Finite Group Databasebeta

← Group #72248328

Character table — Group #72248328

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size111122222222224444444444444444444444444488888888888888888888888888888888161616161616161616161616161616161616161616161616242424244848484848484848484848484848
order122222222236662222222244446666661212121212121212222244446666666666666666121212121212121224446688881212121212122424242424242424222244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11111-1-1-1-111-1-11111-1-1-1-111-1-11-11-11-111-1-111-1-1
χ101111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11111-1-1-1-111-1-11111-1-1-1-1-1-111-11-11-11-1-111-1-111
χ111111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-1-111-1-1-1-1111111-1-1-11-111-111-1-1-1-111
χ121111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-1-111-1-1-1-11111-1-1111-11-1-11-1-11111-1-1
χ131111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-111-1-1-1-1-1-1111111-1-11-11-11-1-1-111-1-111
χ141111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-111-1-1-1-1-1-11111-1-111-11-11-1111-1-111-1-1
χ151111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111-1-1111111-1-1-1-111-1-1-11-111-1-1-11111-1-1
χ161111-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-111-1-1111111-1-1-1-1-1-1111-11-1-1111-1-1-1-111
χ17222222222222222-222-2-22-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000000000000000000022-2-20000000000
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χ482-2-2222-2-2-222-2-222-22-2-22-22-2-222-222-2-22-2-2-2-22222-22-22-22-222-2-222-2-22-22-22-22-22-22-22-22-22000000000000000000000000000000000000000000
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χ864444-44-44-4-44444000000000000-4-44-44-400000000-2-22222-2-200000000-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000
χ874444-44-44-4-4-2-2-2-200000000000022-22-22−2i32i32i3−2i32i3−2i3−2i32i322-2-2-2-22200000000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3000000000000000000000000000000000000000000
χ884444-44-44-4-4-2-2-2-200000000000022-22-22−2i32i32i3−2i32i3−2i3−2i32i3-2-22222-2-2000000001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i3000000000000000000000000000000000000000000
χ894444-44-44-4-4-2-2-2-200000000000022-22-222i3−2i3−2i32i3−2i32i32i3−2i322-2-2-2-22200000000−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i31−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i3000000000000000000000000000000000000000000
χ904444-44-44-4-4-2-2-2-200000000000022-22-222i3−2i3−2i32i3−2i32i32i3−2i3-2-22222-2-2000000001−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i3000000000000000000000000000000000000000000
χ914444-4-4-4-444-2-2-2-24-4-4-4444-4-444-4-22222-222-2-2-2-22200000000-2-22222-2-20000000000000000000000000000000000000000000000000000000000
χ924444-4-4-4-444-2-2-2-2-4444-4-4-44-444-4-22222-222-2-2-2-2220000000022-2-2-2-2220000000000000000000000000000000000000000000000000000000000
χ934-4-4444-4-4-44-222-2444-44-4-4-444-4-42-2-222-2-2-2-2-2222200000000-22-22-22-220000000000000000000000000000000000000000000000000000000000
χ944-4-4444-4-4-44-222-2-4-4-44-444444-4-42-2-222-2-2-2-2-22222000000002-22-22-22-20000000000000000000000000000000000000000000000000000000000
χ954-4-444-4-444-44-4-4400000000000044-4-44-4000000002-22-2-22-22000000002-22-22-22-2-22-22-22-22000000000000000000000000000000000000000000
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χ974-4-444-4-444-4-222-2000000000000-2-222-22−2i32i3−2i32i32i3−2i32i3−2i32-22-2-22-2200000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000000000
χ984-4-444-4-444-4-222-2000000000000-2-222-22−2i32i3−2i32i32i3−2i32i3−2i3-22-222-22-2000000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000000000
χ994-4-444-4-444-4-222-2000000000000-2-222-222i3−2i32i3−2i3−2i32i3−2i32i32-22-2-22-2200000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000000000
χ1004-4-444-4-444-4-222-2000000000000-2-222-222i3−2i32i3−2i3−2i32i3−2i32i3-22-222-22-2000000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000000000
χ1014-4-44-444-44-44-4-440000000000004-444-4-4000000002-2-22-222-2000000002-22-2-22-22-22-222-22-2000000000000000000000000000000000000000000
χ1024-4-44-444-44-44-4-440000000000004-444-4-400000000-222-22-2-2200000000-22-222-22-22-22-2-22-22000000000000000000000000000000000000000000
χ1034-4-44-444-44-4-222-2000000000000-22-2-222−2i32i32i3−2i3−2i32i32i3−2i32-2-22-222-200000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000000000
χ1044-4-44-444-44-4-222-2000000000000-22-2-222−2i32i32i3−2i3−2i32i32i3−2i3-222-22-2-22000000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000000000
χ1054-4-44-444-44-4-222-2000000000000-22-2-2222i3−2i3−2i32i32i3−2i3−2i32i32-2-22-222-200000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000000000
χ1064-4-44-444-44-4-222-2000000000000-22-2-2222i3−2i3−2i32i32i3−2i3−2i32i3-222-22-2-22000000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000000000
χ1074-4-44-4-444-44-222-244-44-44-4-44-44-4222-2-2-2-2-222-2-22200000000-22-222-22-20000000000000000000000000000000000000000000000000000000000
χ1084-4-44-4-444-44-222-2-4-44-44-4444-44-4222-2-2-2-2-222-2-222000000002-22-2-22-220000000000000000000000000000000000000000000000000000000000
χ10988-8-800000088-8-80000000000000000000000000000000000000000000000000000000000000000000000000000000000004-400000000000000
χ11088-8-800000088-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000-4400000000000000
χ1118-88-80000008-88-800000000000000000000000000000000000000000000000000000000000000000000000000000000004-40000000000000000
χ1128-88-80000008-88-80000000000000000000000000000000000000000000000000000000000000000000000000000000000-440000000000000000
χ1131616-16-16000000-8-8880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11416-1616-16000000-88-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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