Finite Group Databasebeta

← Group #363321

Character table — Group #363321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444222244444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171-1-1-1-1-1-11111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ181-1-1-1-1-1-11111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ191-1-1-1-1-1-11111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ201-1-1-1-1-1-11111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ211-1-1-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ221-1-1-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ231-1-1-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ241-1-1-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ251-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ261-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ271-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ281-1-1-1-1-1-11111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ291-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ301-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ311-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ321-1-1-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
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χ342222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ372222-2-2-222-2-22-2-22-200002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000002-22-200000000000000000000000000000000000000002−22−2i2−i2i2−i2i2−i2i2−i22−22−2
χ382222-2-2-222-2-22-2-22-200002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000002-22-20000000000000000000000000000000000000000−22−22−i2i2−i2i2−i2i2−i2i2−22−22
χ392222-2-2-222-2-22-2-22-200002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000-22-2200000000000000000000000000000000000000002−22−2i2−i2i2−i2−i2i2−i2i2−22−22
χ402222-2-2-222-2-22-2-22-200002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000-22-220000000000000000000000000000000000000000−22−22−i2i2−i2i2i2−i2i2−i22−22−2
χ412222-2-2-222-2-22-2-22-20000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000-22-2200000000000000000000000000000000000000002−22−2−i2i2−i2i2i2−i2i2−i2−22−22
χ422222-2-2-222-2-22-2-22-20000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000-22-220000000000000000000000000000000000000000−22−22i2−i2i2−i2−i2i2−i2i22−22−2
χ432222-2-2-222-2-22-2-22-20000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000002-22-200000000000000000000000000000000000000002−22−2−i2i2−i2i2−i2i2−i2i22−22−2
χ442222-2-2-222-2-22-2-22-20000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000002-22-20000000000000000000000000000000000000000−22−22i2−i2i2−i2i2−i2i2−i2−22−22
χ45222-22-2-22-22-2-22-2-2222-2-2000000002i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000000000002-22-200002i−2i2i−2i0000000000000000
χ46222-22-2-22-22-2-22-2-2222-2-2000000002i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i00000000000000000000000000000000-22-220000−2i2i−2i2i0000000000000000
χ47222-22-2-22-22-2-22-2-2222-2-200000000−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i000000000000000000000000000000002-22-20000−2i2i−2i2i0000000000000000
χ48222-22-2-22-22-2-22-2-2222-2-200000000−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i00000000000000000000000000000000-22-2200002i−2i2i−2i0000000000000000
χ49222-22-2-22-22-2-22-2-22-2-222000000002i−2i2i−2i2i−2i2i−2i-2-222−2i2i−2i2i00000000000000000000000000002i−2i2i−2i00002-22-200000000000000000000
χ50222-22-2-22-22-2-22-2-22-2-222000000002i−2i2i−2i2i−2i2i−2i-2-222−2i2i−2i2i0000000000000000000000000000−2i2i−2i2i0000-22-2200000000000000000000
χ51222-22-2-22-22-2-22-2-22-2-22200000000−2i2i−2i2i−2i2i−2i2i-2-2222i−2i2i−2i00000000000000000000000000002i−2i2i−2i0000-22-2200000000000000000000
χ52222-22-2-22-22-2-22-2-22-2-22200000000−2i2i−2i2i−2i2i−2i2i-2-2222i−2i2i−2i0000000000000000000000000000−2i2i−2i2i00002-22-200000000000000000000
χ5322-22-22-2-222-2-2-22-222-22-22i−2i2i−2i2i−2i2i−2i000000002-22-2000000002i−2i2i−2i0000000000002-22-22i−2i2i−2i00000000000000000000000000000000
χ5422-22-22-2-222-2-2-22-222-22-22i−2i2i−2i2i−2i2i−2i000000002-22-2000000002i−2i2i−2i000000000000-22-22−2i2i−2i2i00000000000000000000000000000000
χ5522-22-22-2-222-2-2-22-222-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-200000000−2i2i−2i2i0000000000002-22-2−2i2i−2i2i00000000000000000000000000000000
χ5622-22-22-2-222-2-2-22-222-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-200000000−2i2i−2i2i000000000000-22-222i−2i2i−2i00000000000000000000000000000000
χ5722-22-22-2-222-2-2-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000-22-2200000000−2i2i−2i2i00002-22-22i−2i2i−2i0000000000000000000000000000000000000000
