Finite Group Databasebeta

← Group #72338288

Character table — Group #72338288

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222444444444444444488888888881616161616161616161632323232323232323232323232323232323232323232323232323232323232323232323232326464646464646464
order12222222222222222244444444222222222222224444442244444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111−i−i−i−iiiii
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111iiii−i−i−i−i
χ91111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ111111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ121111111111111-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ131111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ141111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ161111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ17222222222222222222222222222222222222222222-2-2-2-20000-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2-2-2-222000000000000000000000000000000000000
χ192222222222222-2-2-2-2222222222-2-22222-2-2-2-222-2-2-2-222220000-2-222-2-2000000000000000000000000000000000000
χ202222222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-222-2-2-2-2-2-20000-2-22222000000000000000000000000000000000000
χ212222222222-2-2-20000-2222-2-2-22-2000000222200-2-20022-2-200002-200000000000022-2-222-2-200000000000000000000
χ222222222222-2-2-20000-2222-2-2-22-2000000222200-2-20022-2-200002-2000000000000-2-222-2-22200000000000000000000
χ232222222222-2-2-20000-2222-2-2-22-2000000222200-2-200-2-2220000-220000000022-2-20000000022-2-20000000000000000
χ242222222222-2-2-20000-2222-2-2-22-2000000222200-2-200-2-2220000-2200000000-2-22200000000-2-2220000000000000000
χ252222222222-2-2-20000-2222-2-2-22-2000000-2-2-2-200220022-2-20000-22000000002i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ262222222222-2-2-20000-2222-2-2-22-2000000-2-2-2-200220022-2-20000-2200000000−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ272222222222-2-2-20000-2222-2-2-22-2000000-2-2-2-2002200-2-22200002-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ282222222222-2-2-20000-2222-2-2-22-2000000-2-2-2-2002200-2-22200002-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292-2-22222-2-2-222-20000-222-22-2-2-220022-2-200002-200002i−2i2i−2i0000002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ302-2-22222-2-2-222-20000-222-22-2-2-220022-2-200002-200002i−2i2i−2i0000002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ312-2-22222-2-2-222-20000-222-22-2-2-220022-2-200002-20000−2i2i−2i2i000000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ322-2-22222-2-2-222-20000-222-22-2-2-220022-2-200002-20000−2i2i−2i2i000000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ332-2-22222-2-2-222-20000-222-22-2-2-2200-2-2220000-2200002i−2i2i−2i000000−2i2i0000001+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000000000000
χ342-2-22222-2-2-222-20000-222-22-2-2-2200-2-2220000-2200002i−2i2i−2i000000−2i2i000000−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000000000000000
χ352-2-22222-2-2-222-20000-222-22-2-2-2200-2-2220000-220000−2i2i−2i2i0000002i−2i0000001−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i0000000000000000
χ362-2-22222-2-2-222-20000-222-22-2-2-2200-2-2220000-220000−2i2i−2i2i0000002i−2i000000−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i0000000000000000
χ372-2-22222-2-2-2-2-2222-2-2222-2-222-2-22-20000000000002-22i−2i−2i2i000000002i−2i00001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ382-2-22222-2-2-2-2-2222-2-2222-2-222-2-22-20000000000002-22i−2i−2i2i000000002i−2i0000−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ392-2-22222-2-2-2-2-2222-2-2222-2-222-2-22-20000000000002-2−2i2i2i−2i00000000−2i2i00001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ402-2-22222-2-2-2-2-2222-2-2222-2-222-2-22-20000000000002-2−2i2i2i−2i00000000−2i2i0000−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ412-2-22222-2-2-2-2-2222-2-22-2-222-2-2222-222-2-222-2-2-222-2-22000000000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ422-2-22222-2-2-2-2-2222-2-22-2-222-2-2222-222-2-222-2-2-222-2-22000000000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ432-2-22222-2-2-2-2-2222-2-22-2-222-2-2222-2-2-222-2-2222-2-22-220000000000000000000000000000000000000000002−22−2−22−22
χ442-2-22222-2-2-2-2-2222-2-22-2-222-2-2222-2-2-222-2-2222-2-22-22000000000000000000000000000000000000000000−22−222−22−2
χ452-2-22222-2-2-2-2-22-2-222222-2-222-2-2-22000000000000-222i−2i−2i2i00000000−2i2i00001−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
χ462-2-22222-2-2-2-2-22-2-222222-2-222-2-2-22000000000000-222i−2i−2i2i00000000−2i2i0000−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ472-2-22222-2-2-2-2-22-2-222222-2-222-2-2-22000000000000-22−2i2i2i−2i000000002i−2i00001+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ482-2-22222-2-2-2-2-22-2-222222-2-222-2-2-22000000000000-22−2i2i2i−2i000000002i−2i0000−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ492-2-22222-2-2-2-2-22-2-2222-2-222-2-222-2222-2-2-2-222-22-222-20000000000000000000000000000000000000000002−2−222−2−22
