Finite Group Databasebeta

← Group #72271647

Character table — Group #72271647

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222224448888888888881616161616161616224444444448881616161616161616161616163232323232323232336666666661212122424242424242424242424244848484848484848
order122224444888882488161616161616161622444488366661212121224242424246122424484848484848484866121212122424222224444888882488161616161616161622444488
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
χ3111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111-1-1-1-11111-1-1-1-11-11-1-1-11111111111111111-1-1-1-11111-1-1-1-11-11-1-1-11111111111111111-1-1-1-11111-1-1-1-11-11-1-1-111
χ611111111111111-1-1-1-11111-1-1-1-1-11-1111-1-111111111111111-1-1-1-11111-1-1-1-1-11-1111-1-111111111111111-1-1-1-11111-1-1-1-1-11-1111-1-1
χ711111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ11222-2-222-2-200000002i−2ii2i2−i2−i222−2−200000000222-2-222-2-200000002i−2ii2i2−i2−i222−2−200000000222-2-222-2-200000002i−2ii2i2−i2−i222−2−200000000
χ12222-2-222-2-200000002i−2i−i2−i2i2i2−2−22200000000222-2-222-2-200000002i−2i−i2−i2i2i2−2−22200000000222-2-222-2-200000002i−2i−i2−i2i2i2−2−22200000000
χ13222-2-222-2-20000000−2i2ii2i2−i2−i2−2−22200000000222-2-222-2-20000000−2i2ii2i2−i2−i2−2−22200000000222-2-222-2-20000000−2i2ii2i2−i2−i2−2−22200000000
χ14222-2-222-2-20000000−2i2i−i2−i2i2i222−2−200000000222-2-222-2-20000000−2i2i−i2−i2i2i222−2−200000000222-2-222-2-20000000−2i2i−i2−i2i2i222−2−200000000
χ15222-2-2-2-222222-2-20000000000000000002-2222-2-2-2-222222-2-20000000000000000002-2222-2-2-2-222222-2-20000000000000000002-2
χ16222-2-2-2-222222-2-2000000000000000000-22222-2-2-2-222222-2-2000000000000000000-22222-2-2-2-222222-2-2000000000000000000-22
χ17222-2-2-2-222-2-2-222000000000000020-20000222-2-2-2-222-2-2-222000000000000020-20000222-2-2-2-222-2-2-222000000000000020-20000
χ18222-2-2-2-222-2-2-2220000000000000-2020000222-2-2-2-222-2-2-2220000000000000-2020000222-2-2-2-222-2-2-2220000000000000-2020000
χ1922-22-22-22-222-2-22000000002-22-20000000022-22-22-22-222-2-22000000002-22-20000000022-22-22-22-222-2-22000000002-22-200000000
χ2022-22-22-22-222-2-2200000000-22-220000000022-22-22-22-222-2-2200000000-22-220000000022-22-22-22-222-2-2200000000-22-2200000000
χ2122-22-22-22-2-2-222-200002i−2i2i−2i00000000000022-22-22-22-2-2-222-200002i−2i2i−2i00000000000022-22-22-22-2-2-222-200002i−2i2i−2i000000000000
χ2222-22-22-22-2-2-222-20000−2i2i−2i2i00000000000022-22-22-22-2-2-222-20000−2i2i−2i2i00000000000022-22-22-22-2-2-222-20000−2i2i−2i2i000000000000
χ2322-2-222-2-22000002-2002−2−222−2−220000000022-2-222-2-22000002-2002−2−222−2−220000000022-2-222-2-22000002-2002−2−222−2−2200000000
χ2422-2-222-2-22000002-200−222−2−222−20000000022-2-222-2-22000002-200−222−2−222−20000000022-2-222-2-22000002-200−222−2−222−200000000
χ2522-2-222-2-2200000-22002−2−22−222−20000000022-2-222-2-2200000-22002−2−22−222−20000000022-2-222-2-2200000-22002−2−22−222−200000000
χ2622-2-222-2-2200000-2200−222−22−2−220000000022-2-222-2-2200000-2200−222−22−2−220000000022-2-222-2-2200000-2200−222−22−2−2200000000
χ2722-2-22-222-222-22-200000000000000002-20022-2-22-222-222-22-200000000000000002-20022-2-22-222-222-22-200000000000000002-200
χ2822-2-22-222-222-22-20000000000000000-220022-2-22-222-222-22-20000000000000000-220022-2-22-222-222-22-20000000000000000-2200
χ2922-2-22-222-2-2-22-2200000000000020-20000022-2-22-222-2-2-22-2200000000000020-20000022-2-22-222-2-2-22-2200000000000020-200000
χ3022-2-22-222-2-2-22-22000000000000-2020000022-2-22-222-2-2-22-22000000000000-2020000022-2-22-222-2-2-22-22000000000000-20200000
χ3144444-4-4-4-4000000000000000000000000044444-4-4-4-4000000000000000000000000044444-4-4-4-40000000000000000000000000
χ3244-44-4-44-44000000000000000000000000044-44-4-44-44000000000000000000000000044-44-4-44-440000000000000000000000000
χ338-800000004i2−4i2000000000000000000000008-800000004i2−4i2000000000000000000000008-800000004i2−4i200000000000000000000000
