Finite Group Databasebeta

← Group #358421

Character table — Group #358421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12224444222222444444888888888888888822444444444444444444444444448888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1
χ171-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-11-1ii−i−i1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ181-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-11-1ii−i−i1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111-1-111−i−iiiii−i−i−i−iii
χ191-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-11-1−i−iii1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−i−iii
χ201-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-11-1−i−iii1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111-1-111ii−i−i−i−iiiii−i−i
χ211-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-1-11ii−i−i-1111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1-1-111ii−i−i−i−iii−i−iii
χ221-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-1-11ii−i−i-11-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-1−i−iii−i−iiiii−i−i
χ231-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-1-11−i−iii-1111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1-1-111−i−iiiii−i−iii−i−i
χ241-1-11-1-1111-111-1-11-111-1-111111111-1-1-1-1-1-1-1-1-11−i−iii-11-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-1ii−i−iii−i−i−i−iii
χ251-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-1111111111-1ii−i−i1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-11111-1-1ii−i−iii−i−iii−i−i
χ261-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-1111111111-1ii−i−i1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-111−i−iiiii−i−i−i−iii
χ271-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-1111111111-1−i−iii1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-11111-1-1−i−iii−i−iii−i−iii
χ281-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-1111111111-1−i−iii1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i
χ291-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-111111111-11ii−i−i-1111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-1-111ii−i−i−i−iii−i−iii
χ301-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-111111111-11ii−i−i-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iiiii−i−i
χ311-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-111111111-11−i−iii-1111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-111−i−iiiii−i−iii−i−i
χ321-1-11-1-1111-111-1-11-111-1-1-1-1-1-1-1-1-1-111111111-11−i−iii-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−i−i−iii
χ33222222222-2-2-22-22-2-2-22-22222-2-2-2-22222-2-2-2-20000000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i000000000000
χ34222222222-2-2-22-22-2-2-22-22222-2-2-2-22222-2-2-2-2000000000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i000000000000
χ35222222222-2-2-22-22-2-2-22-2-2-2-2-22222-2-2-2-222220000000000002i−2i2i−2i000000000000000000000000−2i2i−2i2i000000000000
χ36222222222-2-2-22-22-2-2-22-2-2-2-2-22222-2-2-2-22222000000000000−2i2i−2i2i0000000000000000000000002i−2i2i−2i000000000000
χ3722222222-222-2-2-2-222-2-2-222-2-222-2-222-2-222-2-200000000000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i00000000
χ3822222222-222-2-2-2-222-2-2-222-2-222-2-222-2-222-2-20000000000000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i00000000
χ3922222222-222-2-2-2-222-2-2-2-2-222-2-222-2-222-2-22200000000000000002i−2i2i−2i000000000000000000000000−2i2i−2i2i00000000
χ4022222222-222-2-2-2-222-2-2-2-2-222-2-222-2-222-2-2220000000000000000−2i2i−2i2i0000000000000000000000002i−2i2i−2i00000000
χ4122222222-2-2-22-22-2-2-22-2222-2-2-2-22222-2-2-2-222000000000000000000002-22-20000000000000000000000002-22-20000
χ4222222222-2-2-22-22-2-2-22-2222-2-2-2-22222-2-2-2-22200000000000000000000-22-22000000000000000000000000-22-220000
χ4322222222-2-2-22-22-2-2-22-22-2-22222-2-2-2-22222-2-2000000000000000000002-22-2000000000000000000000000-22-220000
χ4422222222-2-2-22-22-2-2-22-22-2-22222-2-2-2-22222-2-200000000000000000000-22-220000000000000000000000002-22-20000
χ452222-2-2-2-2222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000002-22-20000000000000000000000002i−2i2i−2i
χ462222-2-2-2-2222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000-22-22000000000000000000000000−2i2i−2i2i
χ472222-2-2-2-2222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-22-2000000000000000000000000−2i2i−2i2i
χ482222-2-2-2-2222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000-22-220000000000000000000000002i−2i2i−2i
χ492222-2-2-2-22-2-2-22-2-2222-222i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i002-22-200000000000000000000002i−2i2i−2i000000000000000000000000
χ502222-2-2-2-22-2-2-22-2-2222-222i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00-22-220000000000000000000000−2i2i−2i2i000000000000000000000000
χ512222-2-2-2-22-2-2-22-2-2222-22−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i002-22-20000000000000000000000−2i2i−2i2i000000000000000000000000
χ522222-2-2-2-22-2-2-22-2-2222-22−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00-22-2200000000000000000000002i−2i2i−2i000000000000000000000000