χ5822-22-22-2-222-2-2-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000-22-2200000000−2i2i−2i2i0000-22-22−2i2i−2i2i0000000000000000000000000000000000000000
χ5922-22-22-2-222-2-2-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000-22-22000000002i−2i2i−2i00002-22-2−2i2i−2i2i0000000000000000000000000000000000000000
χ6022-22-22-2-222-2-2-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000-22-22000000002i−2i2i−2i0000-22-222i−2i2i−2i0000000000000000000000000000000000000000
χ612-22-22-22-222-2-2-222-22-22-22i−2i2i−2i−2i2i−2i2i00000000-22-22000000002i−2i−2i2i0000000000002-2-222i−2i−2i2i00000000000000000000000000000000
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χ652-22-22-22-222-2-2-222-2-22-222i−2i2i−2i−2i2i−2i2i000000002-22-200000000−2i2i2i−2i00002-2-222i−2i−2i2i0000000000000000000000000000000000000000
χ662-22-22-22-222-2-2-222-2-22-222i−2i2i−2i−2i2i−2i2i000000002-22-200000000−2i2i2i−2i0000-222-2−2i2i2i−2i0000000000000000000000000000000000000000
χ672-22-22-22-222-2-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i000000002-22-2000000002i−2i−2i2i00002-2-22−2i2i2i−2i0000000000000000000000000000000000000000
χ682-22-22-22-222-2-2-222-2-22-22−2i2i−2i2i2i−2i2i−2i000000002-22-2000000002i−2i−2i2i0000-222-22i−2i−2i2i0000000000000000000000000000000000000000
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χ742-2-22-2222-22-2-22-22-2-2-222000000002i−2i2i−2i−2i2i−2i2i22-2-2−2i2i2i−2i0000000000000000000000000000-222-200002i−2i−2i2i00000000000000000000
χ752-2-22-2222-22-2-22-22-2-2-22200000000−2i2i−2i2i2i−2i2i−2i22-2-22i−2i−2i2i00000000000000000000000000002-2-2200002i−2i−2i2i00000000000000000000
χ762-2-22-2222-22-2-22-22-2-2-22200000000−2i2i−2i2i2i−2i2i−2i22-2-22i−2i−2i2i0000000000000000000000000000-222-20000−2i2i2i−2i00000000000000000000
χ772-2-2-222222-2-22-2-2-2200002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000002-2-220000000000000000000000000000000000000000i2−i2−i2i2−222−2−222−2i2−i2−i2i2
χ782-2-2-222222-2-22-2-2-2200002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000002-2-220000000000000000000000000000000000000000−i2i2i2−i22−2−222−2−22−i2i2i2−i2
χ792-2-2-222222-2-22-2-2-2200002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000-222-20000000000000000000000000000000000000000i2−i2−i2i2−222−22−2−22−i2i2i2−i2
χ802-2-2-222222-2-22-2-2-2200002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000-222-20000000000000000000000000000000000000000−i2i2i2−i22−2−22−222−2i2−i2−i2i2
χ812-2-2-222222-2-22-2-2-220000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000-222-20000000000000000000000000000000000000000i2−i2−i2i22−2−22−222−2−i2i2i2−i2
χ822-2-2-222222-2-22-2-2-220000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000-222-20000000000000000000000000000000000000000−i2i2i2−i2−222−22−2−22i2−i2−i2i2
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χ852-2-2-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ862-2-2-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ872-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ882-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222222222-2-222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ89444-4-4444-4-44-4-44-4-40000000000004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4444-4-44-4-44-4-4000000000000-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ9144-444-44-44-44-44-4-4-400004-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-444-44-44-44-44-4-4-40000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-444-4-4-4-4-44444-40000000000000000000000000000000000004-44-4000000000000000000000000000000000000000000000000
χ9444-4-444-4-4-4-4-44444-4000000000000000000000000000000000000-44-44000000000000000000000000000000000000000000000000
χ9544-4-4-4-44-4-4444-4-4444-4-4400000000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-4-44-4-4444-4-444-444-40000000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ974-44444-4-4-4444-4-4-4-44-4-440000000000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ984-44444-4-4-4444-4-4-4-4-444-400000000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-44-4-4-4-4444-440000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ1004-444-4-44-4-4-4-4444-44000000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000
χ1014-44-4-44-4-44-44-44-44400004-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-44-4-44-44-44-4440000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-444-4-44-4-44-4-44440000000000004-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-444-4-44-4-44-4-4444000000000000-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000

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