χ348-80000000−4i24i2000000000000000000000008-80000000−4i24i2000000000000000000000008-80000000−4i24i200000000000000000000000
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
χ37111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111
χ38111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1
χ3911111111111111-1-1-1-11111-1-1-1-11-11-1-1-11111111111111111-1-1-1-11111-1-1-1-11-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1
χ4011111111111111-1-1-1-11111-1-1-1-1-11-1111-1-111111111111111-1-1-1-11111-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111
χ4111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4211111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
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
χ45222-2-222-2-200000002i−2ii2i2−i2−i222−2−200000000222-2-222-2-200000002i−2ii2i2−i2−i222−2−200000000-2-2-222-2-2220000000−2i2i−i2−i2i2i2−2−22200000000
χ46222-2-222-2-200000002i−2i−i2−i2i2i2−2−22200000000222-2-222-2-200000002i−2i−i2−i2i2i2−2−22200000000-2-2-222-2-2220000000−2i2ii2i2−i2−i222−2−200000000
χ47222-2-222-2-20000000−2i2ii2i2−i2−i2−2−22200000000222-2-222-2-20000000−2i2ii2i2−i2−i2−2−22200000000-2-2-222-2-22200000002i−2i−i2−i2i2i222−2−200000000
χ48222-2-222-2-20000000−2i2i−i2−i2i2i222−2−200000000222-2-222-2-20000000−2i2i−i2−i2i2i222−2−200000000-2-2-222-2-22200000002i−2ii2i2−i2−i2−2−22200000000
χ49222-2-2-2-222222-2-20000000000000000002-2222-2-2-2-222222-2-20000000000000000002-2-2-2-22222-2-2-2-2-222000000000000000000-22
χ50222-2-2-2-222222-2-2000000000000000000-22222-2-2-2-222222-2-2000000000000000000-22-2-2-22222-2-2-2-2-2220000000000000000002-2
χ51222-2-2-2-222-2-2-222000000000000020-20000222-2-2-2-222-2-2-222000000000000020-20000-2-2-22222-2-2222-2-20000000000000-2020000
χ52222-2-2-2-222-2-2-2220000000000000-2020000222-2-2-2-222-2-2-2220000000000000-2020000-2-2-22222-2-2222-2-2000000000000020-20000
χ5322-22-22-22-222-2-22000000002-22-20000000022-22-22-22-222-2-22000000002-22-200000000-2-22-22-22-22-2-222-200000000-22-2200000000
χ5422-22-22-22-222-2-2200000000-22-220000000022-22-22-22-222-2-2200000000-22-2200000000-2-22-22-22-22-2-222-2000000002-22-200000000
χ5522-22-22-22-2-2-222-200002i−2i2i−2i00000000000022-22-22-22-2-2-222-200002i−2i2i−2i000000000000-2-22-22-22-2222-2-220000−2i2i−2i2i000000000000
χ5622-22-22-22-2-2-222-20000−2i2i−2i2i00000000000022-22-22-22-2-2-222-20000−2i2i−2i2i000000000000-2-22-22-22-2222-2-2200002i−2i2i−2i000000000000
χ5722-2-222-2-22000002-2002−2−222−2−220000000022-2-222-2-22000002-2002−2−222−2−2200000000-2-222-2-222-200000-2200−222−2−222−200000000
χ5822-2-222-2-22000002-200−222−2−222−20000000022-2-222-2-22000002-200−222−2−222−200000000-2-222-2-222-200000-22002−2−222−2−2200000000
χ5922-2-222-2-2200000-22002−2−22−222−20000000022-2-222-2-2200000-22002−2−22−222−200000000-2-222-2-222-2000002-200−222−22−2−2200000000
χ6022-2-222-2-2200000-2200−222−22−2−220000000022-2-222-2-2200000-2200−222−22−2−2200000000-2-222-2-222-2000002-2002−2−22−222−200000000
χ6122-2-22-222-222-22-200000000000000002-20022-2-22-222-222-22-200000000000000002-200-2-222-22-2-22-2-22-220000000000000000-2200
χ6222-2-22-222-222-22-20000000000000000-220022-2-22-222-222-22-20000000000000000-2200-2-222-22-2-22-2-22-2200000000000000002-200
χ6322-2-22-222-2-2-22-2200000000000020-20000022-2-22-222-2-2-22-2200000000000020-200000-2-222-22-2-2222-22-2000000000000-20200000
χ6422-2-22-222-2-2-22-22000000000000-2020000022-2-22-222-2-2-22-22000000000000-20200000-2-222-22-2-2222-22-200000000000020-200000
χ6544444-4-4-4-4000000000000000000000000044444-4-4-4-40000000000000000000000000-4-4-4-4-444440000000000000000000000000
χ6644-44-4-44-44000000000000000000000000044-44-4-44-440000000000000000000000000-4-44-444-44-40000000000000000000000000
χ678-800000004i2−4i2000000000000000000000008-800000004i2−4i200000000000000000000000-880000000−4i24i200000000000000000000000
χ688-80000000−4i24i2000000000000000000000008-80000000−4i24i200000000000000000000000-8800000004i2−4i200000000000000000000000