χ532222-2-2-2-2-222-2-2-22-2-22222i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i220000-2-20000000000000000000000002i−2i2i−2i00000000000000000000
χ542222-2-2-2-2-222-2-2-22-2-22222i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i-2-2000022000000000000000000000000−2i2i−2i2i00000000000000000000
χ552222-2-2-2-2-222-2-2-22-2-2222−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i220000-2-2000000000000000000000000−2i2i−2i2i00000000000000000000
χ562222-2-2-2-2-222-2-2-22-2-2222−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i-2-20000220000000000000000000000002i−2i2i−2i00000000000000000000
χ572222-2-2-2-2-2-2-22-22222-22-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000002-22-20000000000000000000000002i−2i2i−2i0000000000000000
χ582222-2-2-2-2-2-2-22-22222-22-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000-22-22000000000000000000000000−2i2i−2i2i0000000000000000
χ592222-2-2-2-2-2-2-22-22222-22-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000002-22-2000000000000000000000000−2i2i−2i2i0000000000000000
χ602222-2-2-2-2-2-2-22-22222-22-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000-22-220000000000000000000000002i−2i2i−2i0000000000000000
χ612-2-2222-2-222-2-2-22-2-2222-22i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i002i−2i−2i2i0000000000000000000000-222-2000000000000000000000000
χ622-2-2222-2-222-2-2-22-2-2222-22i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00−2i2i2i−2i00000000000000000000002-2-22000000000000000000000000
χ632-2-2222-2-222-2-2-22-2-2222-2−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i002i−2i−2i2i00000000000000000000002-2-22000000000000000000000000
χ642-2-2222-2-222-2-2-22-2-2222-2−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00−2i2i2i−2i0000000000000000000000-222-2000000000000000000000000
χ652-2-2222-2-22-222-2-2-22-2-2222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i−2i2i000000000000000000000000-222-2
χ662-2-2222-2-22-222-2-2-22-2-2222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i2i−2i0000000000000000000000002-2-22
χ672-2-2222-2-22-222-2-2-22-2-222−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i−2i2i0000000000000000000000002-2-22
χ682-2-2222-2-22-222-2-2-22-2-222−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i2i−2i000000000000000000000000-222-2
χ692-2-2222-2-2-22-222-22-22-2-222i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000002-2-220000000000000000000000002i−2i−2i2i0000000000000000
χ702-2-2222-2-2-22-222-22-22-2-222i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i00000000-222-2000000000000000000000000−2i2i2i−2i0000000000000000
χ712-2-2222-2-2-22-222-22-22-2-22−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000002-2-22000000000000000000000000−2i2i2i−2i0000000000000000
χ722-2-2222-2-2-22-222-22-22-2-22−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i00000000-222-20000000000000000000000002i−2i−2i2i0000000000000000
χ732-2-2222-2-2-2-22-22222-22-2-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2-20000-220000000000000000000000002i−2i−2i2i00000000000000000000
χ742-2-2222-2-2-2-22-22222-22-2-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i-2200002-2000000000000000000000000−2i2i2i−2i00000000000000000000
χ752-2-2222-2-2-2-22-22222-22-2-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i2-20000-22000000000000000000000000−2i2i2i−2i00000000000000000000
χ762-2-2222-2-2-2-22-22222-22-2-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i-2200002-20000000000000000000000002i−2i−2i2i00000000000000000000
χ772-2-22-2-22222-2-2-2222-2-2-222222-2-2-2-2-2-2-2-222220000000000002i−2i−2i2i0000000000000000000000002i−2i−2i2i000000000000
χ782-2-22-2-22222-2-2-2222-2-2-222222-2-2-2-2-2-2-2-22222000000000000−2i2i2i−2i000000000000000000000000−2i2i2i−2i000000000000
χ792-2-22-2-22222-2-2-2222-2-2-22-2-2-2-222222222-2-2-2-20000000000002i−2i−2i2i000000000000000000000000−2i2i2i−2i000000000000
χ802-2-22-2-22222-2-2-2222-2-2-22-2-2-2-222222222-2-2-2-2000000000000−2i2i2i−2i0000000000000000000000002i−2i−2i2i000000000000
χ812-2-22-2-222-22-222-2-22-222-222-2-2-2-222-2-22222-2-2000000000000000000002i−2i−2i2i0000000000000000000000002i−2i−2i2i0000
χ822-2-22-2-222-22-222-2-22-222-222-2-2-2-222-2-22222-2-200000000000000000000−2i2i2i−2i000000000000000000000000−2i2i2i−2i0000
χ832-2-22-2-222-22-222-2-22-222-2-2-22222-2-222-2-2-2-222000000000000000000002i−2i−2i2i000000000000000000000000−2i2i2i−2i0000
χ842-2-22-2-222-22-222-2-22-222-2-2-22222-2-222-2-2-2-22200000000000000000000−2i2i2i−2i0000000000000000000000002i−2i−2i2i0000
χ852-2-22-2-222-2-22-222-2-22-22222-2-222-2-2-2-222-2-22200000000000000002-2-220000000000000000000000002-2-2200000000
χ862-2-22-2-222-2-22-222-2-22-22222-2-222-2-2-2-222-2-2220000000000000000-222-2000000000000000000000000-222-200000000
χ872-2-22-2-222-2-22-222-2-22-222-2-222-2-22222-2-222-2-200000000000000002-2-22000000000000000000000000-222-200000000
χ882-2-22-2-222-2-22-222-2-22-222-2-222-2-22222-2-222-2-20000000000000000-222-20000000000000000000000002-2-2200000000
χ8988-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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