Finite Group Databasebeta

← Group #197708

Character table — Group #197708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222444444444488888888224488888888888844442222222244444444448888888822448888888888884444
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
χ91-1-1-111-111-111-11-1-11-1ii−i−iii−i−i1-11-1ii−i−i11-1-1ii−i−ii−i1-11-1-1-111-111-111-11-1-11-1ii−i−iii−i−i1-11-1ii−i−i11-1-1ii−i−ii−i1-1
χ101-1-1-111-111-111-11-1-11-1ii−i−iii−i−i1-11-1−i−iii-1-111ii−i−i−ii-111-1-1-111-111-111-11-1-11-1ii−i−iii−i−i1-11-1−i−iii-1-111ii−i−i−ii-11
χ111-1-1-111-111-111-11-1-11-1ii−i−iii−i−i-11-11ii−i−i11-1-1−i−iii−ii-111-1-1-111-111-111-11-1-11-1ii−i−iii−i−i-11-11ii−i−i11-1-1−i−iii−ii-11
χ121-1-1-111-111-111-11-1-11-1ii−i−iii−i−i-11-11−i−iii-1-111−i−iiii−i1-11-1-1-111-111-111-11-1-11-1ii−i−iii−i−i-11-11−i−iii-1-111−i−iiii−i1-1
χ131-1-1-111-111-111-11-1-11-1−i−iii−i−iii1-11-1ii−i−i-1-111−i−iiii−i-111-1-1-111-111-111-11-1-11-1−i−iii−i−iii1-11-1ii−i−i-1-111−i−iiii−i-11
χ141-1-1-111-111-111-11-1-11-1−i−iii−i−iii1-11-1−i−iii11-1-1−i−iii−ii1-11-1-1-111-111-111-11-1-11-1−i−iii−i−iii1-11-1−i−iii11-1-1−i−iii−ii1-1
χ151-1-1-111-111-111-11-1-11-1−i−iii−i−iii-11-11ii−i−i-1-111ii−i−i−ii1-11-1-1-111-111-111-11-1-11-1−i−iii−i−iii-11-11ii−i−i-1-111ii−i−i−ii1-1
χ161-1-1-111-111-111-11-1-11-1−i−iii−i−iii-11-11−i−iii11-1-1ii−i−ii−i-111-1-1-111-111-111-11-1-11-1−i−iii−i−iii-11-11−i−iii11-1-1ii−i−ii−i-11
χ172222222222-2-2-222-2-2-20000000022-2-200000000000000002222222222-2-2-222-2-2-20000000022-2-20000000000000000
χ182222222222-2-2-222-2-2-200000000-2-22200000000000000002222222222-2-2-222-2-2-200000000-2-2220000000000000000
χ1922222222-2-2222-2-22-2-22222-2-2-2-20000000000000000000022222222-2-2222-2-22-2-22222-2-2-2-200000000000000000000
χ2022222222-2-2222-2-22-2-2-2-2-2-222220000000000000000000022222222-2-2222-2-22-2-2-2-2-2-2222200000000000000000000
χ2122222222-2-2-2-2-2-2-2-222000000000000000000002i−2i2i−2i000022222222-2-2-2-2-2-2-2-222000000000000000000002i−2i2i−2i0000
χ2222222222-2-2-2-2-2-2-2-22200000000000000000000−2i2i−2i2i000022222222-2-2-2-2-2-2-2-22200000000000000000000−2i2i−2i2i0000
χ23222-2-22-2-2002-2-20020000002-22-20000i2−i2i2−i2i2−i2i2−i200000000222-2-22-2-2002-2-20020000002-22-20000i2−i2i2−i2i2−i2i2−i200000000
χ24222-2-22-2-2002-2-20020000002-22-20000−i2i2−i2i2−i2i2−i2i200000000222-2-22-2-2002-2-20020000002-22-20000−i2i2−i2i2−i2i2−i2i200000000
χ25222-2-22-2-2002-2-2002000000-22-220000i2−i2i2−i2−i2i2−i2i200000000222-2-22-2-2002-2-2002000000-22-220000i2−i2i2−i2−i2i2−i2i200000000
χ26222-2-22-2-2002-2-2002000000-22-220000−i2i2−i2i2i2−i2i2−i200000000222-2-22-2-2002-2-2002000000-22-220000−i2i2−i2i2i2−i2i2−i200000000
χ272-2-22-222-2002-2200-20000002i−2i−2i2i00002−2−22−i2i2i2−i2000000002-2-22-222-2002-2200-20000002i−2i−2i2i00002−2−22−i2i2i2−i200000000
χ282-2-22-222-2002-2200-20000002i−2i−2i2i0000−222−2i2−i2−i2i2000000002-2-22-222-2002-2200-20000002i−2i−2i2i0000−222−2i2−i2−i2i200000000
χ292-2-22-222-2002-2200-2000000−2i2i2i−2i00002−2−22i2−i2−i2i2000000002-2-22-222-2002-2200-2000000−2i2i2i−2i00002−2−22i2−i2−i2i200000000
χ302-2-22-222-2002-2200-2000000−2i2i2i−2i0000−222−2−i2i2i2−i2000000002-2-22-222-2002-2200-2000000−2i2i2i−2i0000−222−2−i2i2i2−i200000000
χ312-2-2-222-222-2-2-222-22-22000000002-2-2200000000000000002-2-2-222-222-2-2-222-22-22000000002-2-220000000000000000
