Finite Group Databasebeta

← Group #331111

Character table — Group #331111

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444444444444444444444444444444444443232323232323232
order12222222222244444444444444444444444488888888888888888888888888888888888888888888888824444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-11-11
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111-11-1
χ911111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ1011111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ1111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ1211111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ1311111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-11
χ1411111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111-1
χ1511111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-111-1
χ1611111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111-11-1-11
χ17222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000002222-2-2-2-22222-2-2-2-200000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000-2-2-2-22222-2-2-2-2222200000000
χ19222222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000002222-2-2-2-22222-2-2-2-2000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-22222-2-2222222-2-2-2-2000000000000000000000000000000002222-2-2-2-2-2-2-2-2222200000000
χ2422222222-2-2-2-222-2-2-2-2-2-22222-2-2222222-2-2-2-200000000000000000000000000000000-2-2-2-222222222-2-2-2-200000000
χ2522222222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-222-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-22200000000000000002222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2822222222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2220000000000000000-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2922-22-2-2-220000002i2i−2i−2i002i2i−2i−2i2-2000000002-222−2−222−2−2i2i2−i2−i2i2i2−i2−i200002i2i−2i−2i22-2-20000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ3022-22-2-2-220000002i2i−2i−2i002i2i−2i−2i2-2000000002-222−2−222−2−2i2i2−i2−i2i2i2−i2−i20000−2i−2i2i2i-2-2220000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ3122-22-2-2-220000002i2i−2i−2i002i2i−2i−2i2-2000000002-2−2−222−2−222−i2−i2i2i2−i2−i2i2i200002i2i−2i−2i22-2-20000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ3222-22-2-2-220000002i2i−2i−2i002i2i−2i−2i2-2000000002-2−2−222−2−222−i2−i2i2i2−i2−i2i2i20000−2i−2i2i2i-2-2220000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ3322-22-2-2-220000002i2i−2i−2i00−2i−2i2i2i-2200000000-2222−2−2−2−222−i2−i2i2i2i2i2−i2−i22i2i−2i−2i0000000022-2-2i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ3422-22-2-2-220000002i2i−2i−2i00−2i−2i2i2i-2200000000-2222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i00000000-2-222−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ3522-22-2-2-220000002i2i−2i−2i00−2i−2i2i2i-2200000000-22−2−22222−2−2i2i2−i2−i2−i2−i2i2i22i2i−2i−2i0000000022-2-2−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ3622-22-2-2-220000002i2i−2i−2i00−2i−2i2i2i-2200000000-22−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i00000000-2-222i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ3722-22-2-2-22000000−2i−2i2i2i002i2i−2i−2i-2200000000-2222−2−2−2−222i2i2−i2−i2−i2−i2i2i22i2i−2i−2i00000000-2-222i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ3822-22-2-2-22000000−2i−2i2i2i002i2i−2i−2i-2200000000-2222−2−2−2−222i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i0000000022-2-2−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ3922-22-2-2-22000000−2i−2i2i2i002i2i−2i−2i-2200000000-22−2−22222−2−2−i2−i2i2i2i2i2−i2−i22i2i−2i−2i00000000-2-222−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ4022-22-2-2-22000000−2i−2i2i2i002i2i−2i−2i-2200000000-22−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i0000000022-2-2i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ4122-22-2-2-22000000−2i−2i2i2i00−2i−2i2i2i2-2000000002-222−2−222−2−2−i2−i2i2i2−i2−i2i2i200002i2i−2i−2i-2-2220000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ4222-22-2-2-22000000−2i−2i2i2i00−2i−2i2i2i2-2000000002-222−2−222−2−2−i2−i2i2i2−i2−i2i2i20000−2i−2i2i2i22-2-20000−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ4322-22-2-2-22000000−2i−2i2i2i00−2i−2i2i2i2-2000000002-2−2−222−2−222i2i2−i2−i2i2i2−i2−i200002i2i−2i−2i-2-2220000−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ4422-22-2-2-22000000−2i−2i2i2i00−2i−2i2i2i2-2000000002-2−2−222−2−222i2i2−i2−i2i2i2−i2−i20000−2i−2i2i2i22-2-20000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ452-222-2-22-200002-20000002i−2i2i−2i002i2i−2i−2i2-200002−22−22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i200002-22-22i−2i2i−2i000000000000
χ462-222-2-22-200002-20000002i−2i2i−2i002i2i−2i−2i2-200002−22−22−22−2i2−i2i2−i2i2−i2i2−i2−22−22−22−22−i2i2−i2i2−i2i2−i2i20000-22-22−2i2i−2i2i000000000000
χ472-222-2-22-200002-20000002i−2i2i−2i002i2i−2i−2i2-20000−22−22−22−22−i2i2−i2i2−i2i2−i2i22−22−22−22−2i2−i2i2−i2i2−i2i2−i20000-22-22−2i2i−2i2i000000000000
χ482-222-2-22-200002-20000002i−2i2i−2i002i2i−2i−2i2-20000−22−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i200002-22-22i−2i2i−2i000000000000
χ492-222-2-22-200002-2000000−2i2i−2i2i00−2i−2i2i2i2-200002−22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i200002-22-2−2i2i−2i2i000000000000
χ502-222-2-22-200002-2000000−2i2i−2i2i00−2i−2i2i2i2-200002−22−22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000-22-222i−2i2i−2i000000000000
