Finite Group Databasebeta

← Group #398124

Character table — Group #398124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444488888888888888882222224444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111
χ172222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000222200000000-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000-2-2-2-200000000222200000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000022-2-20000000022-2-200000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000-2-22200000000-2-22200000000000000000000
χ2122222-2-2-22-22-2-2-2-2200002222-2-2-2-200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-22-20000000000000000i2i2−i2−i2i2i2−i2−i200000000
χ2222222-2-2-22-22-2-2-2-2200002222-2-2-2-200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-22-220000000000000000−i2−i2i2i2−i2−i2i2i200000000
χ2322222-2-2-22-22-2-2-2-2200002222-2-2-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002-22-20000000000000000−i2−i2i2i2−i2−i2i2i200000000
χ2422222-2-2-22-22-2-2-2-2200002222-2-2-2-200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000-22-220000000000000000i2i2−i2−i2i2i2−i2−i200000000
χ2522222-2-2-22-22-2-2-2-220000-2-2-2-2222200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002-2-220000000000000000i2i2−i2−i2−i2−i2i2i200000000
χ2622222-2-2-22-22-2-2-2-220000-2-2-2-2222200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000-222-20000000000000000−i2−i2i2i2i2i2−i2−i200000000
χ2722222-2-2-22-22-2-2-2-220000-2-2-2-2222200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002-2-220000000000000000−i2−i2i2i2i2i2−i2−i200000000
χ2822222-2-2-22-22-2-2-2-220000-2-2-2-2222200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000-222-20000000000000000i2i2−i2−i2−i2−i2i2i200000000
χ29222-2-222-2-22-2-2-2-222222-2000000002-2-2-200002i2i−2i−2i2i2i−2i−2i0000000022-2-200002i2i−2i−2i0000000000000000000000000000
χ30222-2-222-2-22-2-2-2-222222-2000000002-2-2-200002i2i−2i−2i2i2i−2i−2i00000000-2-2220000−2i−2i2i2i0000000000000000000000000000
χ31222-2-222-2-22-2-2-2-222222-2000000002-2-2-20000−2i−2i2i2i−2i−2i2i2i0000000022-2-20000−2i−2i2i2i0000000000000000000000000000
χ32222-2-222-2-22-2-2-2-222222-2000000002-2-2-20000−2i−2i2i2i−2i−2i2i2i00000000-2-22200002i2i−2i−2i0000000000000000000000000000
χ3322-22-22-22-2-222-2-22-222-2-22i2i−2i−2i2i2i−2i−2i-222-22i2i−2i−2i0000000000000000000000002i−2i2i−2i22-2-2000000000000000000000000
χ3422-22-22-22-2-222-2-22-222-2-22i2i−2i−2i2i2i−2i−2i-222-22i2i−2i−2i000000000000000000000000−2i2i−2i2i-2-222000000000000000000000000
χ3522-22-22-22-2-222-2-22-222-2-2−2i−2i2i2i−2i−2i2i2i-222-2−2i−2i2i2i0000000000000000000000002i−2i2i−2i-2-222000000000000000000000000
χ3622-22-22-22-2-222-2-22-222-2-2−2i−2i2i2i−2i−2i2i2i-222-2−2i−2i2i2i000000000000000000000000−2i2i−2i2i22-2-2000000000000000000000000
χ3722-22-22-22-2-222-2-22-2-2-2222i2i−2i−2i2i2i−2i−2i2-2-22−2i−2i2i2i000000000000000000000000000000000000000000000000002i−2i2-200
χ3822-22-22-22-2-222-2-22-2-2-2222i2i−2i−2i2i2i−2i−2i2-2-22−2i−2i2i2i00000000000000000000000000000000000000000000000000−2i2i-2200
χ3922-22-22-22-2-222-2-22-2-2-222−2i−2i2i2i−2i−2i2i2i2-2-222i2i−2i−2i000000000000000000000000000000000000000000000000002i−2i-2200
