-2-2-2-222000000000000000000002i2i−2i−2i0000
χ1422222222-2-2-2-2-2-2-2-22200000000000000000000−2i−2i2i2i000022222222-2-2-2-2-2-2-2-22200000000000000000000−2i−2i2i2i0000
χ15222-2-22-2-200220-2-200022−2−222−2−22-200000000002−22−20000222-2-22-2-200220-2-200022−2−222−2−22-200000000002−22−20000
χ16222-2-22-2-200220-2-200022−2−222−2−2-220000000000−22−220000222-2-22-2-200220-2-200022−2−222−2−2-220000000000−22−220000
χ17222-2-22-2-200220-2-2000−2−222−2−2222-20000000000−22−220000222-2-22-2-200220-2-2000−2−222−2−2222-20000000000−22−220000
χ18222-2-22-2-200220-2-2000−2−222−2−222-2200000000002−22−20000222-2-22-2-200220-2-2000−2−222−2−222-2200000000002−22−20000
χ19222-2-22-2-200-2-202200022−2−2−2−222002i−2i00000000i2−i2−i2i20000222-2-22-2-200-2-202200022−2−2−2−222002i−2i00000000i2−i2−i2i20000
χ20222-2-22-2-200-2-202200022−2−2−2−22200−2i2i00000000−i2i2i2−i20000222-2-22-2-200-2-202200022−2−2−2−22200−2i2i00000000−i2i2i2−i20000
χ21222-2-22-2-200-2-2022000−2−22222−2−2002i−2i00000000−i2i2i2−i20000222-2-22-2-200-2-2022000−2−22222−2−2002i−2i00000000−i2i2i2−i20000
χ22222-2-22-2-200-2-2022000−2−22222−2−200−2i2i00000000i2−i2−i2i20000222-2-22-2-200-2-2022000−2−22222−2−200−2i2i00000000i2−i2−i2i20000
χ2322-22-2-22-22-200-2002002i−2i2i−2i00000000i2i2−i2−i222−2−20000000022-22-2-22-22-200-2002002i−2i2i−2i00000000i2i2−i2−i222−2−200000000
χ2422-22-2-22-22-200-2002002i−2i2i−2i00000000−i2−i2i2i2−2−2220000000022-22-2-22-22-200-2002002i−2i2i−2i00000000−i2−i2i2i2−2−22200000000
χ2522-22-2-22-22-200-200200−2i2i−2i2i00000000i2i2−i2−i2−2−2220000000022-22-2-22-22-200-200200−2i2i−2i2i00000000i2i2−i2−i2−2−22200000000
χ2622-22-2-22-22-200-200200−2i2i−2i2i00000000−i2−i2i2i222−2−20000000022-22-2-22-22-200-200200−2i2i−2i2i00000000−i2−i2i2i222−2−200000000
χ272-2222-2-2-2222-2-22-2-22-200000000000000002-22-2000000002-2222-2-2-2222-2-22-2-22-200000000000000002-22-200000000
χ282-2222-2-2-2222-2-22-2-22-20000000000000000-22-22000000002-2222-2-2-2222-2-22-2-22-20000000000000000-22-2200000000
χ292-2222-2-2-222-22-2-22-2-220000000000002-22-20000000000002-2222-2-2-222-22-2-22-2-220000000000002-22-2000000000000
χ302-2222-2-2-222-22-2-22-2-22000000000000-22-220000000000002-2222-2-2-222-22-2-22-2-22000000000000-22-22000000000000
χ312-2222-2-2-2-2-22-222-22-22000000000000000000000000002i−2i2-2222-2-2-2-2-22-222-22-22000000000000000000000000002i−2i
χ322-2222-2-2-2-2-22-222-22-2200000000000000000000000000−2i2i2-2222-2-2-2-2-22-222-22-2200000000000000000000000000−2i2i
χ332-2222-2-2-2-2-2-222-2222-20000000000000000000000002i−2i002-2222-2-2-2-2-2-222-2222-20000000000000000000000002i−2i00
χ342-2222-2-2-2-2-2-222-2222-2000000000000000000000000−2i2i002-2222-2-2-2-2-2-222-2222-2000000000000000000000000−2i2i00
χ352-2-22-22-222-200200-20000002i−2i2i−2i0000i2−i2−i2i22−2−22000000002-2-22-22-222-200200-20000002i−2i2i−2i0000i2−i2−i2i22−2−2200000000
χ362-2-22-22-222-200200-20000002i−2i2i−2i0000−i2i2i2−i2−222−2000000002-2-22-22-222-200200-20000002i−2i2i−2i0000−i2i2i2−i2−222−200000000
χ372-2-22-22-222-200200-2000000−2i2i−2i2i0000i2−i2−i2i2−222−2000000002-2-22-22-222-200200-2000000−2i2i−2i2i0000i2−i2−i2i2−222−200000000
