Finite Group Databasebeta

← Group #72253818

Character table — Group #72253818

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222244444444488888888888888888888121216161616161616161616161616161616162424242424242424242424242424243232323232323232324848969696
order122344622244461212222224444444666121212121222246666666121212121212121222224444444444488824242424242488444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-111111-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-111-11111-1-1-1111-111-1-1-111-1-1-1-11-1-111-1-1-1-1111-1-1
χ6111111111111111111-1-1-1-111-1-1-1-1111-1-111111-1-111-1-1-1-1-1-1-1-111-1-1-1111-111-1-1-111-1-1-1-1-111-1-11111-1-1-111
χ7111111111111111111-1-1-1-111-1-1-1-1111-1-1111-1-11111-1-1-111-11111-1-1-1-1-1-11-1-1111-1-111111-1-111-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1111-1-11111-111-1-11111111-1-1
χ91111111111111111-1-111-1-1-1-111-1-1111-1-11111111-1-111-111-111-1-111-111-111-11-1-1-1-111-1-1-11-1-1-111-1-111-11-1
χ101111111111111111-1-111-1-1-1-111-1-1111-1-111111-1-1-1-111-1-1-1-1-1-1-1-111-111-111-11-1-1-1-111-1-11-1111-1-111-1-11-11
χ111111111111111111-1-111-1-1-1-111-1-1111-1-1111-1-111-1-111-111-111-1-111-1-1-11-1-11-11111-1-111-11-1-1-111-1-1-1-11-11
χ121111111111111111-1-111-1-1-1-111-1-1111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-11-1-11-11111-1-1111-1111-1-11111-11-1
χ131111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1111-1-11-1-111-1-1-1-111-1-11-1-1-1-11111-1-11
χ141111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1111-1-11-1-111-1-1-1-11111-11111-1-1-1-111-1
χ151111111111111111-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-11-1-111-111-1-11111-1-1-1-11-1-1-1-111-1-111-1
χ161111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11-1-111-111-1-11111-1-111-11111-1-111-1-11
χ1722222222-2-22-2-22220000220000-2-22-2-2-2-22-2-2220000002002000000-2-2-200200220000-2-200000000000000
χ1822222222-2-22-2-22220000220000-2-22-2-2-2-22-2-2-2-20000002002000000-22200-200-2-200002200000000000000
χ1922222222-2-22-2-22220000-2-20000222-2-2222-2-222000000-200-20000002-2-200200-2-200002200000000000000
χ2022222222-2-22-2-22220000-2-20000222-2-2222-2-2-2-2000000-200-200000022200-200220000-2-200000000000000
χ212222222-22-2-22-222200220000-2-200-22-200-22-22200002200000000-2-202-202-2020000-2-20000000000000000
χ222222222-22-2-22-222200220000-2-200-22-200-22-2-2-200002200000000-2-20-220-220-20000220000000000000000
χ232222222-22-2-22-222200-2-200002200-22-200-22-2220000-2-2000000002202-20-2-20-20000220000000000000000
χ242222222-22-2-22-222200-2-200002200-22-200-22-2-2-20000-2-200000000220-22022020000-2-20000000000000000
χ252222222-2-22-2-22222220000-2-20000-2-2200-2-2222002200000000-2-2000-2220-22000-2-2000000000000000000
χ262222222-2-22-2-22222220000-2-20000-2-2200-2-22-2-2002200000000-2-20002-2-202-200022000000000000000000
χ272222222-2-22-2-22222-2-20000220000-2-2200-2-222200-2-20000000022000-22-20-2-200022000000000000000000
χ282222222-2-22-2-22222-2-20000220000-2-2200-2-22-2-200-2-200000000220002-22022000-2-2000000000000000000
