Finite Group Databasebeta

← Group #347663

Character table — Group #347663

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222222222222222222224444444444444444444444444444444444444444444444161616161616161632323232
order12222222222244444444444488888888888888884444444444444444444444888888888888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ1211111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ1411111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ1511111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222222-2-22-2-222222222222222222-2-2-2-200000000-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-22-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-200000000222222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-222-222-20000000000000000-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-222-222-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222200000000-2-200000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222200000000-2-20000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-22-2-2222222222-2-2-2-2-2-2-2-2-2-222000000002200000000-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-22-2-22-2-2-2-2-2-2-2-222222222-2-2220000000022000000002222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2222222-222-20000000000000000-2-2222222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-222-20000000000000000-2-222-2-2-2-22222-2-22222-2-2-2-2000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-2000000002200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-200000000220000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ29222-2-2-2-220000002i2i−2i−2i2-202-20i2i2i2i2−i2−i2−i2−i22222−2−2−2−2002i−2i00002i2i−2i−2i0022-2-20000i2i2−i2−i222−2−2i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ30222-2-2-2-220000002i2i−2i−2i2-202-20i2i2i2i2−i2−i2−i2−i22222−2−2−2−2002i−2i0000−2i−2i2i2i00-2-2220000i2i2−i2−i222−2−2−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ31222-2-2-2-220000002i2i−2i−2i2-202-20−i2−i2−i2−i2i2i2i2i2−2−2−2−22222002i−2i00002i2i−2i−2i0022-2-20000−i2−i2i2i2−2−222−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ32222-2-2-2-220000002i2i−2i−2i2-202-20−i2−i2−i2−i2i2i2i2i2−2−2−2−22222002i−2i0000−2i−2i2i2i00-2-2220000−i2−i2i2i2−2−222i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ33222-2-2-2-220000002i2i−2i−2i-220-220i2i2i2i2−i2−i2−i2−i22222−2−2−2−200−2i2i2i2i−2i−2i000000000022-2-2−i2−i2i2i2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-2-2-2-220000002i2i−2i−2i-220-220i2i2i2i2−i2−i2−i2−i22222−2−2−2−200−2i2i−2i−2i2i2i0000000000-2-222−i2−i2i2i2−2−222−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-2-2-2-220000002i2i−2i−2i-220-220−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200−2i2i2i2i−2i−2i000000000022-2-2i2i2−i2−i222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-2-2-2-220000002i2i−2i−2i-220-220−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200−2i2i−2i−2i2i2i0000000000-2-222i2i2−i2−i222−2−222−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ37222-2-2-2-22000000−2i−2i2i2i2-202-20i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200−2i2i00002i2i−2i−2i00-2-2220000i2i2−i2−i2−2−222−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ38222-2-2-2-22000000−2i−2i2i2i2-202-20i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200−2i2i0000−2i−2i2i2i0022-2-20000i2i2−i2−i2−2−222i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ39222-2-2-2-22000000−2i−2i2i2i2-202-20−i2−i2−i2−i2i2i2i2i22222−2−2−2−200−2i2i00002i2i−2i−2i00-2-2220000−i2−i2i2i222−2−2i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ40222-2-2-2-22000000−2i−2i2i2i2-202-20−i2−i2−i2−i2i2i2i2i22222−2−2−2−200−2i2i0000−2i−2i2i2i0022-2-20000−i2−i2i2i222−2−2−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ41222-2-2-2-22000000−2i−2i2i2i-220-220i2i2i2i2−i2−i2−i2−i2−2−2−2−22222002i−2i2i2i−2i−2i0000000000-2-222−i2−i2i2i222−2−222−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ42222-2-2-2-22000000−2i−2i2i2i-220-220i2i2i2i2−i2−i2−i2−i2−2−2−2−22222002i−2i−2i−2i2i2i000000000022-2-2−i2−i2i2i222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ43222-2-2-2-22000000−2i−2i2i2i-220-220−i2−i2−i2−i2i2i2i2i22222−2−2−2−2002i−2i2i2i−2i−2i0000000000-2-222i2i2−i2−i2−2−222−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ44222-2-2-2-22000000−2i−2i2i2i-220-220−i2−i2−i2−i2i2i2i2i22222−2−2−2−2002i−2i−2i−2i2i2i000000000022-2-2i2i2−i2−i2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ4522-222-2-2-222-2-22-22-22-200-20022i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000i2−i2i2−i22−22−20000
χ4622-222-2-2-222-2-22-22-22-200-20022i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000−i2i2−i2i2−22−220000
χ4722-222-2-2-222-2-22-22-22-200-2002−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000i2−i2i2−i2−22−220000
χ4822-222-2-2-222-2-22-22-22-200-2002−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000−i2i2−i2i22−22−20000
χ4922-222-2-2-2-2-2222-2-22-2200-20022i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000i2−i2−i2i22−2−220000
χ5022-222-2-2-2-2-2222-2-22-2200-20022i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000−i2i2i2−i2−222−20000
χ5122-222-2-2-2-2-2222-2-22-2200-2002−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000i2−i2−i2i2−222−20000
χ5222-222-2-2-2-2-2222-2-22-2200-2002−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000−i2i2i2−i22−2−220000
χ532-2-22-2-22200002200002-2-2-22-22i−2i2i−2i2i−2i2i−2i000000002-20000002-22-20000002-22-22i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ542-2-22-2-22200002200002-2-2-22-22i−2i2i−2i2i−2i2i−2i000000002-2000000-22-22000000-22-222i−2i2i−2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ552-2-22-2-22200002200002-2-2-22-2−2i2i−2i2i−2i2i−2i2i000000002-20000002-22-20000002-22-2−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ562-2-22-2-22200002200002-2-2-22-2−2i2i−2i2i−2i2i−2i2i000000002-2000000-22-22000000-22-22−2i2i−2i2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ572-2-22-2-2220000220000-22-22-2-22i−2i2i−2i2i−2i2i−2i00000000-22002-22-20000002-22-20000−2i2i−2i2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ582-2-22-2-2220000220000-22-22-2-22i−2i2i−2i2i−2i2i−2i00000000-2200-22-22000000-22-220000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ592-2-22-2-2220000220000-22-22-2-2−2i2i−2i2i−2i2i−2i2i00000000-22002-22-20000002-22-200002i−2i2i−2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ602-2-22-2-2220000220000-22-22-2-2−2i2i−2i2i−2i2i−2i2i00000000-2200-22-22000000-22-2200002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ612-2-22-2-2220000-2-200002-22-222000000002-22-22-22-2-220000002-22-2000000-22-2200002-22-22-22-2-22-2200000000000000000000
χ622-2-22-2-2220000-2-200002-22-222000000002-22-22-22-2-22000000-22-220000002-22-200002-22-2-22-222-22-200000000000000000000
χ632-2-22-2-2220000-2-200002-22-22200000000-22-22-22-22-220000002-22-2000000-22-220000-22-22-22-222-22-200000000000000000000
χ642-2-22-2-2220000-2-200002-22-22200000000-22-22-22-22-22000000-22-220000002-22-20000-22-222-22-2-22-2200000000000000000000
χ652-2-22-2-2220000-2-20000-2222-22000000002-22-22-22-22-2002-22-2000000-22-2200000000-22-22000000002-22-2-22-22000000000000
χ662-2-22-2-2220000-2-20000-2222-22000000002-22-22-22-22-200-22-220000002-22-200000000-22-2200000000-22-222-22-2000000000000
χ672-2-22-2-2220000-2-20000-2222-2200000000-22-22-22-222-2002-22-2000000-22-22000000002-22-200000000-22-222-22-2000000000000
χ682-2-22-2-2220000-2-20000-2222-2200000000-22-22-22-222-200-22-220000002-22-2000000002-22-2000000002-22-2-22-22000000000000
