Finite Group Databasebeta

← Group #72225499

Character table — Group #72225499

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1122222224444444444444488888888888888888888888161616161616161616161616161616163232323232323232323232323232323232323232323232323232323232323232128128128128
order1224488882444448888161616164444888881616161616163232323232323232161616163232323232323232323232322244444488888888646464646464646464646464646464642488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1
χ9111111111-111-1-1-11-1-111111ii−i−iii−i−i-111-1-1-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1-11-1ii−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i
χ10111111111-111-1-1-11-1-111111ii−i−iii−i−i-111-1-1-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1-11-1ii−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-11−ii
χ11111111111-111-1-1-11-1-111111ii−i−iii−i−i-111-1-1-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i-11-11−i−iii-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i-11−ii
χ12111111111-111-1-1-11-1-111111ii−i−iii−i−i-111-1-1-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i-11-11−i−iii-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1i−i
χ13111111111-111-1-1-11-1-111111−i−iii−i−iii-111-1-1-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1-11-1−i−iii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii
χ14111111111-111-1-1-11-1-111111−i−iii−i−iii-111-1-1-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1-11-1−i−iii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-11i−i
χ15111111111-111-1-1-11-1-111111−i−iii−i−iii-111-1-1-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii-11-11ii−i−i-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii-11i−i
χ16111111111-111-1-1-11-1-111111−i−iii−i−iii-111-1-1-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii-11-11ii−i−i-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1−ii
χ1722222222222222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222222222222-2-2-2-2222222222-2-2-2-2-2-200000000-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ202222222222222222222-2-2-2-2222222222-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ212222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2000000002222000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-20000000022220000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ23222222222-222-2-2-22-2-2222222i2i−2i−2i2i2i−2i−2i-222-2-2-2-2-2-2-2-222222i2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ24222222222-222-2-2-22-2-222222−2i−2i2i2i−2i−2i2i2i-222-2-2-2-2-2-2-2-22222−2i−2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ25222222222-222-2-2-22-2-22-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-2-2222200000000−2i−2i2i2i000000000000000000000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000
χ26222222222-222-2-2-22-2-22-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-2-2222200000000−2i−2i2i2i0000000000000000000000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000
χ27222222222-222-2-2-22-2-22-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2-22222000000002i2i−2i−2i000000000000000000000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000
χ28222222222-222-2-2-22-2-22-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2-22222000000002i2i−2i−2i0000000000000000000000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000
χ2922222-2-2222-2-2-2-22-2-2-222222000000002-2-2-2-2222222-2-2-2-20000-2-2220000000022220000-2-2-2-2000000000000000000000000
χ3022222-2-2222-2-2-2-22-2-2-222222000000002-2-2-2-2222222-2-2-2-20000-2-22200000000-2-2-2-200002222000000000000000000000000
χ3122222-2-2222-2-2-2-22-2-2-222222000000002-2-2-2-222-2-2-2-22222000022-2-200000000000022220000-2-2-2-200000000000000000000
χ3222222-2-2222-2-2-2-22-2-2-222222000000002-2-2-2-222-2-2-2-22222000022-2-2000000000000-2-2-2-20000222200000000000000000000
χ3322222-2-222-2-2-222-2-2222222200000000-2-2-222-2-2222222220000-2-2-2-2000000002-22-20000-2-222000000000000000000000000
χ3422222-2-222-2-2-222-2-2222222200000000-2-2-222-2-2222222220000-2-2-2-200000000-22-22000022-2-2000000000000000000000000
χ3522222-2-222-2-2-222-2-2222222200000000-2-2-222-2-2-2-2-2-2-2-2-2-2000022220000000000002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ3622222-2-222-2-2-222-2-2222222200000000-2-2-222-2-2-2-2-2-2-2-2-2-200002222000000000000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ3722222-2-2-2-2222222-2-2-2-200002222-2-2-2-2-200000022−2−222−2−200002−22−222−2−222−2−20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ3822222-2-2-2-2222222-2-2-2-200002222-2-2-2-2-200000022−2−222−2−200002−22−222−2−222−2−20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ3922222-2-2-2-2222222-2-2-2-200002222-2-2-2-2-2000000−2−222−2−2220000−22−22−2−222−2−2220000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ4022222-2-2-2-2222222-2-2-2-200002222-2-2-2-2-2000000−2−222−2−2220000−22−22−2−222−2−2220000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ4122222-2-2-2-2222222-2-2-2-20000-2-2-2-22222-200000022−2−222−2−200002−22−2−2−222−2−2220000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ4222222-2-2-2-2222222-2-2-2-20000-2-2-2-22222-200000022−2−222−2−200002−22−2−2−222−2−2220000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ4322222-2-2-2-2222222-2-2-2-20000-2-2-2-22222-2000000−2−222−2−2220000−22−2222−2−222−2−20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ4422222-2-2-2-2222222-2-2-2-20000-2-2-2-22222-2000000−2−222−2−2220000−22−2222−2−222−2−20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ4522222-2-2-2-2-222-2-2-2-222-200002i2i−2i−2i−2i−2i2i2i200000022−2−2−2−22200002−2−22i2i2−i2−i2−i2−i2i2i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ4622222-2-2-2-2-222-2-2-2-222-200002i2i−2i−2i−2i−2i2i2i200000022−2−2−2−22200002−2−22i2i2−i2−i2−i2−i2i2i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ4722222-2-2-2-2-222-2-2-2-222-200002i2i−2i−2i−2i−2i2i2i2000000−2−22222−2−20000−222−2−i2−i2i2i2i2i2−i2−i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ4822222-2-2-2-2-222-2-2-2-222-200002i2i−2i−2i−2i−2i2i2i2000000−2−22222−2−20000−222−2−i2−i2i2i2i2i2−i2−i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ4922222-2-2-2-2-222-2-2-2-222-20000−2i−2i2i2i2i2i−2i−2i200000022−2−2−2−22200002−2−22−i2−i2i2i2i2i2−i2−i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ5022222-2-2-2-2-222-2-2-2-222-20000−2i−2i2i2i2i2i−2i−2i200000022−2−2−2−22200002−2−22−i2−i2i2i2i2i2−i2−i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ5122222-2-2-2-2-222-2-2-2-222-20000−2i−2i2i2i2i2i−2i−2i2000000−2−22222−2−20000−222−2i2i2−i2−i2−i2−i2i2i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ5222222-2-2-2-2-222-2-2-2-222-20000−2i−2i2i2i2i2i−2i−2i2000000−2−22222−2−20000−222−2i2i2−i2−i2−i2−i2i2i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ5322-22-200220002i−2i002i−2i-222-2-21+i−1−i1−i−1+i1+i−1−i1−i−1+i0002i−2i002-22-22i−2i2i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i020-21−i−1+i1+i−1−i2i−2i001−i−1+i1+i−1−i00000000000000000000
χ5422-22-200220002i−2i002i−2i-222-2-21+i−1−i1−i−1+i1+i−1−i1−i−1+i0002i−2i002-22-22i−2i2i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0-202−1+i1−i−1−i1+i−2i2i00−1+i1−i−1−i1+i00000000000000000000
χ5522-22-200220002i−2i002i−2i-222-2-21+i−1−i1−i−1+i1+i−1−i1−i−1+i0002i−2i00-22-22−2i2i−2i2i1+i−1−i1−i−1+i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i20-201+i−1−i1−i−1+i002i−2i−1−i1+i−1+i1−i00000000000000000000
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χ5822-22-200220002i−2i002i−2i-222-2-2−1−i1+i−1+i1−i−1−i1+i−1+i1−i0002i−2i002-22-22i−2i2i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0-2021−i−1+i1+i−1−i−2i2i001−i−1+i1+i−1−i00000000000000000000
χ5922-22-200220002i−2i002i−2i-222-2-2−1−i1+i−1+i1−i−1−i1+i−1+i1−i0002i−2i00-22-22−2i2i−2i2i−1−i1+i−1+i1−i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i20-20−1−i1+i−1+i1−i002i−2i1+i−1−i1−i−1+i00000000000000000000
χ6022-22-200220002i−2i002i−2i-222-2-2−1−i1+i−1+i1−i−1−i1+i−1+i1−i0002i−2i00-22-22−2i2i−2i2i−1−i1+i−1+i1−i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i-20201+i−1−i1−i−1+i00−2i2i−1−i1+i−1+i1−i00000000000000000000
χ6122-22-20022000−2i2i00−2i2i-222-2-21−i−1+i1+i−1−i1−i−1+i1+i−1−i000−2i2i002-22-2−2i2i−2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i020-21+i−1−i1−i−1+i−2i2i001+i−1−i1−i−1+i00000000000000000000
χ6222-22-20022000−2i2i00−2i2i-222-2-21−i−1+i1+i−1−i1−i−1+i1+i−1−i000−2i2i002-22-2−2i2i−2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0-202−1−i1+i−1+i1−i2i−2i00−1−i1+i−1+i1−i00000000000000000000
χ6322-22-20022000−2i2i00−2i2i-222-2-21−i−1+i1+i−1−i1−i−1+i1+i−1−i000−2i2i00-22-222i−2i2i−2i1−i−1+i1+i−1−i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i20-201−i−1+i1+i−1−i00−2i2i−1+i1−i−1−i1+i00000000000000000000
χ6422-22-20022000−2i2i00−2i2i-222-2-21−i−1+i1+i−1−i1−i−1+i1+i−1−i000−2i2i00-22-222i−2i2i−2i1−i−1+i1+i−1−i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-2020−1+i1−i−1−i1+i002i−2i1−i−1+i1+i−1−i00000000000000000000
χ6522-22-20022000−2i2i00−2i2i-222-2-2−1+i1−i−1−i1+i−1+i1−i−1−i1+i000−2i2i002-22-2−2i2i−2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i020-2−1−i1+i−1+i1−i−2i2i00−1−i1+i−1+i1−i00000000000000000000
χ6622-22-20022000−2i2i00−2i2i-222-2-2−1+i1−i−1−i1+i−1+i1−i−1−i1+i000−2i2i002-22-2−2i2i−2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0-2021+i−1−i1−i−1+i2i−2i001+i−1−i1−i−1+i00000000000000000000
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χ714444444-4-4-4-4-444-44-4-4-400000000000040000002222−22−222222−22−220000−2222−222200000000000000000000000000000000000000000000
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χ87888-8-8000080000-8000042−4242−42000000000000042−42000000000000000000000000000000000000000000000000000000000000
χ88888-8-8000080000-80000−4242−42420000000000000−4242000000000000000000000000000000000000000000000000000000000000
χ89888-8-80000-800008000042−4242−420000000000000−4242000000000000000000000000000000000000000000000000000000000000
χ90888-8-80000-8000080000−4242−4242000000000000042−42000000000000000000000000000000000000000000000000000000000000
χ9188-8-888800000000-800042−42−424200000000042−420000000000000000000000000000000000000000000000000000000000000000
χ9288-8-888800000000-8000−424242−42000000000−42420000000000000000000000000000000000000000000000000000000000000000
χ9388-8-88-8-800000000800042−42−4242000000000−42420000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-8-8000000008000−424242−4200000000042−420000000000000000000000000000000000000000000000000000000000000000
χ9516-1600082−8282−8208-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9616-1600082−82−82820-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9716-16000−828282−820-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9816-16000−8282−828208-800000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.