Finite Group Databasebeta

← Group #495346

Character table — Group #495346

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222224444444488888888888888881616161611112222222222222244444444888888888888888816161616
order122222444488888888444488884444888816161616161616164444222222444488888888444488884444888816161616161616164444
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
χ5111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-1-11-111-11111-1-1-1-111-1-11-11-1ii−i−iii−i−iii−i−iii−i−i1-11-111-1-1-11-111-11111-1-1-1-111-1-11-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011-1-1-11-111-11111-1-1-1-111-1-11-11-1ii−i−iii−i−i−i−iii−i−iii-11-1111-1-1-11-111-11111-1-1-1-111-1-11-11-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ1111-1-1-11-111-11111-1-1-1-111-1-11-11-1−i−iii−i−iiiii−i−iii−i−i-11-1111-1-1-11-111-11111-1-1-1-111-1-11-11-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ1211-1-1-11-111-11111-1-1-1-111-1-11-11-1−i−iii−i−iii−i−iii−i−iii1-11-111-1-1-11-111-11111-1-1-1-111-1-11-11-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ1311-1-1-11-111-111-1-111-1-1-1-1111-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-1111-1-1-11-111-111-1-111-1-1-1-1111-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411-1-1-11-111-111-1-111-1-1-1-1111-1-11ii−i−i−i−iii−i−iiiii−i−i-111-111-1-1-11-111-111-1-111-1-1-1-1111-1-11ii−i−i−i−iii−i−iiiii−i−i-111-1
χ1511-1-1-11-111-111-1-111-1-1-1-1111-1-11−i−iiiii−i−iii−i−i−i−iii-111-111-1-1-11-111-111-1-111-1-1-1-1111-1-11−i−iiiii−i−iii−i−i−i−iii-111-1
χ1611-1-1-11-111-111-1-111-1-1-1-1111-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-1111-1-1-11-111-111-1-111-1-1-1-1111-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ172222222222-2-22222-2-2-2-2-2-2-2-222000000000000000000002222222222-2-22222-2-2-2-2-2-2-2-22200000000000000000000
χ182222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000002222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000
χ192222-2-222-2-2220000220000-2-20000002i−2i2i−2i0000000000002222-2-222-2-2220000220000-2-20000002i−2i2i−2i000000000000
χ202222-2-222-2-2220000220000-2-2000000−2i2i−2i2i0000000000002222-2-222-2-2220000220000-2-2000000−2i2i−2i2i000000000000
χ212222-2-222-2-2-2-20000-2-2000022002-22-200000000000000002222-2-222-2-2-2-20000-2-2000022002-22-20000000000000000
χ222222-2-222-2-2-2-20000-2-200002200-22-2200000000000000002222-2-222-2-2-2-20000-2-200002200-22-220000000000000000
χ232222-2-2-2-22200222200000000-2-200000000i2−i2i2−i2i2−i2i2−i200002222-2-2-2-22200222200000000-2-200000000i2−i2i2−i2i2−i2i2−i20000
χ242222-2-2-2-22200222200000000-2-200000000−i2i2−i2i2−i2i2−i2i200002222-2-2-2-22200222200000000-2-200000000−i2i2−i2i2−i2i2−i2i20000
χ252222-2-2-2-22200-2-2-2-2000000002200000000i2−i2i2−i2−i2i2−i2i200002222-2-2-2-22200-2-2-2-2000000002200000000i2−i2i2−i2−i2i2−i2i20000
χ262222-2-2-2-22200-2-2-2-2000000002200000000−i2i2−i2i2i2−i2i2−i200002222-2-2-2-22200-2-2-2-2000000002200000000−i2i2−i2i2i2−i2i2−i20000
χ2722-2-22-22-22-20022-2-200000000-22000000002−2−222−2−22000022-2-22-22-22-20022-2-200000000-22000000002−2−222−2−220000
χ2822-2-22-22-22-20022-2-200000000-2200000000−222−2−222−2000022-2-22-22-22-20022-2-200000000-2200000000−222−2−222−20000
χ2922-2-22-22-22-200-2-222000000002-2000000002−2−22−222−2000022-2-22-22-22-200-2-222000000002-2000000002−2−22−222−20000
χ3022-2-22-22-22-200-2-222000000002-200000000−222−22−2−22000022-2-22-22-22-200-2-222000000002-200000000−222−22−2−220000
χ3122-2-22-2-22-22220000-2-20000-220000002-2-2200000000000022-2-22-2-22-22220000-2-20000-220000002-2-22000000000000
χ3222-2-22-2-22-22220000-2-20000-22000000-222-200000000000022-2-22-2-22-22220000-2-20000-22000000-222-2000000000000