χ692-2-2-222-222-22-2000000220-2-202−22−2−22−222−22−2−22−2200002i−2i−2i2i−2i2i2i−2i2-2000000002−2−222−2−22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ702-2-2-222-222-22-2000000220-2-202−22−2−22−222−22−2−22−220000−2i2i2i−2i2i−2i−2i2i2-2000000002−2−222−2−22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ712-2-2-222-222-22-2000000220-2-20−22−222−22−2−22−222−22−200002i−2i−2i2i−2i2i2i−2i2-200000000−222−2−222−2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ722-2-2-222-222-22-2000000220-2-20−22−222−22−2−22−222−22−20000−2i2i2i−2i2i−2i−2i2i2-200000000−222−2−222−2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ732-2-2-222-222-22-2000000-2-202202−22−2−22−222−22−2−22−22000000000000-222-2-22-222-2−222−2−222−22−2−222−2−22−222−22−2−22000000000000
χ742-2-2-222-222-22-2000000-2-202202−22−2−22−222−22−2−22−22000000000000-22-222-22-2-22−222−2−222−2−222−2−222−22−2−22−222−2000000000000
χ752-2-2-222-222-22-2000000-2-20220−22−222−22−2−22−222−22−2000000000000-222-2-22-222-22−2−222−2−22−222−2−222−22−2−22−222−2000000000000
χ762-2-2-222-222-22-2000000-2-20220−22−222−22−2−22−222−22−2000000000000-22-222-22-2-222−2−222−2−222−2−222−2−22−222−22−2−22000000000000
χ772-2-2-222-22-22-22000000220-2-202−22−2−22−22−22−222−22−200002i−2i−2i2i2i−2i−2i2i-22000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ782-2-2-222-22-22-22000000220-2-202−22−2−22−22−22−222−22−20000−2i2i2i−2i−2i2i2i−2i-22000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ792-2-2-222-22-22-22000000220-2-20−22−222−22−22−22−2−22−2200002i−2i−2i2i2i−2i−2i2i-2200000000−222−22−2−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ802-2-2-222-22-22-22000000220-2-20−22−222−22−22−22−2−22−220000−2i2i2i−2i−2i2i2i−2i-2200000000−222−22−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ812-2-2-222-22-22-22000000-2-202202−22−2−22−22−22−222−22−20000000000002-22-2-222-2-22−222−22−2−222−2−222−2−222−2−22−222−2000000000000
χ822-2-2-222-22-22-22000000-2-202202−22−2−22−22−22−222−22−20000000000002-2-222-2-222-2−222−22−2−22−222−2−222−2−222−22−2−22000000000000
χ832-2-2-222-22-22-22000000-2-20220−22−222−22−22−22−2−22−220000000000002-22-2-222-2-222−2−22−222−2−222−2−222−2−222−22−2−22000000000000
χ842-2-2-222-22-22-22000000-2-20220−22−222−22−22−22−2−22−220000000000002-2-222-2-222-22−2−22−222−22−2−222−2−222−2−22−222−2000000000000
χ8544-444-4-4-444-4-4-44-44-4400400-400000000000000000000000000000000000000000000000000000000000000000000000000
χ8644-444-4-4-4-4-444-444-44-400400-400000000000000000000000000000000000000000000000000000000000000000000000000
χ8744-4-4-444-40000004i−4i−4i4i0000002222−22−22−22−222222−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000
χ8844-4-4-444-40000004i−4i−4i4i000000−22−2222222222−22−222i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000
χ8944-4-4-444-4000000−4i4i4i−4i0000002222−22−22−22−2222222i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000
χ9044-4-4-444-4000000−4i4i4i−4i000000−22−2222222222−22−22−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000
χ914-444-44-4-400004-4000000400-44-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ924-444-44-4-400004-4000000400-4-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000
χ934-444-44-4-40000-44000000-4004000000004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ944-444-44-4-40000-44000000-400400000000−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ954-44-44-44-44-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ964-44-44-44-44-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ974-44-44-44-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ984-44-44-44-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000000000000000

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