Finite Group Databasebeta

← Group #72317635

Character table — Group #72317635

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222224444444444448888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232326464646464646464646464646464
order12442224442222224444442222444488888888222244444444444488888888888888888888888888882444444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ51111111111111111111111111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ9111111111111111111111111111111-1-1-1-111111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ10111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1
χ11111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-11111111111-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ12111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ13111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ14111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ15111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111
χ16111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1
χ1722222222222222-2-222-2-222-2-2-222-2-2-222220000002-2002-2000022-2-2220000000000-2-2-2-2000000000000000000000000002-2000000
χ1822222222222222-2-222-2-222-2-2-222-2-2-22222000000-2200-220000-2-222220000000000-2-2-2-200000000000000000000000000-22000000
χ1922222222222222-2-222-2-222-2-2-222-2-2-2-2-2-2-20000002-2002-2000022-2-2-2-20000000000222200000000000000000000000000-22000000
χ2022222222222222-2-222-2-222-2-2-222-2-2-2-2-2-2-2000000-2200-220000-2-222-2-200000000002222000000000000000000000000002-2000000
χ21222222222222-2-222-2-222222-2-2-2-22-2-200000000002200220000-2-2-2-200002222000000000000-2-2-2-20000-2-222000000000000000000
χ22222222222222-2-222-2-222222-2-2-2-22-2-200000000002200220000-2-2-2-20000-2-2-2-20000000000002222000022-2-2000000000000000000
χ23222222222222-2-222-2-222222-2-2-2-22-2-20000000000-2-200-2-20000222200002222000000000000-2-2-2-2000022-2-2000000000000000000
χ24222222222222-2-222-2-222222-2-2-2-22-2-20000000000-2-200-2-2000022220000-2-2-2-200000000000022220000-2-222000000000000000000
χ25222222222222-2-2-2-2-2-2-2-222-222-2-2-22200000000222-2222-2-2-2-2-2-2-222000000000000000000000000000000000000000000002-20000
χ26222222222222-2-2-2-2-2-2-2-222-222-2-2-2220000000022-2222-22-2-2-2-222-2-200000000000000000000000000000000000000000000-220000
χ27222222222222-2-2-2-2-2-2-2-222-222-2-2-22200000000-2-22-2-2-22-22222-2-22200000000000000000000000000000000000000000000-220000
χ28222222222222-2-2-2-2-2-2-2-222-222-2-2-22200000000-2-2-22-2-2-22222222-2-2000000000000000000000000000000000000000000002-20000
χ292222222222-2-222222222-2-2-22-2-2-2-22-2000022220000000000000000002222-2-200000000-2-2-2-222-2-20000000000002-2000000000000
χ302222222222-2-222222222-2-2-22-2-2-2-22-20000222200000000000000000022-2-22200000000-2-2-2-2-2-222000000000000-22000000000000
χ312222222222-2-222222222-2-2-22-2-2-2-22-20000-2-2-2-2000000000000000000-2-222-2-200000000222222-2-2000000000000-22000000000000
χ322222222222-2-222222222-2-2-22-2-2-2-22-20000-2-2-2-2000000000000000000-2-2-2-222000000002222-2-2220000000000002-2000000000000
χ332222222222-2-2-2-222-2-222-2-2-2-2222-2-22000000000000000000000000000022-2-2222200000000-2-222-2-2-2-20000000000002-200000000
χ342222222222-2-2-2-222-2-222-2-2-2-2222-2-22000000000000000000000000000022-2-2-2-2-2-200000000-2-2222222000000000000-2200000000
χ352222222222-2-2-2-222-2-222-2-2-2-2222-2-220000000000000000000000000000-2-22222220000000022-2-2-2-2-2-2000000000000-2200000000
χ362222222222-2-2-2-222-2-222-2-2-2-2222-2-220000000000000000000000000000-2-222-2-2-2-20000000022-2-222220000000000002-200000000
χ3722-2-2222-2-2-2222222-2-2-2-2-2-2-22-22-22-222i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000000022-2-200000000000000
χ3822-2-2222-2-2-2222222-2-2-2-2-2-2-22-22-22-222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i000000000000-2-22200000000000000
χ3922-2-2222-2-2-2222222-2-2-2-2-2-2-22-22-22-22−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i000000000000-2-22200000000000000
χ4022-2-2222-2-2-2222222-2-2-2-2-2-2-22-22-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000000022-2-200000000000000