χ292222-2-2222-2-2-222-2-22-200002-2000022-200-2-2200002-2000000002-2000000200-22-2002-22-200000000000000
χ302222-2-2222-2-2-222-2-22-200002-2000022-200-2-2200002-2000000002-2000000-2002-2200-22-2200000000000000
χ312222-2-2222-2-2-222-2-2-220000-22000022-200-2-220000-2200000000-22000000200-2-22002-2-2200000000000000
χ322222-2-2222-2-2-222-2-2-220000-22000022-200-2-220000-2200000000-22000000-20022-200-222-200000000000000
χ332222-2-222-22-22-22-2-2002-200002-2002-2200-22-20000002-2000000002-2000200-202-22-200-2200000000000000
χ342222-2-222-22-22-22-2-2002-200002-2002-2200-22-20000002-2000000002-2000-20020-22-22002-200000000000000
χ352222-2-222-22-22-22-2-200-220000-22002-2200-22-2000000-2200000000-22000200-20-222-2002-200000000000000
χ362222-2-222-22-22-22-2-200-220000-22002-2200-22-2000000-2200000000-22000-200202-2-2200-2200000000000000
χ372222-2-22-2222-2-22-2-200002-200002-2-222222-2-200000000200-2000000-2002-20-2200-222-20000000000000000
χ382222-2-22-2222-2-22-2-200002-200002-2-222222-2-200000000200-2000000-200-2202-2002-2-220000000000000000
χ392222-2-22-2222-2-22-2-20000-220000-22-222-2-22-2-200000000-2002000000200220-2-200-22-220000000000000000
χ402222-2-22-2222-2-22-2-20000-220000-22-222-2-22-2-200000000-2002000000200-2-2022002-22-20000000000000000
χ412222-2-22-2-2-22222-2-22-22-2-22-22-222-2-2-2-22222200002-22-2-200200-22-22-200000000000000000000000000000
χ422222-2-22-2-2-22222-2-22-2-222-2-222-2-22-2-2-2-2-222200002-2-22200-200-222-2200000000000000000000000000000
χ432222-2-22-2-2-22222-2-2-222-22-22-2-22-22-2-2-2-2-22220000-222-2200-2002-2-22200000000000000000000000000000
χ442222-2-22-2-2-22222-2-2-22-22-222-22-22-2-2-2-2222220000-22-22-2002002-22-2-200000000000000000000000000000
χ45222-122-1222222-1-1-1222222222222-1-1-1-1-1-1-1-10022-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000222-1-1-1-1-1-100000
χ46222-122-1222222-1-1-1222222222222-1-1-1-1-1-1-1-100-2-2-1-1-1-1-111-111-1-1-1-1-1000000000000000-2-2-211111100000
χ47222-122-1222222-1-1-122-2-2-2-222-2-2-2-2-1-1-111-1-1-10022-1-1111-1-11-1-1-1-11110000000000000002-2-2-1-1111100000
χ48222-122-1222222-1-1-122-2-2-2-222-2-2-2-2-1-1-111-1-1-100-2-2-1-111111111-1-1111000000000000000-22211-1-1-1-100000
χ49222-122-1222222-1-1-1-2-222-2-2-2-222-2-2-1-1-111-1-1-1002211-1-11-1-11-1-111-1-11000000000000000-22-211-1-11100000
χ50222-122-1222222-1-1-1-2-222-2-2-2-222-2-2-1-1-111-1-1-100-2-211-1-111111111-1-110000000000000002-22-1-111-1-100000
χ51222-122-1222222-1-1-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-100221111-1-1-1-1-1-11111-1000000000000000-2-221111-1-100000
χ52222-122-1222222-1-1-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-100-2-21111-111-1111111-100000000000000022-2-1-1-1-11100000
χ53222-1-2-2-1-2-2-2222-1112-22-2-22-22-222-2111-1-1-1-1-10000-11-111i3−i3-1i3−i31-11-11000000000000000000i3−i3i3−i3i3−i300000
χ54222-1-2-2-1-2-2-2222-1112-22-2-22-22-222-2111-1-1-1-1-10000-11-111−i3i3-1−i3i31-11-11000000000000000000−i3i3−i3i3−i3i300000
χ55222-1-2-2-1-2-2-2222-1112-2-222-2-222-2-2211111-1-1-10000-111-1-1i3−i31i3−i31-1-11-1000000000000000000i3−i3−i3i3−i3i300000