χ502-2-22222-2-2-2-2-22-2-2222-2-222-2-222-2222-2-2-2-222-22-222-2000000000000000000000000000000000000000000−222−2−222−2
χ512-2-22222-2-2-2-2-22-2-2222-2-222-2-222-22-2-22222-2-22-22-22-2000000000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ522-2-22222-2-2-2-2-22-2-2222-2-222-2-222-22-2-22222-2-22-22-22-2000000000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ53444444444444444444-4-4-4-4-4-4-4-444000000000000-4-400000000000000000000000000000000000000000000000000
χ544444444444444-4-4-4-44-4-4-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ554444444444-4-4-40000-4-4-4-4444-440044440000-4-4000000000000000000000000000000000000000000000000000000
χ564444444444-4-4-40000-4-4-4-4444-4400-4-4-4-4000044000000000000000000000000000000000000000000000000000000
χ5744444-4-44-4-400000000000-44-404004-44-400000000000000000000000022-2-20000000000000000000022-2-200000000
χ5844444-4-44-4-400000000000-44-404004-44-4000000000000000000000000-2-22200000000000000000000-2-22200000000
χ5944444-4-44-4-400000000000-44-40400-44-4400000000000000000000000022-2-200000000000000000000-2-22200000000
χ6044444-4-44-4-400000000000-44-40400-44-44000000000000000000000000-2-2220000000000000000000022-2-200000000
χ614444-44-4-44-4000000004-4-4000400000004-44-4000000000022-2-20000000000000000000000000000002-22-200000000
χ624444-44-4-44-4000000004-4-4000400000004-44-40000000000-2-222000000000000000000000000000000-22-2200000000
χ634444-44-4-44-4000000004-4-400040000000-44-44000000000022-2-2000000000000000000000000000000-22-2200000000
χ644444-44-4-44-4000000004-4-400040000000-44-440000000000-2-2220000000000000000000000000000002-22-200000000
χ654444-4-44-4-444-4-44444400000000-4-400000000000000000000000000000000000000000000000022-2-22-2-2200000000
χ664444-4-44-4-444-4-44444400000000-4-4000000000000000000000000000000000000000000000000-2-222-222-200000000
χ674444-4-44-4-444-4-4-4-4-4-44000000004400000000000000000000000000000000000000000000000022-2-2-222-200000000
χ684444-4-44-4-444-4-4-4-4-4-440000000044000000000000000000000000000000000000000000000000-2-2222-2-2200000000
χ694-4-44444-4-4-444-40000-4-4-44-4444-400000044-4-400-440000000000000000000000000000000000000000000000000000
χ704-4-44444-4-4-444-40000-4-4-44-4444-4000000-4-444004-40000000000000000000000000000000000000000000000000000
χ714-4-444-4-4-44400000000000-4-4404004-4-44000000000000002-22-2000000000000000000000000002-22-2000000000000
χ724-4-444-4-4-44400000000000-4-4404004-4-4400000000000000-22-2200000000000000000000000000-22-22000000000000
χ734-4-444-4-4-44400000000000-4-440400-444-4000000000000002-22-200000000000000000000000000-22-22000000000000
χ744-4-444-4-4-44400000000000-4-440400-444-400000000000000-22-22000000000000000000000000002-22-2000000000000
χ754-4-44-44-44-4400000000-44-4000400000004-4-44000000000000000000002-22-200000000000000002-2-22000000000000
χ764-4-44-44-44-4400000000-44-4000400000004-4-4400000000000000000000-22-220000000000000000-222-2000000000000
χ774-4-44-44-44-4400000000-44-400040000000-444-4000000000000000000002-22-20000000000000000-222-2000000000000
χ784-4-44-44-44-4400000000-44-400040000000-444-400000000000000000000-22-2200000000000000002-2-22000000000000
χ794-4-44-4-4444-4-44-444-4-4400000000-440000000000000000002-2-220000002-2-2200000000000000000000000000000000
χ804-4-44-4-4444-4-44-444-4-4400000000-44000000000000000000-222-2000000-222-200000000000000000000000000000000
χ814-4-44-4-4444-4-44-4-4-4444000000004-40000000000000000002-2-22000000-222-200000000000000000000000000000000
χ824-4-44-4-4444-4-44-4-4-4444000000004-4000000000000000000-222-20000002-2-2200000000000000000000000000000000
χ8388888-8-88-8-8000000000008-880-8000000000000000000000000000000000000000000000000000000000000000000
χ848888-88-8-88-800000000-888000-80000000000000000000000000000000000000000000000000000000000000000000
χ858888-8-88-8-88-8880000-800000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-8-8-8880000000000088-80-8000000000000000000000000000000000000000000000000000000000000000000
χ878-8-88-88-88-88000000008-88000-80000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88-8-8888-88-880000-800000000000000000000000000000000000000000000000000000000000000000000000000
χ891616-16-160000000008-88-8000000000000000000000000000000000000000000000000000000000000000000000000000
χ901616-16-16000000000-88-88000000000000000000000000000000000000000000000000000000000000000000000000000
χ9116-1616-160000000008-8-88000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-1616-16000000000-888-8000000000000000000000000000000000000000000000000000000000000000000000000000

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