χ382-2-22-22-222-200200-2000000−2i2i−2i2i0000−i2i2i2−i22−2−22000000002-2-22-22-222-200200-2000000−2i2i−2i2i0000−i2i2i2−i22−2−2200000000
χ3944-44-4-44-4-4400400-400000000000000000000000000000044-44-4-44-4-4400400-4000000000000000000000000000000
χ4044-4-44-4-4400000000002i2−2i2−2i22i200000000000000000000000044-4-44-4-4400000000002i2−2i2−2i22i2000000000000000000000000
χ4144-4-44-4-440000000000−2i22i22i2−2i200000000000000000000000044-4-44-4-440000000000−2i22i22i2−2i2000000000000000000000000
χ424-44-4-4-444004-40-4400000000000000000000000000000004-44-4-4-444004-40-440000000000000000000000000000000
χ434-44-4-4-44400-4404-400000000000000000000000000000004-44-4-4-44400-4404-40000000000000000000000000000000
χ444-4-44-44-44-4400-40040000000000000000000000000000004-4-44-44-44-4400-4004000000000000000000000000000000
χ454-4-4-4444-4000000000000002i2−2i2−2i22i2000000000000000000004-4-4-4444-4000000000000002i2−2i2−2i22i200000000000000000000
χ464-4-4-4444-400000000000000−2i22i22i2−2i2000000000000000000004-4-4-4444-400000000000000−2i22i22i2−2i200000000000000000000
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
χ48111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ4911111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
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
χ51111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111
χ52111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1
χ53111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1
χ54111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ552222222222-2-22-2-22-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-222-222-222-2-2-2-2222200000000000000000000
χ562222222222-2-22-2-22-2-2-2-2-2-2222200000000000000000000-2-2-2-2-2-2-2-2-2-222-222-2222222-2-2-2-200000000000000000000
χ5722222222-2-222-222-2-2-20000000022-2-20000000000000000-2-2-2-2-2-2-2-222-2-22-2-222200000000-2-2220000000000000000
χ5822222222-2-222-222-2-2-200000000-2-2220000000000000000-2-2-2-2-2-2-2-222-2-22-2-22220000000022-2-20000000000000000
χ5922222222-2-2-2-2-2-2-2-222000000000000000000002i2i−2i−2i0000-2-2-2-2-2-2-2-222222222-2-200000000000000000000−2i−2i2i2i0000
χ6022222222-2-2-2-2-2-2-2-22200000000000000000000−2i−2i2i2i0000-2-2-2-2-2-2-2-222222222-2-2000000000000000000002i2i−2i−2i0000
χ61222-2-22-2-200220-2-200022−2−222−2−22-200000000002−22−20000-2-2-222-22200-2-2022000−2−222−2−222-220000000000−22−220000
χ62222-2-22-2-200220-2-200022−2−222−2−2-220000000000−22−220000-2-2-222-22200-2-2022000−2−222−2−2222-200000000002−22−20000
χ63222-2-22-2-200220-2-2000−2−222−2−2222-20000000000−22−220000-2-2-222-22200-2-202200022−2−222−2−2-2200000000002−22−20000
χ64222-2-22-2-200220-2-2000−2−222−2−222-2200000000002−22−20000-2-2-222-22200-2-202200022−2−222−2−22-20000000000−22−220000
χ65222-2-22-2-200-2-202200022−2−2−2−222002i−2i00000000i2−i2−i2i20000-2-2-222-22200220-2-2000−2−22222−2−200−2i2i00000000−i2i2i2−i20000
χ66222-2-22-2-200-2-202200022−2−2−2−22200−2i2i00000000−i2i2i2−i20000-2-2-222-22200220-2-2000−2−22222−2−2002i−2i00000000i2−i2−i2i20000
χ67222-2-22-2-200-2-2022000−2−22222−2−2002i−2i00000000−i2i2i2−i20000-2-2-222-22200220-2-200022−2−2−2−22200−2i2i00000000i2−i2−i2i20000
