Finite Group Databasebeta

← Group #72271631

Character table — Group #72271631

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222224448888888888881616161616161616224444444448881616161616161616161616163232323232323232336666666661212122424242424242424242424244848484848484848
order122224444888884488161616161616161622248888366661212121224242424241212242448484848484848486661224242424222224444888884488161616161616161622248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-11111-1-1-1-111-1-111-1-111111111111111-1-1-1-11111-1-1-1-111-1-111-1-111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ9222222222-2-2-2-2-222-2-20000000000000000222222222-2-2-2-2-222-2-20000000000000000222222222-2-2-2-2-222-2-20000000000000000
χ10222222222-2-2-2-2-2-2-2220000000000000000222222222-2-2-2-2-2-2-2220000000000000000222222222-2-2-2-2-2-2-2220000000000000000
χ1122222-2-2-2-2000002-200i2i2−i2−i2i2i2−i2−i20000000022222-2-2-2-2000002-200i2i2−i2−i2i2i2−i2−i20000000022222-2-2-2-2000002-200i2i2−i2−i2i2i2−i2−i200000000
χ1222222-2-2-2-2000002-200−i2−i2i2i2−i2−i2i2i20000000022222-2-2-2-2000002-200−i2−i2i2i2−i2−i2i2i20000000022222-2-2-2-2000002-200−i2−i2i2i2−i2−i2i2i200000000
χ1322222-2-2-2-200000-2200i2i2−i2−i2−i2−i2i2i20000000022222-2-2-2-200000-2200i2i2−i2−i2−i2−i2i2i20000000022222-2-2-2-200000-2200i2i2−i2−i2−i2−i2i2i200000000
χ1422222-2-2-2-200000-2200−i2−i2i2i2i2i2−i2−i20000000022222-2-2-2-200000-2200−i2−i2i2i2i2i2−i2−i20000000022222-2-2-2-200000-2200−i2−i2i2i2i2i2−i2−i200000000
χ15222-2-222-2-2222-2-2000000002i−2i2i−2i00000000222-2-222-2-2222-2-2000000002i−2i2i−2i00000000222-2-222-2-2222-2-2000000002i−2i2i−2i00000000
χ16222-2-222-2-2222-2-200000000−2i2i−2i2i00000000222-2-222-2-2222-2-200000000−2i2i−2i2i00000000222-2-222-2-2222-2-200000000−2i2i−2i2i00000000
χ17222-2-222-2-2-2-2-22200002i−2i2i−2i000000000000222-2-222-2-2-2-2-22200002i−2i2i−2i000000000000222-2-222-2-2-2-2-22200002i−2i2i−2i000000000000
χ18222-2-222-2-2-2-2-2220000−2i2i−2i2i000000000000222-2-222-2-2-2-2-2220000−2i2i−2i2i000000000000222-2-222-2-2-2-2-2220000−2i2i−2i2i000000000000
χ19222-2-2-2-22200000002-22−2−222−2−2200000000222-2-2-2-22200000002-22−2−222−2−2200000000222-2-2-2-22200000002-22−2−222−2−2200000000
χ20222-2-2-2-22200000002-2−222−2−222−200000000222-2-2-2-22200000002-2−222−2−222−200000000222-2-2-2-22200000002-2−222−2−222−200000000
χ21222-2-2-2-2220000000-222−2−22−222−200000000222-2-2-2-2220000000-222−2−22−222−200000000222-2-2-2-2220000000-222−2−22−222−200000000
χ22222-2-2-2-2220000000-22−222−22−2−2200000000222-2-2-2-2220000000-22−222−22−2−2200000000222-2-2-2-2220000000-22−222−22−2−2200000000
χ2322-22-2-222-222-2-2200000000000000002-20022-22-2-222-222-2-2200000000000000002-20022-22-2-222-222-2-2200000000000000002-200
χ2422-22-2-222-222-2-220000000000000000-220022-22-2-222-222-2-220000000000000000-220022-22-2-222-222-2-220000000000000000-2200
χ2522-22-2-222-2-2-222-20000000000000000002i−2i22-22-2-222-2-2-222-20000000000000000002i−2i22-22-2-222-2-2-222-20000000000000000002i−2i
χ2622-22-2-222-2-2-222-2000000000000000000−2i2i22-22-2-222-2-2-222-2000000000000000000−2i2i22-22-2-222-2-2-222-2000000000000000000−2i2i