χ512-222-2-22-200002-2000000−2i2i−2i2i00−2i−2i2i2i2-20000−22−22−22−22i2−i2i2−i2i2−i2i2−i22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000-22-222i−2i2i−2i000000000000
χ522-222-2-22-200002-2000000−2i2i−2i2i00−2i−2i2i2i2-20000−22−22−22−22i2−i2i2−i2i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i200002-22-2−2i2i−2i2i000000000000
χ532-222-2-22-20000-220000002i−2i2i−2i00−2i−2i2i2i-2200002−22−2−22−22i2−i2i2−i2−i2i2−i2i22−22−2−22−22−i2i2−i2i2i2−i2i2−i22-22-2000000002i−2i2i−2i00000000
χ542-222-2-22-20000-220000002i−2i2i−2i00−2i−2i2i2i-2200002−22−2−22−22i2−i2i2−i2−i2i2−i2i2−22−222−22−2i2−i2i2−i2−i2i2−i2i2-22-2200000000−2i2i−2i2i00000000
χ552-222-2-22-20000-220000002i−2i2i−2i00−2i−2i2i2i-220000−22−222−22−2−i2i2−i2i2i2−i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i2-22-2200000000−2i2i−2i2i00000000
χ562-222-2-22-20000-220000002i−2i2i−2i00−2i−2i2i2i-220000−22−222−22−2−i2i2−i2i2i2−i2i2−i2−22−222−22−2i2−i2i2−i2−i2i2−i2i22-22-2000000002i−2i2i−2i00000000
χ572-222-2-22-20000-22000000−2i2i−2i2i002i2i−2i−2i-2200002−22−2−22−22−i2i2−i2i2i2−i2i2−i22−22−2−22−22i2−i2i2−i2−i2i2−i2i22-22-200000000−2i2i−2i2i00000000
χ582-222-2-22-20000-22000000−2i2i−2i2i002i2i−2i−2i-2200002−22−2−22−22−i2i2−i2i2i2−i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i2-22-22000000002i−2i2i−2i00000000
χ592-222-2-22-20000-22000000−2i2i−2i2i002i2i−2i−2i-220000−22−222−22−2i2−i2i2−i2−i2i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i2-22-22000000002i−2i2i−2i00000000
χ602-222-2-22-20000-22000000−2i2i−2i2i002i2i−2i−2i-220000−22−222−22−2i2−i2i2−i2−i2i2−i2i2−22−222−22−2−i2i2−i2i2i2−i2i2−i22-22-200000000−2i2i−2i2i00000000
χ612-2-2222-2-222-2-20000002-22-2-22000000002-20000002-2-2200002-2-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ622-2-2222-2-222-2-20000002-22-2-22000000002-20000002-2-2200002-2-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ632-2-2222-2-222-2-20000002-22-2-22000000002-2000000-222-20000-222-2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ642-2-2222-2-222-2-20000002-22-2-22000000002-2000000-222-20000-222-2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ652-2-2222-2-222-2-2000000-22-222-200000000-22002-2-220000-222-20000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ662-2-2222-2-222-2-2000000-22-222-200000000-22002-2-220000-222-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ672-2-2222-2-222-2-2000000-22-222-200000000-2200-222-200002-2-220000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ682-2-2222-2-222-2-2000000-22-222-200000000-2200-222-200002-2-220000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ692-2-2222-2-2-2-2220000002-2-222-2000000002-20000002-2-220000-222-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ702-2-2222-2-2-2-2220000002-2-222-2000000002-20000002-2-220000-222-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ712-2-2222-2-2-2-2220000002-2-222-2000000002-2000000-222-200002-2-22i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ722-2-2222-2-2-2-2220000002-2-222-2000000002-2000000-222-200002-2-22−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ732-2-2222-2-2-2-222000000-222-2-2200000000-22002-2-2200002-2-220000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ742-2-2222-2-2-2-222000000-222-2-2200000000-22002-2-2200002-2-220000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ752-2-2222-2-2-2-222000000-222-2-2200000000-2200-222-20000-222-20000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ762-2-2222-2-2-2-222000000-222-2-2200000000-2200-222-20000-222-20000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ77444-44-4-4-44-44-44-44-44-4000000000000-44000000000000000000000000000000000000000000000000000000000000
χ78444-44-4-4-44-44-4-44-44-440000000000004-4000000000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-4-44-444-4-44-44000000000000-44000000000000000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-44-44-444-44-40000000000004-4000000000000000000000000000000000000000000000000000000000000
χ8144-4-4-444-40000004i−4i−4i4i4-40000004i−4i4i−4i00-440000000000000000000000000000000000000000000000000000000000
χ8244-4-4-444-40000004i−4i−4i4i-44000000−4i4i−4i4i004-40000000000000000000000000000000000000000000000000000000000
χ8344-4-4-444-4000000−4i4i4i−4i4-4000000−4i4i−4i4i00-440000000000000000000000000000000000000000000000000000000000
χ8444-4-4-444-4000000−4i4i4i−4i-440000004i−4i4i−4i004-40000000000000000000000000000000000000000000000000000000000
χ854-44-4-44-440000440000440000440000-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000
χ864-44-4-44-440000440000-4-40000-4-40000-4-4444400000000000000000000000000000000000000000000000000000000
χ874-44-4-44-440000-4-40000440000-4-4000044-4-44400000000000000000000000000000000000000000000000000000000
χ884-44-4-44-440000-4-40000-4-400004400004444-4-400000000000000000000000000000000000000000000000000000000
χ894-4-4-44-4444-4-440000000000004-4-444-40000-4400000000000000000000000000000000000000000000000000000000
χ904-4-4-44-4444-4-44000000000000-444-4-4400004-400000000000000000000000000000000000000000000000000000000
χ914-4-4-44-444-444-40000000000004-44-4-440000-4400000000000000000000000000000000000000000000000000000000
χ924-4-4-44-444-444-4000000000000-44-444-400004-400000000000000000000000000000000000000000000000000000000

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