χ4122-2-2222-2-2-22222-2-2-2-222-2-22-222-2-22-22i2i−2i−2i000000000000000000002i−2i0000002i2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i00000000002-20000000000
χ4222-2-2222-2-2-22222-2-2-2-222-2-22-222-2-22-22i2i−2i−2i000000000000000000002i−2i000000−2i−2i2i2i−2i−2i2i2i00000000−2i−2i2i2i0000000000-220000000000
χ4322-2-2222-2-2-22222-2-2-2-222-2-22-222-2-22-2−2i−2i2i2i00000000000000000000−2i2i0000002i2i−2i−2i2i2i−2i−2i000000002i2i−2i−2i0000000000-220000000000
χ4422-2-2222-2-2-22222-2-2-2-222-2-22-222-2-22-2−2i−2i2i2i00000000000000000000−2i2i000000−2i−2i2i2i2i2i−2i−2i00000000−2i−2i2i2i00000000002-20000000000
χ4522-2-2222-2-2-2-2-22222-2-2-2-222222-22-2-2-200002i2i−2i−2i2-2002-20022-2-20000002i−2i000000000000−2i−2i2i2i000000000000000000000000002i−2i00
χ4622-2-2222-2-2-2-2-22222-2-2-2-222222-22-2-2-200002i2i−2i−2i-2200-2200-2-2220000002i−2i000000000000−2i−2i2i2i00000000000000000000000000−2i2i00
χ4722-2-2222-2-2-2-2-22222-2-2-2-222222-22-2-2-20000−2i−2i2i2i2-2002-20022-2-2000000−2i2i0000000000002i2i−2i−2i00000000000000000000000000−2i2i00
χ4822-2-2222-2-2-2-2-22222-2-2-2-222222-22-2-2-20000−2i−2i2i2i-2200-2200-2-222000000−2i2i0000000000002i2i−2i−2i000000000000000000000000002i−2i00
χ4922-2-2222-2-2-2-2-2-2-2-2-2222222-2222-22-2-2000000002-2002-200-2-2220000000000002i2i−2i−2i000000000000−2i−2i2i2i000000000000000000002i−2i
χ5022-2-2222-2-2-2-2-2-2-2-2-2222222-2222-22-2-2000000002-2002-200-2-222000000000000−2i−2i2i2i0000000000002i2i−2i−2i00000000000000000000−2i2i
χ5122-2-2222-2-2-2-2-2-2-2-2-2222222-2222-22-2-200000000-2200-220022-2-20000000000002i2i−2i−2i000000000000−2i−2i2i2i00000000000000000000−2i2i
χ5222-2-2222-2-2-2-2-2-2-2-2-2222222-2222-22-2-200000000-2200-220022-2-2000000000000−2i−2i2i2i0000000000002i2i−2i−2i000000000000000000002i−2i
χ534444444444-4-444-4-444-4-4-4-44-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000000000
χ544444444444-4-4-4-4-4-4-4-4-4-4-4-444-44444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ5544444-4-4-44-400004-4004-40000000000222200002-200-22002-22-20000-2-200000000002-22-20000004-400000000000000000000000000
χ5644444-4-4-44-400004-4004-4000000000022220000-22002-200-22-220000-2-200000000002-22-2000000-4400000000000000000000000000
χ5744444-4-4-44-400004-4004-40000000000-2-2-2-200002-200-22002-22-20000220000000000-22-22000000-4400000000000000000000000000
χ5844444-4-4-44-400004-4004-40000000000-2-2-2-20000-22002-200-22-220000220000000000-22-220000004-400000000000000000000000000
χ5944444-4-4-44-40000-4400-440000000000222200002-200-2200-22-220000-2-20000000000-22-2200004-40000000000000000000000000000
χ6044444-4-4-44-40000-4400-44000000000022220000-22002-2002-22-20000-2-20000000000-22-220000-440000000000000000000000000000
χ6144444-4-4-44-40000-4400-440000000000-2-2-2-200002-200-2200-22-2200002200000000002-22-20000-440000000000000000000000000000
χ6244444-4-4-44-40000-4400-440000000000-2-2-2-20000-22002-2002-22-200002200000000002-22-200004-40000000000000000000000000000
χ634444-44-4-4-444-4000000004-40000000000002222000000000000004-400-2-200002-22-200002-22-200002-22-20000000000000000000000
χ644444-44-4-4-444-4000000004-4000000000000222200000000000000-4400-2-20000-22-2200002-22-20000-22-220000000000000000000000
χ654444-44-4-4-444-4000000004-4000000000000-2-2-2-2000000000000004-400220000-22-220000-22-220000-22-220000000000000000000000
χ664444-44-4-4-444-4000000004-4000000000000-2-2-2-200000000000000-44002200002-22-20000-22-2200002-22-20000000000000000000000
χ674444-44-4-4-44-4400000000-4400000000000022220000000000004-40000-2-200002-22-20000-22-220000-22-220000000000000000000000
χ684444-44-4-4-44-4400000000-440000000000002222000000000000-440000-2-20000-22-220000-22-2200002-22-20000000000000000000000
χ694444-44-4-4-44-4400000000-44000000000000-2-2-2-20000000000004-40000220000-22-2200002-22-200002-22-20000000000000000000000
χ704444-44-4-4-44-4400000000-44000000000000-2-2-2-2000000000000-4400002200002-22-200002-22-20000-22-220000000000000000000000
χ7144-4-4444-4-4-444-4-44444-4-4-4-4-4-44-4444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ7244-4-4444-4-4-444-4-4-4-44444-4-444-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000
