Finite Group Databasebeta

← Group #347665

Character table — Group #347665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222222222222222222224444444444444444444444444444444444444444444444161616161616161632323232
order12222222222244444444444488888888888888882222222244444444444444888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-11-1
χ911111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222-2-2-2-2-2-2-222-200000000000000002222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-222-20000000000000000-2-2-2-2-2-2-2-222-2-2-2-222222222000000000000000000000000000000000000
χ19222222222222-2-22222222-2-22222222222222222200000000-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ20222222222222-2-22222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-200000000222222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-2222200000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-222220000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2322222222-2-2-2-222-2-22222-222-200000000000000002222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000000000
χ2422222222-2-2-2-222-2-22222-222-20000000000000000-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2-2-22-2-2222222222-2-2-2-2-2-2-2-20000000022-2-22200000000-2-2-2-222220000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-22-2-22-2-2-2-2-2-2-2-2222222220000000022-2-222000000002222-2-2-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002222-2-200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002222-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ292222-2-2-2-222-2-2220000000-2-202222−2−2−2−22222−2−2−2−222-2-222-2-22-200000000000022−2−222−2−222−2−222−2−222−2−222−2−2000000000000
χ302222-2-2-2-222-2-2220000000-2-202222−2−2−2−22222−2−2−2−2-2-222-2-2222-200000000000022−2−222−2−2−2−222−2−222−2−222−2−222000000000000
χ312222-2-2-2-222-2-2220000000-2-20−2−2−2−22222−2−2−2−2222222-2-222-2-22-2000000000000−2−222−2−222−2−222−2−222−2−222−2−222000000000000
χ322222-2-2-2-222-2-2220000000-2-20−2−2−2−22222−2−2−2−22222-2-222-2-2222-2000000000000−2−222−2−22222−2−222−2−222−2−222−2−2000000000000
χ332222-2-2-2-222-2-2-2-200000002202222−2−2−2−22222−2−2−2−200000000-2200002i2i−2i−2i2i2i−2i−2i−2−222−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ342222-2-2-2-222-2-2-2-200000002202222−2−2−2−22222−2−2−2−200000000-220000−2i−2i2i2i−2i−2i2i2i−2−222−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ352222-2-2-2-222-2-2-2-20000000220−2−2−2−22222−2−2−2−2222200000000-2200002i2i−2i−2i2i2i−2i−2i22−2−222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ362222-2-2-2-222-2-2-2-20000000220−2−2−2−22222−2−2−2−2222200000000-220000−2i−2i2i2i−2i−2i2i2i22−2−222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372222-2-2-2-2-2-222220000000-2-202222−2−2−2−2−2−2−2−2222222-2-2-2-222-2200000000000022−2−2−2−22222−2−222−2−2−2−222−2−222000000000000
χ382222-2-2-2-2-2-222220000000-2-202222−2−2−2−2−2−2−2−22222-2-22222-2-2-2200000000000022−2−2−2−222−2−222−2−22222−2−222−2−2000000000000
χ392222-2-2-2-2-2-222220000000-2-20−2−2−2−222222222−2−2−2−222-2-2-2-222-22000000000000−2−22222−2−2−2−222−2−22222−2−222−2−2000000000000
χ402222-2-2-2-2-2-222220000000-2-20−2−2−2−222222222−2−2−2−2-2-22222-2-2-22000000000000−2−22222−2−222−2−222−2−2−2−222−2−222000000000000
χ412222-2-2-2-2-2-222-2-200000002202222−2−2−2−2−2−2−2−22222000000002-200002i2i−2i−2i−2i−2i2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ422222-2-2-2-2-2-222-2-200000002202222−2−2−2−2−2−2−2−22222000000002-20000−2i−2i2i2i2i2i−2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ432222-2-2-2-2-2-222-2-20000000220−2−2−2−222222222−2−2−2−2000000002-200002i2i−2i−2i−2i−2i2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ442222-2-2-2-2-2-222-2-20000000220−2−2−2−222222222−2−2−2−2000000002-20000−2i−2i2i2i2i2i−2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ4522-2-22-2-222-22-2002-222-2-2200-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000i2−i2i2−i22−22−20000
