Finite Group Databasebeta

← Group #358673

Character table — Group #358673

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12222222222244444444444444444444444422222222444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ911111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1211111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ17111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ18111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ19111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ20111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ21111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ22111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ23111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ24111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ25111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ26111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ27111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ28111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ29111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ30111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
χ31111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ32111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ3322222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-222000000002-22-22-22-20000000000000000000000000000000000000000
χ3422222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-22200000000-22-22-22-220000000000000000000000000000000000000000
χ3522222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-222000000002-22-2-22-220000000000000000000000000000000000000000
χ3622222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22200000000-22-222-22-20000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2000000002-2-222-2-220000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-200000000-222-2-222-20000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2000000002-2-22-222-20000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-200000000-222-22-2-220000000000000000000000000000000000000000
χ412222-2-2-2-222-2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i22-2-22-20000000000000000000000000000000000000000000000002-22-22i−2i2i−2i
χ422222-2-2-2-222-2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i22-2-22-2000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i
χ432222-2-2-2-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-22-20000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i
χ442222-2-2-2-222-2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-22-2000000000000000000000000000000000000000000000000-22-222i−2i2i−2i
χ452222-2-2-2-222-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2-222-220000000000000000000000000000000000000000000000002i−2i−2i2i-222-2
χ462222-2-2-2-222-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2-222-22000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22
χ472222-2-2-2-222-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2-222-220000000000000000000000000000000000000000000000002i−2i−2i2i2-2-22
χ482222-2-2-2-222-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2-222-22000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2
χ492222-2-2-2-2-2-2222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-2222-200000000000000000000000000000000000000002i−2i2i−2i2-22-200000000
χ502222-2-2-2-2-2-2222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-2222-20000000000000000000000000000000000000000−2i2i−2i2i-22-2200000000
χ512222-2-2-2-2-2-2222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-2222-200000000000000000000000000000000000000002i−2i2i−2i-22-2200000000
χ522222-2-2-2-2-2-2222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-2222-20000000000000000000000000000000000000000−2i2i−2i2i2-22-200000000
χ532222-2-2-2-2-2-222-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i22-2-2-2200000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ542222-2-2-2-2-2-222-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i22-2-2-220000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ552222-2-2-2-2-2-222-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i22-2-2-2200000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ562222-2-2-2-2-2-222-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i22-2-2-220000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ5722-2-222-2-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-2-2200002-22-20000000000002i−2i2i−2i00000000000000000000000000000000
χ5822-2-222-2-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-2-220000-22-22000000000000−2i2i−2i2i00000000000000000000000000000000
χ5922-2-222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2-2200002-22-2000000000000−2i2i−2i2i00000000000000000000000000000000
χ6022-2-222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-2-220000-22-220000000000002i−2i2i−2i00000000000000000000000000000000
χ6122-2-222-2-22-22-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-22-222-200002-2-220000000000002i−2i−2i2i00000000000000000000000000000000
χ6222-2-222-2-22-22-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-22-222-20000-222-2000000000000−2i2i2i−2i00000000000000000000000000000000
χ6322-2-222-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-22-222-200002-2-22000000000000−2i2i2i−2i00000000000000000000000000000000
χ6422-2-222-2-22-22-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-22-222-20000-222-20000000000002i−2i−2i2i00000000000000000000000000000000
χ6522-2-222-2-2-22-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i-22-22-222-22-20000000000002i−2i2i−2i000000000000000000000000000000000000
χ6622-2-222-2-2-22-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i-22-22-22-22-22000000000000−2i2i−2i2i000000000000000000000000000000000000
χ6722-2-222-2-2-22-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i-22-22-222-22-2000000000000−2i2i−2i2i000000000000000000000000000000000000
χ6822-2-222-2-2-22-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i-22-22-22-22-220000000000002i−2i2i−2i000000000000000000000000000000000000
χ6922-2-222-2-2-22-22-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2-22-22-22-2-220000000000002i−2i−2i2i000000000000000000000000000000000000
χ7022-2-222-2-2-22-22-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2-22-22-2-222-2000000000000−2i2i2i−2i000000000000000000000000000000000000
χ7122-2-222-2-2-22-22-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2-22-22-22-2-22000000000000−2i2i2i−2i000000000000000000000000000000000000
χ7222-2-222-2-2-22-22-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2-22-22-2-222-20000000000002i−2i−2i2i000000000000000000000000000000000000
χ7322-2-2-2-2222-2-22222-2-222-2-222-2-222-2-222-2-22-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ7422-2-2-2-2222-2-22222-2-222-2-222-2-222-2-222-2-22-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ7522-2-2-2-2222-2-2222-222-2-222-2-222-2-222-22-2-22-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ7622-2-2-2-2222-2-2222-222-2-222-2-222-2-222-22-2-22-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ7722-2-2-2-2222-2-22-2-22-2-222-2-22-222-2-222-2-222-2220000000000000000000000002-2-222-2-22000000000000000000000000
χ7822-2-2-2-2222-2-22-2-22-2-222-2-22-222-2-222-2-222-222000000000000000000000000-222-2-222-2000000000000000000000000
χ7922-2-2-2-2222-2-22-2-2-222-2-222-22-2-222-2-22-222-2220000000000000000000000002-2-22-222-2000000000000000000000000
χ8022-2-2-2-2222-2-22-2-2-222-2-222-22-2-222-2-22-222-222000000000000000000000000-222-22-2-22000000000000000000000000
χ8122-2-2-2-222-222-2222-2-22-222-22-2-22-222-2-222-2-2-2000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ8222-2-2-2-222-222-2222-2-22-222-22-2-22-222-2-222-2-2-200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ8322-2-2-2-222-222-222-222-22-2-22-222-22-2-22-222-2-2-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ8422-2-2-2-222-222-222-222-22-2-22-222-22-2-22-222-2-2-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ8522-2-2-2-222-222-2-2-22-2-22-222-2-222-22-2-222-2-2222000000000000000000000000000000002-2-222-2-220000000000000000
χ8622-2-2-2-222-222-2-2-22-2-22-222-2-222-22-2-222-2-222200000000000000000000000000000000-222-2-222-20000000000000000
χ8722-2-2-2-222-222-2-2-2-222-22-2-222-2-22-222-22-2-2222000000000000000000000000000000002-2-22-222-20000000000000000
χ8822-2-2-2-222-222-2-2-2-222-22-2-222-2-22-222-22-2-222200000000000000000000000000000000-222-22-2-220000000000000000
χ898-88-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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