χ4022-22-22-22-2-222-2-22-2-2-222−2i−2i2i2i−2i−2i2i2i2-2-222i2i−2i−2i00000000000000000000000000000000000000000000000000−2i2i2-200
χ4122-2-222-2-22-2-2-2222-222-2200000000-2-2-220000000000002i2i−2i−2i2i2i−2i−2i000000002-2-22000000002i2i−2i−2i0000000000000000
χ4222-2-222-2-22-2-2-2222-222-2200000000-2-2-220000000000002i2i−2i−2i2i2i−2i−2i00000000-222-200000000−2i−2i2i2i0000000000000000
χ4322-2-222-2-22-2-2-2222-222-2200000000-2-2-22000000000000−2i−2i2i2i−2i−2i2i2i000000002-2-2200000000−2i−2i2i2i0000000000000000
χ4422-2-222-2-22-2-2-2222-222-2200000000-2-2-22000000000000−2i−2i2i2i−2i−2i2i2i00000000-222-2000000002i2i−2i−2i0000000000000000
χ452-222-2-22-22-2-22-222-22-22200000000-22-2-200002i−2i2i−2i2i−2i2i−2i000000000000000000002-22-200002i−2i2i−2i0000000000000000
χ462-222-2-22-22-2-22-222-22-22200000000-22-2-200002i−2i2i−2i2i−2i2i−2i00000000000000000000-22-220000−2i2i−2i2i0000000000000000
χ472-222-2-22-22-2-22-222-22-22200000000-22-2-20000−2i2i−2i2i−2i2i−2i2i000000000000000000002-22-20000−2i2i−2i2i0000000000000000
χ482-222-2-22-22-2-22-222-22-22200000000-22-2-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000-22-2200002i−2i2i−2i0000000000000000
χ492-22-222-2-2-2222-22-2-200002i−2i2i−2i2i−2i2i−2i00000000i2−i2−i2i2−i2i2i2−i22−22−22−22−200000000000000002-22i−2i00002−22−2i2−i2i2−i200000000
χ502-22-222-2-2-2222-22-2-200002i−2i2i−2i2i−2i2i−2i00000000i2−i2−i2i2−i2i2i2−i22−22−22−22−20000000000000000-22−2i2i0000−22−22−i2i2−i2i200000000
χ512-22-222-2-2-2222-22-2-200002i−2i2i−2i2i−2i2i−2i00000000−i2i2i2−i2i2−i2−i2i2−22−22−22−2200000000000000002-22i−2i0000−22−22−i2i2−i2i200000000
χ522-22-222-2-2-2222-22-2-200002i−2i2i−2i2i−2i2i−2i00000000−i2i2i2−i2i2−i2−i2i2−22−22−22−220000000000000000-22−2i2i00002−22−2i2−i2i2−i200000000
χ532-22-222-2-2-2222-22-2-20000−2i2i−2i2i−2i2i−2i2i00000000i2−i2−i2i2−i2i2i2−i2−22−22−22−2200000000000000002-2−2i2i0000−22−22i2−i2i2−i200000000
χ542-22-222-2-2-2222-22-2-20000−2i2i−2i2i−2i2i−2i2i00000000i2−i2−i2i2−i2i2i2−i2−22−22−22−220000000000000000-222i−2i00002−22−2−i2i2−i2i200000000
χ552-22-222-2-2-2222-22-2-20000−2i2i−2i2i−2i2i−2i2i00000000−i2i2i2−i2i2−i2−i2i22−22−22−22−200000000000000002-2−2i2i00002−22−2−i2i2−i2i200000000
χ562-22-222-2-2-2222-22-2-20000−2i2i−2i2i−2i2i−2i2i00000000−i2i2i2−i2i2−i2−i2i22−22−22−22−20000000000000000-222i−2i0000−22−22i2−i2i2−i200000000
χ572-22-22-222-2-22-22-22-22-22-22i−2i2i−2i−2i2i−2i2i-2-2222i−2i2i−2i2-2-222-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ582-22-22-222-2-22-22-22-22-22-22i−2i2i−2i−2i2i−2i2i-2-2222i−2i2i−2i-222-2-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ592-22-22-222-2-22-22-22-22-22-2−2i2i−2i2i2i−2i2i−2i-2-222−2i2i−2i2i2-2-222-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ602-22-22-222-2-22-22-22-22-22-2−2i2i−2i2i2i−2i2i−2i-2-222−2i2i−2i2i-222-2-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ612-22-22-222-2-22-22-22-2-22-222i−2i2i−2i−2i2i−2i2i22-2-2−2i2i−2i2i00000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ622-22-22-222-2-22-22-22-2-22-222i−2i2i−2i−2i2i−2i2i22-2-2−2i2i−2i2i0000000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ632-22-22-222-2-22-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i22-2-22i−2i2i−2i00000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ642-22-22-222-2-22-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i22-2-22i−2i2i−2i0000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ652-2-222-2-2-2-22-222-2222-2-2-20000000022-220000000000002-2-22-222-22-22-2000000002-2-22000000000000000000000000