χ3322-2-22-2-22-22-2-200002200002-2002i−2i−2i2i000000000000000022-2-22-2-22-22-2-200002200002-2002i−2i−2i2i0000000000000000
χ3422-2-22-2-22-22-2-200002200002-200−2i2i2i−2i000000000000000022-2-22-2-22-22-2-200002200002-200−2i2i2i−2i0000000000000000
χ3522-2-2-22-222-2-2-222-2-222-2-222-222-20000000000000000000022-2-2-22-222-2-2-222-2-222-2-222-222-200000000000000000000
χ3622-2-2-22-222-2-2-2-2-2222222-2-2-22-220000000000000000000022-2-2-22-222-2-2-2-2-2222222-2-2-22-2200000000000000000000
χ37444444-4-4-4-4000000000000000000000000000000000000444444-4-4-4-4000000000000000000000000000000000000
χ3844-4-4-444-4-4400000000000000000000000000000000000044-4-4-444-4-44000000000000000000000000000000000000
χ394-44-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-20000000000000000000000004-44-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-2000000000000000000000000
χ404-44-40000002i2−2i2−2i22i2−2i22i22i2−2i2-22-220000000000000000000000004-44-40000002i2−2i2−2i22i2−2i22i22i2−2i2-22-22000000000000000000000000
χ414-44-4000000−2i22i22i2−2i22i2−2i2−2i22i2-22-220000000000000000000000004-44-4000000−2i22i22i2−2i22i2−2i2−2i22i2-22-22000000000000000000000000
χ424-44-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-20000000000000000000000004-44-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-2000000000000000000000000
χ434-4-440000002i2−2i22i2−2i2−2i22i2−2i22i22-2-220000000000000000000000004-4-440000002i2−2i22i2−2i2−2i22i2−2i22i22-2-22000000000000000000000000
χ444-4-440000002i2−2i2−2i22i22i2−2i2−2i22i2-222-20000000000000000000000004-4-440000002i2−2i2−2i22i22i2−2i2−2i22i2-222-2000000000000000000000000
χ454-4-44000000−2i22i22i2−2i2−2i22i22i2−2i2-222-20000000000000000000000004-4-44000000−2i22i22i2−2i2−2i22i22i2−2i2-222-2000000000000000000000000
χ464-4-44000000−2i22i2−2i22i22i2−2i22i2−2i22-2-220000000000000000000000004-4-44000000−2i22i2−2i22i22i2−2i22i2−2i22-2-22000000000000000000000000
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
χ51111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-111
χ52111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-1
χ53111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ54111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ5511-1-1-11-111-11111-1-1-1-111-1-11-11-1ii−i−iii−i−iii−i−iii−i−i1-11-1-1-1111-11-1-11-1-1-1-11111-1-111-11-11−i−iii−i−iii−i−iii−i−iii-11-11
χ5611-1-1-11-111-11111-1-1-1-111-1-11-11-1ii−i−iii−i−i−i−iii−i−iii-11-11-1-1111-11-1-11-1-1-1-11111-1-111-11-11−i−iii−i−iiiii−i−iii−i−i1-11-1
χ5711-1-1-11-111-11111-1-1-1-111-1-11-11-1−i−iii−i−iiiii−i−iii−i−i-11-11-1-1111-11-1-11-1-1-1-11111-1-111-11-11ii−i−iii−i−i−i−iii−i−iii1-11-1
χ5811-1-1-11-111-11111-1-1-1-111-1-11-11-1−i−iii−i−iii−i−iii−i−iii1-11-1-1-1111-11-1-11-1-1-1-11111-1-111-11-11ii−i−iii−i−iii−i−iii−i−i-11-11
χ5911-1-1-11-111-111-1-111-1-1-1-1111-1-11ii−i−i−i−iiiii−i−i−i−iii1-1-11-1-1111-11-1-11-1-111-1-11111-1-1-111-1−i−iiiii−i−i−i−iiiii−i−i-111-1
χ6011-1-1-11-111-111-1-111-1-1-1-1111-1-11ii−i−i−i−iii−i−iiiii−i−i-111-1-1-1111-11-1-11-1-111-1-11111-1-1-111-1−i−iiiii−i−iii−i−i−i−iii1-1-11
χ6111-1-1-11-111-111-1-111-1-1-1-1111-1-11−i−iiiii−i−iii−i−i−i−iii-111-1-1-1111-11-1-11-1-111-1-11111-1-1-111-1ii−i−i−i−iii−i−iiiii−i−i1-1-11
χ6211-1-1-11-111-111-1-111-1-1-1-1111-1-11−i−iiiii−i−i−i−iiiii−i−i1-1-11-1-1111-11-1-11-1-111-1-11111-1-1-111-1ii−i−i−i−iiiii−i−i−i−iii-111-1
χ632222222222-2-22222-2-2-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-200000000000000000000
χ642222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2222200000000000000000000
