Finite Group Databasebeta

← Group #72216407

Character table — Group #72216407

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11111111222222222222444444448888888888888888161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232323232323232323232323264646464
order122244442222224444444444444444444444888888882244888888888888888888882224444444444444448888161616161616161616161616161616168888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ511111111111111111111111111111111111111111111-1-1-1-111111111111111111111-11-111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-11-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ811111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ91111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1111-11-11-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1
χ101111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11-11111iiii−i−i−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11
χ111111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1111-11-11-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ121111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11-11111−i−i−i−iiiii11-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11
χ131111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-11-1-11-1-11−i−i−i−iiiii-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11
χ141111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-11-1−i−i−i−iiiii-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ151111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-11-1-11-1-11iiii−i−i−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ161111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-11-1iiii−i−i−i−i-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1
χ17222222222222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000200000020000000000-2-2-2-200000000000000000000
χ18222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2000000-20000000000222200000000000000000000
χ192222222222222222222222222222-2-2-2-2-2-2-2-222-2-222-2-200002-22-200000000000000000020022002000000000000000000000000000000-2-2
χ202222222222222222222222222222-2-2-2-2-2-2-2-222-2-222-2-200002-22-2000000000000000000-200-2-200-200000000000000000000000000000022
χ212222222222222222222222222222-2-2-2-2-2-2-2-2-2-222-2-2220000-22-22000000000000000002022000200000000000000000000000000000-2-200
χ222222222222222222222222222222-2-2-2-2-2-2-2-2-2-222-2-2220000-22-2200000000000000000-20-2-2000-2000000000000000000000000000002200
χ232222222222-2-2-2-22-2-2-2-2222-2-22-22-20000000000-2-200-2-200000202i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2020-2-200020000000000000i2i2−i2−i2i2i2−i2−i2000000000000
χ242222222222-2-2-2-22-2-2-2-2222-2-22-22-20000000000-2-200-2-200000202i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20-2022000-20000000000000−i2−i2i2i2−i2−i2i2i2000000000000
χ252222222222-2-2-2-22-2-2-2-2222-2-22-22-20000000000-2-200-2-200000202−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2020-2-200020000000000000−i2−i2i2i2−i2−i2i2i2000000000000
χ262222222222-2-2-2-22-2-2-2-2222-2-22-22-20000000000-2-200-2-200000202−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20-2022000-20000000000000i2i2−i2−i2i2i2−i2−i2000000000000
χ272222222222-2-2-2-22-2-2-2-22-2-222-22-2200000000-2-200-2-20000002020i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200200-2-200200000000000000000000i2i2−i2−i2i2i2−i2−i20000
χ282222222222-2-2-2-22-2-2-2-22-2-222-22-2200000000-2-200-2-20000002020i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-2002200-200000000000000000000−i2−i2i2i2−i2−i2i2i20000
χ292222222222-2-2-2-22-2-2-2-22-2-222-22-2200000000-2-200-2-20000002020−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200200-2-200200000000000000000000−i2−i2i2i2−i2−i2i2i20000
χ302222222222-2-2-2-22-2-2-2-22-2-222-22-2200000000-2-200-2-20000002020−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-2002200-200000000000000000000i2i2−i2−i2i2i2−i2−i20000
χ3122222222-2-222-2-2-2-2-222-22-22-2-2-22222-2-222-2-200000000222200000000000000000000-2000000-200000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000
χ3222222222-2-222-2-2-2-2-222-22-22-2-2-22222-2-222-2-200000000222200000000000000000000-2000000-200000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000
χ3322222222-2-222-2-2-2-2-222-22-22-2-2-22222-2-222-2-200000000-2-2-2-2000000000000000000002000000200000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000
χ3422222222-2-222-2-2-2-2-222-22-22-2-2-22222-2-222-2-200000000-2-2-2-2000000000000000000002000000200000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000
χ352222-2-2-2-2222222-2-2-2-2-2-2-22-22-2-22222-2-2-2-2220000000022-2-2000000000000000000002000000-2000000000000002−22−2−22−222−22−2−22−220000
χ362222-2-2-2-2222222-2-2-2-2-2-2-22-22-2-22222-2-2-2-2220000000022-2-2000000000000000000002000000-200000000000000−22−222−22−2−22−222−22−20000