χ322-2-2-222-222-2-2-222-22-2200000000-222-200000000000000002-2-2-222-222-2-2-222-22-2200000000-222-20000000000000000
χ332-2-2-222-22-2222-2-22-2-222i2i−2i−2i−2i−2i2i2i000000000000000000002-2-2-222-22-2222-2-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ342-2-2-222-22-2222-2-22-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000002-2-2-222-22-2222-2-22-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ352-2-2-222-22-22-2-22-2222-2000000000000000000002-2-2200002-2-2-222-22-22-2-22-2222-2000000000000000000002-2-220000
χ362-2-2-222-22-22-2-22-2222-200000000000000000000-222-200002-2-2-222-22-22-2-22-2222-200000000000000000000-222-20000
χ37444-4-44-4-400-44400-4000000000000000000000000000000444-4-44-4-400-44400-4000000000000000000000000000000
χ3844-444-4-4-44-4000-44000000000000000000000000000000044-444-4-4-44-4000-440000000000000000000000000000000
χ3944-444-4-4-4-440004-4000000000000000000000000000000044-444-4-4-4-440004-40000000000000000000000000000000
χ4044-4-4-4-444000000000022−2222−2200000000000000000000000044-4-4-4-444000000000022−2222−22000000000000000000000000
χ4144-4-4-4-4440000000000−2222−222200000000000000000000000044-4-4-4-4440000000000−2222−2222000000000000000000000000
χ424-444-4-4-4400000000002i2−2i2−2i22i20000000000000000000000004-444-4-4-4400000000002i2−2i2−2i22i2000000000000000000000000
χ434-444-4-4-440000000000−2i22i22i2−2i20000000000000000000000004-444-4-4-440000000000−2i22i22i2−2i2000000000000000000000000
χ444-44-44-44-444000-4-400000000000000000000000000000004-44-44-44-444000-4-40000000000000000000000000000000
χ454-44-44-44-4-4-40004400000000000000000000000000000004-44-44-44-4-4-4000440000000000000000000000000000000
χ464-4-44-444-400-44-40040000000000000000000000000000004-4-44-444-400-44-4004000000000000000000000000000000
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
χ551-1-1-111-111-111-11-1-11-1ii−i−iii−i−i1-11-1ii−i−i11-1-1ii−i−ii−i1-1-1111-1-11-1-11-1-11-111-11−i−iii−i−iii-11-11−i−iii-1-111−i−iii−ii-11
χ561-1-1-111-111-111-11-1-11-1ii−i−iii−i−i1-11-1−i−iii-1-111ii−i−i−ii-11-1111-1-11-1-11-1-11-111-11−i−iii−i−iii-11-11ii−i−i11-1-1−i−iiii−i1-1
χ571-1-1-111-111-111-11-1-11-1ii−i−iii−i−i-11-11ii−i−i11-1-1−i−iii−ii-11-1111-1-11-1-11-1-11-111-11−i−iii−i−iii1-11-1−i−iii-1-111ii−i−ii−i1-1
χ581-1-1-111-111-111-11-1-11-1ii−i−iii−i−i-11-11−i−iii-1-111−i−iiii−i1-1-1111-1-11-1-11-1-11-111-11−i−iii−i−iii1-11-1ii−i−i11-1-1ii−i−i−ii-11
χ591-1-1-111-111-111-11-1-11-1−i−iii−i−iii1-11-1ii−i−i-1-111−i−iiii−i-11-1111-1-11-1-11-1-11-111-11ii−i−iii−i−i-11-11−i−iii11-1-1ii−i−i−ii1-1
χ601-1-1-111-111-111-11-1-11-1−i−iii−i−iii1-11-1−i−iii11-1-1−i−iii−ii1-1-1111-1-11-1-11-1-11-111-11ii−i−iii−i−i-11-11ii−i−i-1-111ii−i−ii−i-11
χ611-1-1-111-111-111-11-1-11-1−i−iii−i−iii-11-11ii−i−i-1-111ii−i−i−ii1-1-1111-1-11-1-11-1-11-111-11ii−i−iii−i−i1-11-1−i−iii11-1-1−i−iiii−i-11
χ621-1-1-111-111-111-11-1-11-1−i−iii−i−iii-11-11−i−iii11-1-1ii−i−ii−i-11-1111-1-11-1-11-1-11-111-11ii−i−iii−i−i1-11-1ii−i−i-1-111−i−iii−ii1-1
χ632222222222-2-2-222-2-2-20000000022-2-20000000000000000-2-2-2-2-2-2-2-2-2-2222-2-222200000000-2-2220000000000000000
χ642222222222-2-2-222-2-2-200000000-2-2220000000000000000-2-2-2-2-2-2-2-2-2-2222-2-22220000000022-2-20000000000000000
χ6522222222-2-2222-2-22-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-222-2-2-222-222-2-2-2-2222200000000000000000000
χ6622222222-2-2222-2-22-2-2-2-2-2-2222200000000000000000000-2-2-2-2-2-2-2-222-2-2-222-2222222-2-2-2-200000000000000000000