χ652222-2-222-2-2220000220000-2-20000002i−2i2i−2i000000000000-2-2-2-222-2-222-2-20000-2-2000022000000−2i2i−2i2i000000000000
χ662222-2-222-2-2220000220000-2-2000000−2i2i−2i2i000000000000-2-2-2-222-2-222-2-20000-2-20000220000002i−2i2i−2i000000000000
χ672222-2-222-2-2-2-20000-2-2000022002-22-20000000000000000-2-2-2-222-2-222220000220000-2-200-22-220000000000000000
χ682222-2-222-2-2-2-20000-2-200002200-22-220000000000000000-2-2-2-222-2-222220000220000-2-2002-22-20000000000000000
χ692222-2-2-2-22200222200000000-2-200000000i2−i2i2−i2i2−i2i2−i20000-2-2-2-22222-2-200-2-2-2-2000000002200000000−i2i2−i2i2−i2i2−i2i20000
χ702222-2-2-2-22200222200000000-2-200000000−i2i2−i2i2−i2i2−i2i20000-2-2-2-22222-2-200-2-2-2-2000000002200000000i2−i2i2−i2i2−i2i2−i20000
χ712222-2-2-2-22200-2-2-2-2000000002200000000i2−i2i2−i2−i2i2−i2i20000-2-2-2-22222-2-200222200000000-2-200000000−i2i2−i2i2i2−i2i2−i20000
χ722222-2-2-2-22200-2-2-2-2000000002200000000−i2i2−i2i2i2−i2i2−i20000-2-2-2-22222-2-200222200000000-2-200000000i2−i2i2−i2−i2i2−i2i20000
χ7322-2-22-22-22-20022-2-200000000-22000000002−2−222−2−220000-2-222-22-22-2200-2-222000000002-200000000−222−2−222−20000
χ7422-2-22-22-22-20022-2-200000000-2200000000−222−2−222−20000-2-222-22-22-2200-2-222000000002-2000000002−2−222−2−220000
χ7522-2-22-22-22-200-2-222000000002-2000000002−2−22−222−20000-2-222-22-22-220022-2-200000000-2200000000−222−22−2−220000
χ7622-2-22-22-22-200-2-222000000002-200000000−222−22−2−220000-2-222-22-22-220022-2-200000000-22000000002−2−22−222−20000
χ7722-2-22-2-22-22220000-2-20000-220000002-2-22000000000000-2-222-222-22-2-2-200002200002-2000000-222-2000000000000
χ7822-2-22-2-22-22220000-2-20000-22000000-222-2000000000000-2-222-222-22-2-2-200002200002-20000002-2-22000000000000
χ7922-2-22-2-22-22-2-200002200002-2002i−2i−2i2i0000000000000000-2-222-222-22-2220000-2-20000-2200−2i2i2i−2i0000000000000000
χ8022-2-22-2-22-22-2-200002200002-200−2i2i2i−2i0000000000000000-2-222-222-22-2220000-2-20000-22002i−2i−2i2i0000000000000000
χ8122-2-2-22-222-2-2-222-2-222-2-222-222-200000000000000000000-2-2222-22-2-2222-2-222-2-222-2-22-2-2200000000000000000000
χ8222-2-2-22-222-2-2-2-2-2222222-2-2-22-2200000000000000000000-2-2222-22-2-222222-2-2-2-2-2-2222-22-200000000000000000000
χ83444444-4-4-4-4000000000000000000000000000000000000-4-4-4-4-4-44444000000000000000000000000000000000000
χ8444-4-4-444-4-44000000000000000000000000000000000000-4-4444-4-444-4000000000000000000000000000000000000
χ854-44-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-2000000000000000000000000-44-44000000−2i22i2−2i22i2−2i22i2−2i22i2-22-22000000000000000000000000
χ864-44-40000002i2−2i2−2i22i2−2i22i22i2−2i2-22-22000000000000000000000000-44-44000000−2i22i22i2−2i22i2−2i2−2i22i22-22-2000000000000000000000000
χ874-44-4000000−2i22i22i2−2i22i2−2i2−2i22i2-22-22000000000000000000000000-44-440000002i2−2i2−2i22i2−2i22i22i2−2i22-22-2000000000000000000000000
χ884-44-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-2000000000000000000000000-44-440000002i2−2i22i2−2i22i2−2i22i2−2i2-22-22000000000000000000000000
χ894-4-440000002i2−2i22i2−2i2−2i22i2−2i22i22-2-22000000000000000000000000-444-4000000−2i22i2−2i22i22i2−2i22i2−2i2-222-2000000000000000000000000
χ904-4-440000002i2−2i2−2i22i22i2−2i2−2i22i2-222-2000000000000000000000000-444-4000000−2i22i22i2−2i2−2i22i22i2−2i22-2-22000000000000000000000000
χ914-4-44000000−2i22i22i2−2i2−2i22i22i2−2i2-222-2000000000000000000000000-444-40000002i2−2i2−2i22i22i2−2i2−2i22i22-2-22000000000000000000000000
χ924-4-44000000−2i22i2−2i22i22i2−2i22i2−2i22-2-22000000000000000000000000-444-40000002i2−2i22i2−2i2−2i22i2−2i22i2-222-2000000000000000000000000

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