χ2722-2-22-22-2222-22-2000000000000002-2000022-2-22-22-2222-22-2000000000000002-2000022-2-22-22-2222-22-2000000000000002-20000
χ2822-2-22-22-2222-22-200000000000000-22000022-2-22-22-2222-22-200000000000000-22000022-2-22-22-2222-22-200000000000000-220000
χ2922-2-22-22-22-2-22-220000000000002-200000022-2-22-22-22-2-22-220000000000002-200000022-2-22-22-22-2-22-220000000000002-2000000
χ3022-2-22-22-22-2-22-22000000000000-2200000022-2-22-22-22-2-22-22000000000000-2200000022-2-22-22-22-2-22-22000000000000-22000000
χ3144-44-44-4-44000000000000000000000000044-44-44-4-44000000000000000000000000044-44-44-4-440000000000000000000000000
χ3244-4-444-44-4000000000000000000000000044-4-444-44-4000000000000000000000000044-4-444-44-40000000000000000000000000
χ338-8000000042−42000000000000000000000008-8000000042−42000000000000000000000008-8000000042−4200000000000000000000000
χ348-80000000−4242000000000000000000000008-80000000−4242000000000000000000000008-80000000−424200000000000000000000000
χ3511111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3611111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ37111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ38111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ3911111111111111-1-1-1-11111-1-1-1-111-1-111-1-111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ4011111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ4111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ4211111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ43222222222-2-2-2-2-222-2-20000000000000000222222222-2-2-2-2-222-2-20000000000000000-2-2-2-2-2-2-2-2-222222-2-2220000000000000000
χ44222222222-2-2-2-2-2-2-2220000000000000000222222222-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-2-22222222-2-20000000000000000
χ4522222-2-2-2-2000002-200i2i2−i2−i2i2i2−i2−i20000000022222-2-2-2-2000002-200i2i2−i2−i2i2i2−i2−i200000000-2-2-2-2-2222200000-2200−i2−i2i2i2−i2−i2i2i200000000
χ4622222-2-2-2-2000002-200−i2−i2i2i2−i2−i2i2i20000000022222-2-2-2-2000002-200−i2−i2i2i2−i2−i2i2i200000000-2-2-2-2-2222200000-2200i2i2−i2−i2i2i2−i2−i200000000
χ4722222-2-2-2-200000-2200i2i2−i2−i2−i2−i2i2i20000000022222-2-2-2-200000-2200i2i2−i2−i2−i2−i2i2i200000000-2-2-2-2-22222000002-200−i2−i2i2i2i2i2−i2−i200000000
χ4822222-2-2-2-200000-2200−i2−i2i2i2i2i2−i2−i20000000022222-2-2-2-200000-2200−i2−i2i2i2i2i2−i2−i200000000-2-2-2-2-22222000002-200i2i2−i2−i2−i2−i2i2i200000000
χ49222-2-222-2-2222-2-2000000002i−2i2i−2i00000000222-2-222-2-2222-2-2000000002i−2i2i−2i00000000-2-2-222-2-222-2-2-22200000000−2i2i−2i2i00000000
χ50222-2-222-2-2222-2-200000000−2i2i−2i2i00000000222-2-222-2-2222-2-200000000−2i2i−2i2i00000000-2-2-222-2-222-2-2-222000000002i−2i2i−2i00000000
χ51222-2-222-2-2-2-2-22200002i−2i2i−2i000000000000222-2-222-2-2-2-2-22200002i−2i2i−2i000000000000-2-2-222-2-222222-2-20000−2i2i−2i2i000000000000
χ52222-2-222-2-2-2-2-2220000−2i2i−2i2i000000000000222-2-222-2-2-2-2-2220000−2i2i−2i2i000000000000-2-2-222-2-222222-2-200002i−2i2i−2i000000000000
χ53222-2-2-2-22200000002-22−2−222−2−2200000000222-2-2-2-22200000002-22−2−222−2−2200000000-2-2-22222-2-20000000-22−222−2−222−200000000