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
χ71222222222222222222-2-2-2-2-2-2-2-22-22-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1110000000000000000000000000000000000
χ72222222222222222222-2-2-2-2-2-2-2-2-22-22-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-10000000000000000000000000000000000
χ7322222222222222-2-2-2-22222-2-2-2-22-22-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-10000000000000000000000000000000000
χ7422222222222222-2-2-2-22222-2-2-2-2-22-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-1110000000000000000000000000000000000
χ7522222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111110000000000000000000000000000000000
χ7622222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000000000000000000000
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
χ79444-4-444-4-400000004i−4i2i22i2−2i2−2i22222−22−2200000000-2-2-222-2-2220000000−2i2i−i2−i2i2i2−2−222000000000000000000000000000000000000000000
χ80444-4-444-4-400000004i−4i−2i2−2i22i22i2−22−22222200000000-2-2-222-2-2220000000−2i2ii2i2−i2−i222−2−2000000000000000000000000000000000000000000
χ81444-4-444-4-40000000−4i4i2i22i2−2i2−2i2−22−22222200000000-2-2-222-2-22200000002i−2i−i2−i2i2i222−2−2000000000000000000000000000000000000000000
χ82444-4-444-4-40000000−4i4i−2i2−2i22i22i22222−22−2200000000-2-2-222-2-22200000002i−2ii2i2−i2−i2−2−222000000000000000000000000000000000000000000
χ83444-4-4-4-444444-4-40000000000000000004-4-2-2-22222-2-2-2-2-222000000000000000000-220000000000000000000000000000000000
χ84444-4-4-4-444444-4-4000000000000000000-44-2-2-22222-2-2-2-2-2220000000000000000002-20000000000000000000000000000000000
χ85444-4-4-4-444-4-4-444000000000000040-40000-2-2-22222-2-2222-2-20000000000000-20200000000000000000000000000000000000000
χ86444-4-4-4-444-4-4-4440000000000000-4040000-2-2-22222-2-2222-2-2000000000000020-200000000000000000000000000000000000000
χ8744-44-44-44-444-4-44000000004-44-400000000-2-22-22-22-22-2-222-200000000-22-22000000000000000000000000000000000000000000
χ8844-44-44-44-444-4-4400000000-44-4400000000-2-22-22-22-22-2-222-2000000002-22-2000000000000000000000000000000000000000000
χ8944-44-44-44-4-4-444-400004i−4i4i−4i000000000000-2-22-22-22-2222-2-220000−2i2i−2i2i0000000000000000000000000000000000000000000000
χ9044-44-44-44-4-4-444-40000−4i4i−4i4i000000000000-2-22-22-22-2222-2-2200002i−2i2i−2i0000000000000000000000000000000000000000000000
χ9144-4-444-4-44000004-40022−22−222222−22−222200000000-2-222-2-222-200000-2200−222−2−222−2000000000000000000000000000000000000000000
χ9244-4-444-4-44000004-400−222222−22−222222−2200000000-2-222-2-222-200000-22002−2−222−2−22000000000000000000000000000000000000000000
χ9344-4-444-4-4400000-440022−22−2222−222222−2200000000-2-222-2-222-2000002-200−222−22−2−22000000000000000000000000000000000000000000
χ9444-4-444-4-4400000-4400−222222−2222−22−222200000000-2-222-2-222-2000002-2002−2−22−222−2000000000000000000000000000000000000000000
χ9544-4-44-444-444-44-400000000000000004-400-2-222-22-2-22-2-22-220000000000000000-22000000000000000000000000000000000000
χ9644-4-44-444-444-44-40000000000000000-4400-2-222-22-2-22-2-22-2200000000000000002-2000000000000000000000000000000000000
χ9744-4-44-444-4-4-44-4400000000000040-400000-2-222-22-2-2222-22-2000000000000-202000000000000000000000000000000000000000
χ9844-4-44-444-4-4-44-44000000000000-40400000-2-222-22-2-2222-22-200000000000020-2000000000000000000000000000000000000000
χ9988888-8-8-8-80000000000000000000000000-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000
χ10088-88-8-88-880000000000000000000000000-4-44-444-44-400000000000000000000000000000000000000000000000000000000000
χ10116-1600000008i2−8i200000000000000000000000-880000000−4i24i2000000000000000000000000000000000000000000000000000000000
χ10216-160000000−8i28i200000000000000000000000-8800000004i2−4i2000000000000000000000000000000000000000000000000000000000

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