Finite Group Databasebeta

← Group #357461

Character table — Group #357461

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12222222222222222222444444444444444422222222444444444444444444444444444444444444444444444444
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
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ17111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ18111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ19111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ20111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ21111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ22111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ23111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ24111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-111-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-111-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-11111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-11111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
χ3322222222-2-2-2-222-2-222-2-22222-2-2-2-22222-2-2-2-2000000002-22-22-22-20000000000000000000000000000000000000000
χ3422222222-2-2-2-222-2-222-2-22222-2-2-2-22222-2-2-2-200000000-22-22-22-220000000000000000000000000000000000000000
χ3522222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-22222000000002-22-2-22-220000000000000000000000000000000000000000
χ3622222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-2222200000000-22-222-22-20000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-2-2-22222000000002-2-222-2-220000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000-222-2-222-20000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2000000002-2-22-222-20000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000-222-22-2-220000000000000000000000000000000000000000
χ41222-2-2-2-2222-2-2222-2-2-22-222-2-222-2-222-2-222-2-200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ42222-2-2-2-2222-2-2222-2-2-22-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ43222-2-2-2-2222-2-2222-2-2-22-2-2-222-2-222-2-222-2-22200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ44222-2-2-2-2222-2-2222-2-2-22-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ45222-2-2-2-2222-2-2-2-2-2222-2222-2-222-2-2-2-222-2-22200000000000000000000000000000000000000002-2-222-2-2200000000
χ46222-2-2-2-2222-2-2-2-2-2222-2222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000-222-2-222-200000000
χ47222-2-2-2-2222-2-2-2-2-2222-22-2-222-2-22222-2-222-2-200000000000000000000000000000000000000002-2-22-222-200000000
χ48222-2-2-2-2222-2-2-2-2-2222-22-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000-222-22-2-2200000000
χ49222-2-2-2-22-2-22222-22-2-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ50222-2-2-2-22-2-22222-22-2-2-2222-2-2-2-22222-2-2-2-22200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ51222-2-2-2-22-2-22222-22-2-2-22-2-22222-2-2-2-22222-2-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ52222-2-2-2-22-2-22222-22-2-2-22-2-22222-2-2-2-22222-2-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ53222-2-2-2-22-2-222-2-22-2222-222-2-2-2-222-2-22222-2-2000000000000000000000000000000002-2-222-2-220000000000000000
χ54222-2-2-2-22-2-222-2-22-2222-222-2-2-2-222-2-22222-2-200000000000000000000000000000000-222-2-222-20000000000000000
χ55222-2-2-2-22-2-222-2-22-2222-2-2-22222-2-222-2-2-2-222000000000000000000000000000000002-2-22-222-20000000000000000
χ56222-2-2-2-22-2-222-2-22-2222-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000-222-22-2-220000000000000000
χ572-2-222-2-222-22-22-2222-2-2-22-22-22-22-22-22-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ582-2-222-2-222-22-22-2222-2-2-22-22-22-22-22-22-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
χ592-2-222-2-222-22-22-2222-2-2-2-22-22-22-22-22-22-22-220000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i
χ602-2-222-2-222-22-22-2222-2-2-2-22-22-22-22-22-22-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ612-2-222-2-222-22-2-22-2-2-22222-22-22-22-2-22-22-22-220000000000000000000000000000000000000000000000002-2-222-2-22
χ622-2-222-2-222-22-2-22-2-2-22222-22-22-22-2-22-22-22-22000000000000000000000000000000000000000000000000-222-2-222-2
χ632-2-222-2-222-22-2-22-2-2-2222-22-22-22-222-22-22-22-20000000000000000000000000000000000000000000000002-2-22-222-2
χ642-2-222-2-222-22-2-22-2-2-2222-22-22-22-222-22-22-22-2000000000000000000000000000000000000000000000000-222-22-2-22
χ652-2-222-2-22-22-222-2-2-22-2222-22-2-22-222-22-2-22-220000000000000000000000002-22-22-22-2000000000000000000000000
χ662-2-222-2-22-22-222-2-2-22-2222-22-2-22-222-22-2-22-22000000000000000000000000-22-22-22-22000000000000000000000000
χ672-2-222-2-22-22-222-2-2-22-222-22-222-22-2-22-222-22-20000000000000000000000002-22-2-22-22000000000000000000000000
χ682-2-222-2-22-22-222-2-2-22-222-22-222-22-2-22-222-22-2000000000000000000000000-22-222-22-2000000000000000000000000
χ692-2-222-2-22-22-22-2222-22-2-22-22-2-22-22-22-222-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ702-2-222-2-22-22-22-2222-22-2-22-22-2-22-22-22-222-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ712-2-222-2-22-22-22-2222-22-2-2-22-222-22-22-22-2-22-220000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ722-2-222-2-22-22-22-2222-22-2-2-22-222-22-22-22-2-22-22000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ732-2-2-2-22222-2-222-22-2-22-222-2-222-2-222-2-222-2-222-22-20000000000002-22-2000000000000000000000000000000000000
χ742-2-2-2-22222-2-222-22-2-22-222-2-222-2-222-2-222-2-22-22-22000000000000-22-22000000000000000000000000000000000000
χ752-2-2-2-22222-2-222-22-2-22-22-222-2-222-2-222-2-222-22-2-220000000000002-2-22000000000000000000000000000000000000
χ762-2-2-2-22222-2-222-22-2-22-22-222-2-222-2-222-2-222-2-222-2000000000000-222-2000000000000000000000000000000000000
χ772-2-2-2-22222-2-22-22-222-22-22-2-222-2-22-222-2-222-22-22-2000000000000-22-22000000000000000000000000000000000000
χ782-2-2-2-22222-2-22-22-222-22-22-2-222-2-22-222-2-222-2-22-220000000000002-22-2000000000000000000000000000000000000
χ792-2-2-2-22222-2-22-22-222-22-2-222-2-222-22-2-222-2-222-2-22000000000000-222-2000000000000000000000000000000000000
χ802-2-2-2-22222-2-22-22-222-22-2-222-2-222-22-2-222-2-22-222-20000000000002-2-22000000000000000000000000000000000000
χ812-2-2-2-2222-222-22-2-22-222-22-2-22-222-22-2-22-222-200002-22-20000000000002-22-200000000000000000000000000000000
χ822-2-2-2-2222-222-22-2-22-222-22-2-22-222-22-2-22-222-20000-22-22000000000000-22-2200000000000000000000000000000000
χ832-2-2-2-2222-222-22-2-22-222-2-222-22-2-22-222-22-2-2200002-2-220000000000002-2-2200000000000000000000000000000000
χ842-2-2-2-2222-222-22-2-22-222-2-222-22-2-22-222-22-2-220000-222-2000000000000-222-200000000000000000000000000000000
χ852-2-2-2-2222-222-2-222-22-2-222-2-22-222-2-222-22-2-2200002-2-22000000000000-222-200000000000000000000000000000000
χ862-2-2-2-2222-222-2-222-22-2-222-2-22-222-2-222-22-2-220000-222-20000000000002-2-2200000000000000000000000000000000
χ872-2-2-2-2222-222-2-222-22-2-22-222-22-2-222-2-22-222-200002-22-2000000000000-22-2200000000000000000000000000000000
χ882-2-2-2-2222-222-2-222-22-2-22-222-22-2-222-2-22-222-20000-22-220000000000002-22-200000000000000000000000000000000
χ8988-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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