χ56222-1-2-2-1-2-2-2222-1112-2-222-2-222-2-2211111-1-1-10000-111-1-1−i3i31−i3i31-1-11-1000000000000000000−i3i3i3−i3i3−i300000
χ57222-1-2-2-1-2-2-2222-111-222-22-22-2-22-2211111-1-1-100001-1-11-1i3−i31i3−i3-111-1-1000000000000000000−i3i3i3−i3−i3i300000
χ58222-1-2-2-1-2-2-2222-111-222-22-22-2-22-2211111-1-1-100001-1-11-1−i3i31−i3i3-111-1-1000000000000000000i3−i3−i3i3i3−i300000
χ59222-1-2-2-1-2-2-2222-111-22-22-222-22-22-2111-1-1-1-1-100001-11-11i3−i3-1i3−i3-11-111000000000000000000−i3i3−i3i3i3−i300000
χ60222-1-2-2-1-2-2-2222-111-22-22-222-22-22-2111-1-1-1-1-100001-11-11−i3i3-1−i3i3-11-111000000000000000000i3−i3i3−i3−i3i300000
χ61444-244-24-4-44-4-4-2-2-20000440000-4-4-22222-22200000000-200-2000000200000000000000000000000000000
χ62444-244-24-4-44-4-4-2-2-20000-4-4000044-222-2-2-222000000002002000000-200000000000000000000000000000
χ63444-244-2-44-4-44-4-2-2-200440000-4-4002-22002-22000000-2-20000000022000000000000000000000000000000
χ64444-244-2-44-4-44-4-2-2-200-4-4000044002-22002-220000002200000000-2-2000000000000000000000000000000
χ65444-244-2-4-44-4-44-2-2-2440000-4-4000022-20022-20000-2-2000000002200000000000000000000000000000000
χ66444-244-2-4-44-4-44-2-2-2-4-4000044000022-20022-200002200000000-2-200000000000000000000000000000000
χ67444-2-4-4-244-4-4-44-2224-400004-40000-2-220022-20000-2200000000-2200000000000000000000000000000000
χ68444-2-4-4-244-4-4-44-222-440000-440000-2-220022-200002-2000000002-200000000000000000000000000000000
χ69444-2-4-4-24-44-44-4-222004-400004-400-22-2002-22000000-2200000000-22000000000000000000000000000000
χ70444-2-4-4-24-44-44-4-22200-440000-4400-22-2002-220000002-2000000002-2000000000000000000000000000000
χ71444-2-4-4-2-4444-4-4-22200004-400004-42-2-2-2-2-22200000000-2002000000200000000000000000000000000000
χ72444-2-4-4-2-4444-4-4-2220000-440000-442-2-222-22200000000200-2000000-200000000000000000000000000000
χ7344-44-444000000-44-4000000000000000000004-42-200000220-2-2000000000000000000000000000002-2000
χ7444-44-444000000-44-4000000000000000000004-4-2200000-2-202200000000000000000000000000000-22000
χ7544-44-444000000-44-400000000000000000000-442-200000220-2-200000000000000000000000000000-22000
χ7644-44-444000000-44-400000000000000000000-44-2200000-2-2022000000000000000000000000000002-2000
χ7788-888-88000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-48-8-400000044-4000000000000000000000000000002i3−2i30−2i32i30000000000000000000000000000000000
χ7988-8-48-8-400000044-400000000000000000000000000000−2i32i302i3−2i30000000000000000000000000000000000
χ8088-8-4-88-40000004-4400000000000000000000004-400000-2-20220000000000000000000000000000000000
χ8188-8-4-88-40000004-440000000000000000000000-4400000220-2-20000000000000000000000000000000000
χ8216-1601600-1600000000000000000000000000000000000000000000000000000000000000000000000000000
χ8316-160-80080000000000000000000000004i3−4i3000000000000000000000000000000000000000000000000000
χ8416-160-8008000000000000000000000000−4i34i3000000000000000000000000000000000000000000000000000

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