Finite Group Databasebeta

← Group #392893

Character table — Group #392893

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111111112222222222224444444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444222244444444444444444444888888888888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ17111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−ii−ii−i1-11-11-11-1
χ18111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−ii−ii-11-11-11-11
χ19111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−i−ii−ii1-11-1-11-11
χ20111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−ii−iii−ii−i-11-111-11-1
χ21111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−ii−ii−i-11-11-11-11
χ22111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−ii−ii1-11-11-11-1
χ23111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−ii−ii−i−ii−ii-11-111-11-1
χ24111-11-1-1-111-1-11-1-1-1111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−iii−ii−i1-11-1-11-11
χ25111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii1-1-111-1-11
χ26111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i-111-1-111-1
χ27111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i1-1-11-111-1
χ28111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii-111-11-1-11
χ29111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii-111-1-111-1
χ30111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i1-1-111-1-11
χ31111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i-111-11-1-11
χ32111-11-1-1-111-1-11-1-1-1111-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii1-1-11-111-1
χ33222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ34222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ3722222222-2-2-2-222-2-22-2-222-22-22-22-2000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ3822222222-2-2-2-222-2-22-2-222-22-22-22-20000000000000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222222-2-2-2-222-2-22-2-22-22-22-22-22000000000000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ4022222222-2-2-2-222-2-22-2-22-22-22-22-220000000000000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ4122222222-2-2-2-2-2-222-222-22-22-2-22-2222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-222-222-22-22-2-22-22-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-222-222-2-22-222-22-222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-222-222-2-22-222-22-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ45222-22-2-2-222-2-2-2222-2-2-2222-2-2-2-2220000000000000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ46222-22-2-2-222-2-2-2222-2-2-2222-2-2-2-22200000000000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ47222-22-2-2-222-2-2-2222-2-2-22-2-22222-2-20000000000000000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ48222-22-2-2-222-2-2-2222-2-2-22-2-22222-2-200000000000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ49222-22-2-2-2-2-2222-2222-2-2-22-2-222-2-22000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ50222-22-2-2-2-2-2222-2222-2-2-22-2-222-2-220000000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ51222-22-2-2-2-2-2222-2222-2-2-2-222-2-222-2000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ52222-22-2-2-2-2-2222-2222-2-2-2-222-2-222-20000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ53222-22-2-2-2-2-222-22-2-2-22222-2-22-222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ54222-22-2-2-2-2-222-22-2-2-22222-2-22-222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ55222-22-2-2-2-2-222-22-2-2-2222-222-22-2-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ56222-22-2-2-2-2-222-22-2-2-2222-222-22-2-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ572-2-2222-2-22-22-22-22-2-22-2200000000000000002i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i2-22-22-22-2000000000000000000000000
χ582-2-2222-2-22-22-22-22-2-22-2200000000000000002i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i−2i2i−2i2i-22-22-22-22000000000000000000000000
χ592-2-2222-2-22-22-22-22-2-22-220000000000000000−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i2i−2i2i−2i-22-22-22-22000000000000000000000000
χ602-2-2222-2-22-22-22-22-2-22-220000000000000000−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-2000000000000000000000000
χ612-2-2222-2-22-22-2-22-222-22-2000000002i−2i2i−2i2i−2i2i−2i000000002-22-22-22-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ622-2-2222-2-22-22-2-22-222-22-2000000002i−2i2i−2i2i−2i2i−2i00000000-22-22-22-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ632-2-2222-2-22-22-2-22-222-22-200000000−2i2i−2i2i−2i2i−2i2i000000002-22-22-22-200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ642-2-2222-2-22-22-2-22-222-22-200000000−2i2i−2i2i−2i2i−2i2i00000000-22-22-22-22000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ652-2-2222-2-2-22-222-2-22-2-222000000002i−2i−2i2i2i−2i−2i2i00000000000000002i−2i−2i2i2i−2i−2i2i000000002-22-22-22-20000000000000000
χ662-2-2222-2-2-22-222-2-22-2-222000000002i−2i−2i2i2i−2i−2i2i0000000000000000−2i2i2i−2i−2i2i2i−2i00000000-22-22-22-220000000000000000
χ672-2-2222-2-2-22-222-2-22-2-22200000000−2i2i2i−2i−2i2i2i−2i00000000000000002i−2i−2i2i2i−2i−2i2i00000000-22-22-22-220000000000000000
χ682-2-2222-2-2-22-222-2-22-2-22200000000−2i2i2i−2i−2i2i2i−2i0000000000000000−2i2i2i−2i−2i2i2i−2i000000002-22-22-22-20000000000000000
χ692-2-2222-2-2-22-22-222-222-2-200000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-2200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ702-2-2222-2-2-22-22-222-222-2-200000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ712-2-2222-2-2-22-22-222-222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-220000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ722-2-2222-2-2-22-22-222-222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ732-2-2-22-2222-2-2222-22-22-2-200000000000000002-22-2-22-22000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ742-2-2-22-2222-2-2222-22-22-2-200000000000000002-22-2-22-2200000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ752-2-2-22-2222-2-2222-22-22-2-20000000000000000-22-222-22-2000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ762-2-2-22-2222-2-2222-22-22-2-20000000000000000-22-222-22-200000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ772-2-2-22-2222-2-22-2-22-22-222000000002-22-2-22-22000000002-22-2-22-22000000002-2-22-222-2000000000000000000000000
χ782-2-2-22-2222-2-22-2-22-22-222000000002-22-2-22-2200000000-22-222-22-200000000-222-22-2-22000000000000000000000000
χ792-2-2-22-2222-2-22-2-22-22-22200000000-22-222-22-2000000002-22-2-22-2200000000-222-22-2-22000000000000000000000000
χ802-2-2-22-2222-2-22-2-22-22-22200000000-22-222-22-200000000-22-222-22-2000000002-2-22-222-2000000000000000000000000
χ812-2-2-22-222-222-2222-2-2-22-2000000002-2-22-222-200000000000000002i−2i−2i2i−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ822-2-2-22-222-222-2222-2-2-22-2000000002-2-22-222-20000000000000000−2i2i2i−2i2i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ832-2-2-22-222-222-2222-2-2-22-200000000-222-22-2-2200000000000000002i−2i−2i2i−2i2i2i−2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ842-2-2-22-222-222-2222-2-2-22-200000000-222-22-2-220000000000000000−2i2i2i−2i2i−2i−2i2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ852-2-2-22-222-222-2-2-2-2222-2200000000000000002-2-22-222-22-2-22-222-200000000000000002-2-22-222-20000000000000000
χ862-2-2-22-222-222-2-2-2-2222-2200000000000000002-2-22-222-2-222-22-2-220000000000000000-222-22-2-220000000000000000
χ872-2-2-22-222-222-2-2-2-2222-220000000000000000-222-22-2-222-2-22-222-20000000000000000-222-22-2-220000000000000000
χ882-2-2-22-222-222-2-2-2-2222-220000000000000000-222-22-2-22-222-22-2-2200000000000000002-2-22-222-20000000000000000
χ8988-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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