χ54222-2-2-2-22200000002-2−222−2−222−200000000222-2-2-2-22200000002-2−222−2−222−200000000-2-2-22222-2-20000000-222−2−222−2−2200000000
χ55222-2-2-2-2220000000-222−2−22−222−200000000222-2-2-2-2220000000-222−2−22−222−200000000-2-2-22222-2-200000002-2−222−22−2−2200000000
χ56222-2-2-2-2220000000-22−222−22−2−2200000000222-2-2-2-2220000000-22−222−22−2−2200000000-2-2-22222-2-200000002-22−2−22−222−200000000
χ5722-22-2-222-222-2-2200000000000000002-20022-22-2-222-222-2-2200000000000000002-200-2-22-222-2-22-2-222-20000000000000000-2200
χ5822-22-2-222-222-2-220000000000000000-220022-22-2-222-222-2-220000000000000000-2200-2-22-222-2-22-2-222-200000000000000002-200
χ5922-22-2-222-2-2-222-20000000000000000002i−2i22-22-2-222-2-2-222-20000000000000000002i−2i-2-22-222-2-2222-2-22000000000000000000−2i2i
χ6022-22-2-222-2-2-222-2000000000000000000−2i2i22-22-2-222-2-2-222-2000000000000000000−2i2i-2-22-222-2-2222-2-220000000000000000002i−2i
χ6122-2-22-22-2222-22-2000000000000002-2000022-2-22-22-2222-22-2000000000000002-20000-2-222-22-22-2-2-22-2200000000000000-220000
χ6222-2-22-22-2222-22-200000000000000-22000022-2-22-22-2222-22-200000000000000-220000-2-222-22-22-2-2-22-22000000000000002-20000
χ6322-2-22-22-22-2-22-220000000000002-200000022-2-22-22-22-2-22-220000000000002-2000000-2-222-22-22-222-22-2000000000000-22000000
χ6422-2-22-22-22-2-22-22000000000000-2200000022-2-22-22-22-2-22-22000000000000-22000000-2-222-22-22-222-22-20000000000002-2000000
χ6544-44-44-4-44000000000000000000000000044-44-44-4-440000000000000000000000000-4-44-44-444-40000000000000000000000000
χ6644-4-444-44-4000000000000000000000000044-4-444-44-40000000000000000000000000-4-444-4-44-440000000000000000000000000
χ678-8000000042−42000000000000000000000008-8000000042−4200000000000000000000000-880000000−424200000000000000000000000
χ688-80000000−4242000000000000000000000008-80000000−424200000000000000000000000-88000000042−4200000000000000000000000
χ692222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ7022222222222222222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000000000000000000000
χ71222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111110000000000000000000000000000000000
χ72222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-10000000000000000000000000000000000
χ7322222222222222-2-2-2-22222-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1110000000000000000000000000000000000
χ7422222222222222-2-2-2-22222-2-2-2-2-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-10000000000000000000000000000000000
χ7522222222222222-2-2-2-2-2-2-2-2222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-10000000000000000000000000000000000
χ7622222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1110000000000000000000000000000000000
χ77444444444-4-4-4-4-444-4-40000000000000000-2-2-2-2-2-2-2-2-222222-2-22200000000000000000000000000000000000000000000000000
χ78444444444-4-4-4-4-4-4-4440000000000000000-2-2-2-2-2-2-2-2-22222222-2-200000000000000000000000000000000000000000000000000