χ4622-2-22-2-222-22-2002-222-2-2200-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000−i2i2−i2i2−22−220000
χ4722-2-22-2-222-22-2002-222-2-2200-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000i2−i2i2−i2−22−220000
χ4822-2-22-2-222-22-2002-222-2-2200-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000−i2i2−i2i22−22−20000
χ4922-2-22-2-22-22-22002-2-2-222200-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000i2−i2−i2i22−2−220000
χ5022-2-22-2-22-22-22002-2-2-222200-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000−i2i2i2−i2−222−20000
χ5122-2-22-2-22-22-22002-2-2-222200-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000i2−i2−i2i2−222−20000
χ5222-2-22-2-22-22-22002-2-2-222200-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000−i2i2i2−i22−2−220000
χ532-2-2222-2-200002-2002i−2i2i−2i02-202−22−22−22−2i2−i2i2−i2i2−i2i2−i200002-22-200002i−2i2i−2i2i−2i00002−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ542-2-2222-2-200002-2002i−2i2i−2i02-202−22−22−22−2i2−i2i2−i2i2−i2i2−i20000-22-2200002i−2i−2i2i−2i2i00002−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ552-2-2222-2-200002-2002i−2i2i−2i02-20−22−22−22−22−i2i2−i2i2−i2i2−i2i200002-22-200002i−2i2i−2i2i−2i0000−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ562-2-2222-2-200002-2002i−2i2i−2i02-20−22−22−22−22−i2i2−i2i2−i2i2−i2i20000-22-2200002i−2i−2i2i−2i2i0000−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ572-2-2222-2-200002-200−2i2i−2i2i02-202−22−22−22−2−i2i2−i2i2−i2i2−i2i200002-22-20000−2i2i−2i2i−2i2i00002−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ582-2-2222-2-200002-200−2i2i−2i2i02-202−22−22−22−2−i2i2−i2i2−i2i2−i2i20000-22-220000−2i2i2i−2i2i−2i00002−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ592-2-2222-2-200002-200−2i2i−2i2i02-20−22−22−22−22i2−i2i2−i2i2−i2i2−i200002-22-20000−2i2i−2i2i−2i2i0000−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ602-2-2222-2-200002-200−2i2i−2i2i02-20−22−22−22−22i2−i2i2−i2i2−i2i2−i20000-22-220000−2i2i2i−2i2i−2i0000−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ612-2-2222-2-20000-22002i−2i2i−2i0-2202−22−22−22−2i2−i2i2−i2i2−i2i2−i22-22-200000000−2i2i00002i−2i2i−2i−22−22−i2i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ622-2-2222-2-20000-22002i−2i2i−2i0-2202−22−22−22−2i2−i2i2−i2i2−i2i2−i2-22-2200000000−2i2i0000−2i2i−2i2i−22−22−i2i2−i2i2−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ632-2-2222-2-20000-22002i−2i2i−2i0-220−22−22−22−22−i2i2−i2i2−i2i2−i2i22-22-200000000−2i2i00002i−2i2i−2i2−22−2i2−i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ642-2-2222-2-20000-22002i−2i2i−2i0-220−22−22−22−22−i2i2−i2i2−i2i2−i2i2-22-2200000000−2i2i0000−2i2i−2i2i2−22−2i2−i2i2−i22−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ652-2-2222-2-20000-2200−2i2i−2i2i0-2202−22−22−22−2−i2i2−i2i2−i2i2−i2i22-22-2000000002i−2i0000−2i2i−2i2i−22−22i2−i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ662-2-2222-2-20000-2200−2i2i−2i2i0-2202−22−22−22−2−i2i2−i2i2−i2i2−i2i2-22-22000000002i−2i00002i−2i2i−2i−22−22i2−i2i2−i2−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ672-2-2222-2-20000-2200−2i2i−2i2i0-220−22−22−22−22i2−i2i2−i2i2−i2i2−i22-22-2000000002i−2i0000−2i2i−2i2i2−22−2−i2i2−i2i2−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ682-2-2222-2-20000-2200−2i2i−2i2i0-220−22−22−22−22i2−i2i2−i2i2−i2i2−i2-22-22000000002i−2i00002i−2i2i−2i2−22−2−i2i2−i2i22−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ692-2-22-2-22200002-2220000-2-22-2000000002i−2i2i−2i−2i2i−2i2i00002-2-22002-2000000-222-200002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ702-2-22-2-22200002-2220000-2-22-2000000002i−2i2i−2i−2i2i−2i2i0000-222-2002-20000002-2-2200002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ712-2-22-2-22200002-2220000-2-22-200000000−2i2i−2i2i2i−2i2i−2i00002-2-22002-2000000-222-20000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ722-2-22-2-22200002-2220000-2-22-200000000−2i2i−2i2i2i−2i2i−2i0000-222-2002-20000002-2-220000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ732-2-22-2-22200002-2-2-200002-2222-22-2-22-220000000000002-2-2200-220000002-2-222-2-220000000000002-2-222-2-22000000000000