χ662-2-222-2-2-2-22-222-2222-2-2-20000000022-220000000000002-2-22-222-2-22-2200000000-222-2000000000000000000000000
χ672-2-222-2-2-2-22-222-2222-2-2-20000000022-22000000000000-222-22-2-222-22-200000000-222-2000000000000000000000000
χ682-2-222-2-2-2-22-222-2222-2-2-20000000022-22000000000000-222-22-2-22-22-22000000002-2-22000000000000000000000000
χ692-2-2-2-2-2-22222-2-22222-2-222-2-22-222-22-22-22-2-2200000000000000002-2-220000000000000000-222-20000000000000000
χ702-2-2-2-2-2-22222-2-22222-2-222-2-22-222-22-22-22-2-220000000000000000-222-200000000000000002-2-220000000000000000
χ712-2-2-2-2-2-22222-2-22222-2-22-222-22-2-222-22-2-222-200000000000000002-2-2200000000000000002-2-220000000000000000
χ722-2-2-2-2-2-22222-2-22222-2-22-222-22-2-222-22-2-222-20000000000000000-222-20000000000000000-222-20000000000000000
χ732-2-2-2-2-2-22222-2-2222-222-22-2-22-222-2-22-22-222-20000000000000000000000000000000000000000000000002-200002-2
χ742-2-2-2-2-2-22222-2-2222-222-22-2-22-222-2-22-22-222-2000000000000000000000000000000000000000000000000-220000-22
χ752-2-2-2-2-2-22222-2-2222-222-2-222-22-2-22-22-222-2-220000000000000000000000000000000000000000000000002-20000-22
χ762-2-2-2-2-2-22222-2-2222-222-2-222-22-2-22-22-222-2-22000000000000000000000000000000000000000000000000-2200002-2
χ77444-4-444-4-44-4-4-4-444-4-4-4400000000-4444000000000000000000000000000000000000000000000000000000000000
χ78444-4-4-4-44-4-4-4444-44000000000000000000002222−22−22−22−222222000000000000000000000000000000000000000000000000
χ79444-4-4-4-44-4-4-4444-4400000000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000000000
χ8044-44-4-44-4-444-444-4-400004i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000000000000000
χ8144-44-4-44-4-444-444-4-40000−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ8244-4-444-4-44-4-4-4444-4-4-44-400000000444-4000000000000000000000000000000000000000000000000000000000000
χ8344-4-44-44444-44-4-4-4-400000000000000000000000000002222−22−22−22−2222220000000000000000000000000000000000000000
χ8444-4-44-44444-44-4-4-4-40000000000000000000000000000−22−2222222222−22−220000000000000000000000000000000000000000
χ854-444-44-4444-4-44-4-4-40000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000000000000000
χ864-444-44-4444-4-44-4-4-400000000000000000000−2222−222222−2222−22000000000000000000000000000000000000000000000000
χ874-444-4-44-44-4-44-444-4-44-4-4000000004-444000000000000000000000000000000000000000000000000000000000000
χ884-4-444444-4-4-4-4-44-4400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ894-4-444444-4-4-4-4-44-440000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ904-4-444-4-4-4-44-444-444-444400000000-4-44-4000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-444-44-4444-4-4400004-4-444-4-440000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-444-44-4444-4-440000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000

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