χ7344-4-4444-4-4-4-4-444-4-4-4-44444-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000000000
χ7444-4-4444-4-4-4-4-4-4-44444-4-4444-4-44-4-44400000000000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-44-4400004-400-4400000000002i2i−2i−2i00002200-2-2002-2-220000−2i2i00004i−4i00002i−2i−2i2i0000000000000000000000000000000000
χ7644-4-44-4-44-4400004-400-4400000000002i2i−2i−2i0000-2-2002200-222-20000−2i2i0000−4i4i00002i−2i−2i2i0000000000000000000000000000000000
χ7744-4-44-4-44-4400004-400-440000000000−2i−2i2i2i00002200-2-2002-2-2200002i−2i0000−4i4i0000−2i2i2i−2i0000000000000000000000000000000000
χ7844-4-44-4-44-4400004-400-440000000000−2i−2i2i2i0000-2-2002200-222-200002i−2i00004i−4i0000−2i2i2i−2i0000000000000000000000000000000000
χ7944-4-44-4-44-440000-44004-400000000002i2i−2i−2i00002200-2-200-222-20000−2i2i004i−4i000000−2i2i2i−2i0000000000000000000000000000000000
χ8044-4-44-4-44-440000-44004-400000000002i2i−2i−2i0000-2-20022002-2-220000−2i2i00−4i4i000000−2i2i2i−2i0000000000000000000000000000000000
χ8144-4-44-4-44-440000-44004-40000000000−2i−2i2i2i00002200-2-200-222-200002i−2i00−4i4i0000002i−2i−2i2i0000000000000000000000000000000000
χ8244-4-44-4-44-440000-44004-40000000000−2i−2i2i2i0000-2-20022002-2-2200002i−2i004i−4i0000002i−2i−2i2i0000000000000000000000000000000000
χ8344-4-4-44-444-44-400000000-440000000000002i2i−2i−2i0004000-40000000000−2i2i00002i−2i−2i2i00002i−2i−2i2i00002i−2i−2i2i0000000000000000000000
χ8444-4-4-44-444-44-400000000-440000000000002i2i−2i−2i000-400040000000000−2i2i0000−2i2i2i−2i00002i−2i−2i2i0000−2i2i2i−2i0000000000000000000000
χ8544-4-4-44-444-44-400000000-44000000000000−2i−2i2i2i0004000-400000000002i−2i0000−2i2i2i−2i0000−2i2i2i−2i0000−2i2i2i−2i0000000000000000000000
χ8644-4-4-44-444-44-400000000-44000000000000−2i−2i2i2i000-4000400000000002i−2i00002i−2i−2i2i0000−2i2i2i−2i00002i−2i−2i2i0000000000000000000000
χ8744-4-4-44-444-4-44000000004-40000000000002i2i−2i−2i004000-400000000000−2i2i00002i−2i−2i2i0000−2i2i2i−2i0000−2i2i2i−2i0000000000000000000000
χ8844-4-4-44-444-4-44000000004-40000000000002i2i−2i−2i00-4000400000000000−2i2i0000−2i2i2i−2i0000−2i2i2i−2i00002i−2i−2i2i0000000000000000000000
χ8944-4-4-44-444-4-44000000004-4000000000000−2i−2i2i2i004000-4000000000002i−2i0000−2i2i2i−2i00002i−2i−2i2i00002i−2i−2i2i0000000000000000000000
χ9044-4-4-44-444-4-44000000004-4000000000000−2i−2i2i2i00-40004000000000002i−2i00002i−2i−2i2i00002i−2i−2i2i0000−2i2i2i−2i0000000000000000000000
χ918888-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000004-4000000000000000000
χ928888-8-888-8-800000000000000000000000000000000000000000000000000000000000000000000000000-44000000000000000000
χ9388-8-8-8-88-8880000000000000000000000000000000000000000000000000000000000000000000000004-400000000000000000000
χ9488-8-8-8-88-888000000000000000000000000000000000000000000000000000000000000000000000000-4400000000000000000000
χ958-88i−8i000000004-4004i−4i0000000000004ζ−4ζ4ζ3−4ζ34ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000002-22i−2i00000000000000
χ968-88i−8i000000004-4004i−4i0000000000004ζ−4ζ4ζ3−4ζ3−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000000000-22−2i2i00000000000000
χ978-88i−8i000000004-4004i−4i000000000000−4ζ4ζ−4ζ34ζ34ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000000000-22−2i2i00000000000000
χ988-88i−8i000000004-4004i−4i000000000000−4ζ4ζ−4ζ34ζ3−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000002-22i−2i00000000000000
χ998-8−8i8i000000004-400−4i4i0000000000004ζ3−4ζ34ζ−4ζ4ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000002-2−2i2i00000000000000
χ1008-8−8i8i000000004-400−4i4i0000000000004ζ3−4ζ34ζ−4ζ−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000000000-222i−2i00000000000000
χ1018-8−8i8i000000004-400−4i4i000000000000−4ζ34ζ3−4ζ4ζ4ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000-222i−2i00000000000000
χ1028-8−8i8i000000004-400−4i4i000000000000−4ζ34ζ3−4ζ4ζ−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000002-2−2i2i00000000000000
χ10316-1616i−16i00000000-8800−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10416-16−16i16i00000000-88008i−8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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