χ6722222222-2-2-2-2-2-2-2-222000000000000000000002i−2i2i−2i0000-2-2-2-2-2-2-2-222222222-2-200000000000000000000−2i2i−2i2i0000
χ6822222222-2-2-2-2-2-2-2-22200000000000000000000−2i2i−2i2i0000-2-2-2-2-2-2-2-222222222-2-2000000000000000000002i−2i2i−2i0000
χ69222-2-22-2-2002-2-20020000002-22-20000i2−i2i2−i2i2−i2i2−i200000000-2-2-222-22200-22200-2000000-22-220000−i2i2−i2i2−i2i2−i2i200000000
χ70222-2-22-2-2002-2-20020000002-22-20000−i2i2−i2i2−i2i2−i2i200000000-2-2-222-22200-22200-2000000-22-220000i2−i2i2−i2i2−i2i2−i200000000
χ71222-2-22-2-2002-2-2002000000-22-220000i2−i2i2−i2−i2i2−i2i200000000-2-2-222-22200-22200-20000002-22-20000−i2i2−i2i2i2−i2i2−i200000000
χ72222-2-22-2-2002-2-2002000000-22-220000−i2i2−i2i2i2−i2i2−i200000000-2-2-222-22200-22200-20000002-22-20000i2−i2i2−i2−i2i2−i2i200000000
χ732-2-22-222-2002-2200-20000002i−2i−2i2i00002−2−22−i2i2i2−i200000000-222-22-2-2200-22-2002000000−2i2i2i−2i0000−222−2i2−i2−i2i200000000
χ742-2-22-222-2002-2200-20000002i−2i−2i2i0000−222−2i2−i2−i2i200000000-222-22-2-2200-22-2002000000−2i2i2i−2i00002−2−22−i2i2i2−i200000000
χ752-2-22-222-2002-2200-2000000−2i2i2i−2i00002−2−22i2−i2−i2i200000000-222-22-2-2200-22-20020000002i−2i−2i2i0000−222−2−i2i2i2−i200000000
χ762-2-22-222-2002-2200-2000000−2i2i2i−2i0000−222−2−i2i2i2−i200000000-222-22-2-2200-22-20020000002i−2i−2i2i00002−2−22i2−i2−i2i200000000
χ772-2-2-222-222-2-2-222-22-22000000002-2-220000000000000000-2222-2-22-2-2222-2-22-22-200000000-222-20000000000000000
χ782-2-2-222-222-2-2-222-22-2200000000-222-20000000000000000-2222-2-22-2-2222-2-22-22-2000000002-2-220000000000000000
χ792-2-2-222-22-2222-2-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000-2222-2-22-22-2-2-222-222-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ802-2-2-222-22-2222-2-22-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000-2222-2-22-22-2-2-222-222-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ812-2-2-222-22-22-2-22-2222-2000000000000000000002-2-220000-2222-2-22-22-222-22-2-2-2200000000000000000000-222-20000
χ822-2-2-222-22-22-2-22-2222-200000000000000000000-222-20000-2222-2-22-22-222-22-2-2-22000000000000000000002-2-220000
χ83444-4-44-4-400-44400-4000000000000000000000000000000-4-4-444-444004-4-4004000000000000000000000000000000
χ8444-444-4-4-44-4000-440000000000000000000000000000000-4-44-4-4444-440004-40000000000000000000000000000000
χ8544-444-4-4-4-440004-40000000000000000000000000000000-4-44-4-44444-4000-440000000000000000000000000000000
χ8644-4-4-4-444000000000022−2222−22000000000000000000000000-4-44444-4-40000000000−2222−2222000000000000000000000000
χ8744-4-4-4-4440000000000−2222−2222000000000000000000000000-4-44444-4-4000000000022−2222−22000000000000000000000000
χ884-444-4-4-4400000000002i2−2i2−2i22i2000000000000000000000000-44-4-4444-40000000000−2i22i22i2−2i2000000000000000000000000
χ894-444-4-4-440000000000−2i22i22i2−2i2000000000000000000000000-44-4-4444-400000000002i2−2i2−2i22i2000000000000000000000000
χ904-44-44-44-444000-4-40000000000000000000000000000000-44-44-44-44-4-4000440000000000000000000000000000000
χ914-44-44-44-4-4-4000440000000000000000000000000000000-44-44-44-4444000-4-40000000000000000000000000000000
χ924-4-44-444-400-44-4004000000000000000000000000000000-444-44-4-44004-4400-4000000000000000000000000000000

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