χ742-2-22-2-22200002-2-2-200002-2222-22-2-22-22000000000000-222-200-22000000-222-22-2-22000000000000-222-2-222-2000000000000
χ752-2-22-2-22200002-2-2-200002-222-22-222-22-20000000000002-2-2200-220000002-2-22-222-2000000000000-222-2-222-2000000000000
χ762-2-22-2-22200002-2-2-200002-222-22-222-22-2000000000000-222-200-22000000-222-2-222-20000000000002-2-222-2-22000000000000
χ772-2-22-2-2220000-22220000-22-2-2000000002i−2i2i−2i−2i2i−2i2i2-2-22000000-2200-222-200000000−2i2i2i−2i000000002i−2i−2i2i−2i2i2i−2i000000000000
χ782-2-22-2-2220000-22220000-22-2-2000000002i−2i2i−2i−2i2i−2i2i-222-2000000-22002-2-2200000000−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i000000000000
χ792-2-22-2-2220000-22220000-22-2-200000000−2i2i−2i2i2i−2i2i−2i2-2-22000000-2200-222-2000000002i−2i−2i2i00000000−2i2i2i−2i2i−2i−2i2i000000000000
χ802-2-22-2-2220000-22220000-22-2-200000000−2i2i−2i2i2i−2i2i−2i-222-2000000-22002-2-22000000002i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i000000000000
χ812-2-22-2-2220000-22-2-2000022-222-22-2-22-22000000002-2-220000002-2002-2-220000-222-200002-2-22-222-200000000000000000000
χ822-2-22-2-2220000-22-2-2000022-222-22-2-22-2200000000-222-20000002-200-222-20000-222-20000-222-22-2-2200000000000000000000
χ832-2-22-2-2220000-22-2-2000022-22-22-222-22-2000000002-2-220000002-2002-2-2200002-2-220000-222-22-2-2200000000000000000000
χ842-2-22-2-2220000-22-2-2000022-22-22-222-22-200000000-222-20000002-200-222-200002-2-2200002-2-22-222-200000000000000000000
χ8544-4-44-4-444-44-400-44-4-444-400400000000000000000000000000000000000000000000000000000000000000000000000000
χ8644-4-44-4-44-44-4400-4444-4-4-400400000000000000000000000000000000000000000000000000000000000000000000000000
χ8744-4-4-444-44-4-440000000000002i22i2−2i2−2i2−2i2−2i22i22i22i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000
χ8844-4-4-444-44-4-44000000000000−2i2−2i22i22i22i22i2−2i2−2i2−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000
χ8944-4-4-444-4-444-40000000000002i22i2−2i2−2i2−2i2−2i22i22i2−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000
χ9044-4-4-444-4-444-4000000000000−2i2−2i22i22i22i22i2−2i2−2i22i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000
χ914-44-44-44-4000000004i−4i−4i4i00002i2−2i2−2i22i22i2−2i2−2i22i2−222222−22−222222−220000000000000000000000000000000000000000000000000000000000
χ924-44-44-44-4000000004i−4i−4i4i0000−2i22i22i2−2i2−2i22i22i2−2i222−22−222222−22−22220000000000000000000000000000000000000000000000000000000000
χ934-44-44-44-400000000−4i4i4i−4i00002i2−2i2−2i22i22i2−2i2−2i22i222−22−222222−22−22220000000000000000000000000000000000000000000000000000000000
χ944-44-44-44-400000000−4i4i4i−4i0000−2i22i22i2−2i2−2i22i22i2−2i2−222222−22−222222−220000000000000000000000000000000000000000000000000000000000
χ954-44-4-44-440000004-40000-4004000000004-4-44-444-40000000000000000000000000000000000000000000000000000000000
χ964-44-4-44-440000004-40000-400400000000-444-44-4-440000000000000000000000000000000000000000000000000000000000
χ974-44-4-44-44000000-440000400-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ984-44-4-44-44000000-440000400-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000

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