χ372222-2-2-2-2222222-2-2-2-2-2-2-22-22-2-22222-2-2-2-22200000000-2-22200000000000000000000-20000002000000000000002−22−2−22−22−22−222−22−20000
χ382222-2-2-2-2222222-2-2-2-2-2-2-22-22-2-22222-2-2-2-22200000000-2-22200000000000000000000-2000000200000000000000−22−222−22−22−22−2−22−220000
χ392222-2-2-2-2-2-222-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000-200000020000000000-2-22200000000000000000000
χ402222-2-2-2-2-2-222-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-222-2-22200000000000000002000000-2000000000022-2-200000000000000000000
χ412222-2-2-2-2-2-222-2-2222-2-22-2-2-2-22222-2-2-2-2222222-2-2-2-22200002-2-220000000000000000002002-200-2000000000000000000000000000000-22
χ422222-2-2-2-2-2-222-2-2222-2-22-2-2-2-22222-2-2-2-2222222-2-2-2-22200002-2-22000000000000000000-200-220020000000000000000000000000000002-2
χ432222-2-2-2-2-2-222-2-2222-2-22-2-2-2-22222-2-2-2-22222-2-22222-2-20000-222-200000000000000000202-2000-200000000000000000000000000000-2200
χ442222-2-2-2-2-2-222-2-2222-2-22-2-2-2-22222-2-2-2-22222-2-22222-2-20000-222-200000000000000000-20-220002000000000000000000000000000002-200
χ452222-2-2-2-2-2-2-2-2222-2-222222-2-2-22-2200000000-2-2002200000020-2022−2−222−2−2−2−222−2−22200200-2200-20000000000000000000022−2−2−2−2220000
χ462222-2-2-2-2-2-2-2-2222-2-222222-2-2-22-2200000000-2-2002200000020-2022−2−222−2−2−2−222−2−22200-2002-200200000000000000000000−2−22222−2−20000
χ472222-2-2-2-2-2-2-2-2222-2-222222-2-2-22-2200000000-2-2002200000020-20−2−222−2−22222−2−222−2−200200-2200-200000000000000000000−2−22222−2−20000
χ482222-2-2-2-2-2-2-2-2222-2-222222-2-2-22-2200000000-2-2002200000020-20−2−222−2−22222−2−222−2−200-2002-20020000000000000000000022−2−2−2−2220000
χ492222-2-2-2-2-2-2-2-2222-2-2222-2-2222-22-20000000000-2-200220000020-22222−2−2−2−2−2−2−2−22222020-22000-2000000000000022−2−2−2−222000000000000
χ502222-2-2-2-2-2-2-2-2222-2-2222-2-2222-22-20000000000-2-200220000020-22222−2−2−2−2−2−2−2−222220-202-200020000000000000−2−22222−2−2000000000000
χ512222-2-2-2-2-2-2-2-2222-2-2222-2-2222-22-20000000000-2-200220000020-2−2−2−2−222222222−2−2−2−2020-22000-20000000000000−2−22222−2−2000000000000
χ522222-2-2-2-2-2-2-2-2222-2-2222-2-2222-22-20000000000-2-200220000020-2−2−2−2−222222222−2−2−2−20-202-20002000000000000022−2−2−2−222000000000000
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χ9188-8-88i−8i8i−8i00008-808i−8i00000000000000000000000000000000000000000000000000000000000002-22i−2i2i−2i2-2000000000000000000000000
χ9288-8-88i−8i8i−8i00008-808i−8i0000000000000000000000000000000000000000000000000000000000000-22−2i2i−2i2i-22000000000000000000000000
χ9388-8-88i−8i8i−8i0000-880−8i8i00000000000000000000000000000000000000000000000000000000000002i−2i2-2-22−2i2i000000000000000000000000
χ9488-8-88i−8i8i−8i0000-880−8i8i0000000000000000000000000000000000000000000000000000000000000−2i2i-222-22i−2i000000000000000000000000
χ9588-8-8−8i8i−8i8i00008-80−8i8i00000000000000000000000000000000000000000000000000000000000002-2−2i2i−2i2i2-2000000000000000000000000
χ9688-8-8−8i8i−8i8i00008-80−8i8i0000000000000000000000000000000000000000000000000000000000000-222i−2i2i−2i-22000000000000000000000000
χ9788-8-8−8i8i−8i8i0000-8808i−8i00000000000000000000000000000000000000000000000000000000000002i−2i-222-2−2i2i000000000000000000000000
χ9888-8-8−8i8i−8i8i0000-8808i−8i0000000000000000000000000000000000000000000000000000000000000−2i2i2-2-222i−2i000000000000000000000000
χ998-88-88i−8i−8i8i008-8000008i−8i00000000000000000000000004-44i−4i00000000000000000000000000000000000000000000000000000000000000
χ1008-88-88i−8i−8i8i008-8000008i−8i0000000000000000000000000-44−4i4i00000000000000000000000000000000000000000000000000000000000000
χ1018-88-88i−8i−8i8i00-8800000−8i8i000000000000000000000000000000000000000000000000000000000000000000022−222i2−2i200000000000000000000
χ1028-88-88i−8i−8i8i00-8800000−8i8i0000000000000000000000000000000000000000000000000000000000000000000−2222−2i22i200000000000000000000
χ1038-88-8−8i8i8i−8i008-800000−8i8i00000000000000000000000004-4−4i4i00000000000000000000000000000000000000000000000000000000000000
χ1048-88-8−8i8i8i−8i008-800000−8i8i0000000000000000000000000-444i−4i00000000000000000000000000000000000000000000000000000000000000
χ1058-88-8−8i8i8i−8i00-88000008i−8i000000000000000000000000000000000000000000000000000000000000000000022−22−2i22i200000000000000000000
χ1068-88-8−8i8i8i−8i00-88000008i−8i0000000000000000000000000000000000000000000000000000000000000000000−22222i2−2i200000000000000000000
χ1078-8-8888-8-8-880000-800008000000004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-8888-8-8-880000-80000800000000-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-8-8888-80000-800008000000004-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-8-8888-80000-80000800000000-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.