χ68222-2-22-2-200-2-2022000−2−22222−2−200−2i2i00000000i2−i2−i2i20000-2-2-222-22200220-2-200022−2−2−2−222002i−2i00000000−i2i2i2−i20000
χ6922-22-2-22-22-200-2002002i−2i2i−2i00000000i2i2−i2−i222−2−200000000-2-22-222-22-2200200-200−2i2i−2i2i00000000−i2−i2i2i2−2−22200000000
χ7022-22-2-22-22-200-2002002i−2i2i−2i00000000−i2−i2i2i2−2−22200000000-2-22-222-22-2200200-200−2i2i−2i2i00000000i2i2−i2−i222−2−200000000
χ7122-22-2-22-22-200-200200−2i2i−2i2i00000000i2i2−i2−i2−2−22200000000-2-22-222-22-2200200-2002i−2i2i−2i00000000−i2−i2i2i222−2−200000000
χ7222-22-2-22-22-200-200200−2i2i−2i2i00000000−i2−i2i2i222−2−200000000-2-22-222-22-2200200-2002i−2i2i−2i00000000i2i2−i2−i2−2−22200000000
χ732-2222-2-2-2222-2-22-2-22-200000000000000002-22-200000000-22-2-2-2222-2-2-222-222-220000000000000000-22-2200000000
χ742-2222-2-2-2222-2-22-2-22-20000000000000000-22-2200000000-22-2-2-2222-2-2-222-222-2200000000000000002-22-200000000
χ752-2222-2-2-222-22-2-22-2-220000000000002-22-2000000000000-22-2-2-2222-2-22-222-222-2000000000000-22-22000000000000
χ762-2222-2-2-222-22-2-22-2-22000000000000-22-22000000000000-22-2-2-2222-2-22-222-222-20000000000002-22-2000000000000
χ772-2222-2-2-2-2-22-222-22-22000000000000000000000000002i−2i-22-2-2-222222-22-2-22-22-200000000000000000000000000−2i2i
χ782-2222-2-2-2-2-22-222-22-2200000000000000000000000000−2i2i-22-2-2-222222-22-2-22-22-2000000000000000000000000002i−2i
χ792-2222-2-2-2-2-2-222-2222-20000000000000000000000002i−2i00-22-2-2-2222222-2-22-2-2-22000000000000000000000000−2i2i00
χ802-2222-2-2-2-2-2-222-2222-2000000000000000000000000−2i2i00-22-2-2-2222222-2-22-2-2-220000000000000000000000002i−2i00
χ812-2-22-22-222-200200-20000002i−2i2i−2i0000i2−i2−i2i22−2−2200000000-222-22-22-2-2200-2002000000−2i2i−2i2i0000−i2i2i2−i2−222−200000000
χ822-2-22-22-222-200200-20000002i−2i2i−2i0000−i2i2i2−i2−222−200000000-222-22-22-2-2200-2002000000−2i2i−2i2i0000i2−i2−i2i22−2−2200000000
χ832-2-22-22-222-200200-2000000−2i2i−2i2i0000i2−i2−i2i2−222−200000000-222-22-22-2-2200-20020000002i−2i2i−2i0000−i2i2i2−i22−2−2200000000
χ842-2-22-22-222-200200-2000000−2i2i−2i2i0000−i2i2i2−i22−2−2200000000-222-22-22-2-2200-20020000002i−2i2i−2i0000i2−i2−i2i2−222−200000000
χ8544-44-4-44-4-4400400-4000000000000000000000000000000-4-44-444-444-400-4004000000000000000000000000000000
χ8644-4-44-4-4400000000002i2−2i2−2i22i2000000000000000000000000-4-444-444-40000000000−2i22i22i2−2i2000000000000000000000000
χ8744-4-44-4-440000000000−2i22i22i2−2i2000000000000000000000000-4-444-444-400000000002i2−2i2−2i22i2000000000000000000000000
χ884-44-4-4-444004-40-440000000000000000000000000000000-44-4444-4-400-4404-40000000000000000000000000000000
χ894-44-4-4-44400-4404-40000000000000000000000000000000-44-4444-4-4004-40-440000000000000000000000000000000
χ904-4-44-44-44-4400-4004000000000000000000000000000000-444-44-44-44-400400-4000000000000000000000000000000
χ914-4-4-4444-4000000000000002i2−2i2−2i22i200000000000000000000-4444-4-4-4400000000000000−2i22i22i2−2i200000000000000000000
χ924-4-4-4444-400000000000000−2i22i22i2−2i200000000000000000000-4444-4-4-44000000000000002i2−2i2−2i22i200000000000000000000

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