χ7944444-4-4-4-4000004-4002i22i2−2i2−2i22i22i2−2i2−2i200000000-2-2-2-2-2222200000-2200−i2−i2i2i2−i2−i2i2i2000000000000000000000000000000000000000000
χ8044444-4-4-4-4000004-400−2i2−2i22i22i2−2i2−2i22i22i200000000-2-2-2-2-2222200000-2200i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000000000000000
χ8144444-4-4-4-400000-44002i22i2−2i2−2i2−2i2−2i22i22i200000000-2-2-2-2-22222000002-200−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000000000
χ8244444-4-4-4-400000-4400−2i2−2i22i22i22i22i2−2i2−2i200000000-2-2-2-2-22222000002-200i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000000000
χ83444-4-444-4-4444-4-4000000004i−4i4i−4i00000000-2-2-222-2-222-2-2-22200000000−2i2i−2i2i000000000000000000000000000000000000000000
χ84444-4-444-4-4444-4-400000000−4i4i−4i4i00000000-2-2-222-2-222-2-2-222000000002i−2i2i−2i000000000000000000000000000000000000000000
χ85444-4-444-4-4-4-4-44400004i−4i4i−4i000000000000-2-2-222-2-222222-2-20000−2i2i−2i2i0000000000000000000000000000000000000000000000
χ86444-4-444-4-4-4-4-4440000−4i4i−4i4i000000000000-2-2-222-2-222222-2-200002i−2i2i−2i0000000000000000000000000000000000000000000000
χ87444-4-4-4-44400000004-422−22−222222−22−222200000000-2-2-22222-2-20000000-22−222−2−222−2000000000000000000000000000000000000000000
χ88444-4-4-4-44400000004-4−222222−22−222222−2200000000-2-2-22222-2-20000000-222−2−222−2−22000000000000000000000000000000000000000000
χ89444-4-4-4-4440000000-4422−22−2222−222222−2200000000-2-2-22222-2-200000002-2−222−22−2−22000000000000000000000000000000000000000000
χ90444-4-4-4-4440000000-44−222222−2222−22−222200000000-2-2-22222-2-200000002-22−2−22−222−2000000000000000000000000000000000000000000
χ9144-44-4-444-444-4-4400000000000000004-400-2-22-222-2-22-2-222-20000000000000000-22000000000000000000000000000000000000
χ9244-44-4-444-444-4-440000000000000000-4400-2-22-222-2-22-2-222-200000000000000002-2000000000000000000000000000000000000
χ9344-44-4-444-4-4-444-40000000000000000004i−4i-2-22-222-2-2222-2-22000000000000000000−2i2i0000000000000000000000000000000000
χ9444-44-4-444-4-4-444-4000000000000000000−4i4i-2-22-222-2-2222-2-220000000000000000002i−2i0000000000000000000000000000000000
χ9544-4-44-44-4444-44-4000000000000004-40000-2-222-22-22-2-2-22-2200000000000000-2200000000000000000000000000000000000000
χ9644-4-44-44-4444-44-400000000000000-440000-2-222-22-22-2-2-22-22000000000000002-200000000000000000000000000000000000000
χ9744-4-44-44-44-4-44-440000000000004-4000000-2-222-22-22-222-22-2000000000000-220000000000000000000000000000000000000000
χ9844-4-44-44-44-4-44-44000000000000-44000000-2-222-22-22-222-22-20000000000002-20000000000000000000000000000000000000000
χ9988-88-88-8-880000000000000000000000000-4-44-44-444-400000000000000000000000000000000000000000000000000000000000
χ10088-8-888-88-80000000000000000000000000-4-444-4-44-4400000000000000000000000000000000000000000000000000000000000
χ10116-16000000082−8200000000000000000000000-880000000−4242000000000000000000000000000000000000000000000000000000000
χ10216-160000000−828200000000000000000000000-88000000042−42000000000000000000000000000000000000000000000000000000000

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