Finite Group Databasebeta

← Group #72251674

Character table — Group #72251674

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1122222224444444488888888881616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616163232323264646464646464646464646464646464
order12222222222224444222222224422222222444444444444444444444444444444444444444424444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ511111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ711111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ9111111111111111111111111111-1-111-1-111-1-111-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ10111111111111111111111111111-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ11111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ12111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ13111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ14111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-111
χ15111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ16111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1
χ172222222222222222222-2-2-2-2-2-2-2-2220000002200000000002222-2-2-2-200000000-2-2-2-20000000022-2-20000000000000000
χ182222222222222222222-2-2-2-2-2-2-2-222000000220000000000-2-2-2-2222200000000-2-2-2-200000000-2-2220000000000000000
χ192222222222222222222-2-2-2-2-2-2-2-2-2-2000000-2-200000000002222-2-2-2-200000000222200000000-2-2220000000000000000
χ202222222222222222222-2-2-2-2-2-2-2-2-2-2000000-2-20000000000-2-2-2-222220000000022220000000022-2-20000000000000000
χ212222222222222-2-2-2-2-2-222-222-2-2-22-20000002-20000000000000000002222-2-2-2-222-2-2000000000000002-2000000000000
χ222222222222222-2-2-2-2-2-222-222-2-2-22-20000002-2000000000000000000-2-2-2-2222222-2-200000000000000-22000000000000
χ232222222222222-2-2-2-2-2-222-222-2-2-2-22000000-220000000000000000002222-2-2-2-2-2-22200000000000000-22000000000000
χ242222222222222-2-2-2-2-2-222-222-2-2-2-22000000-22000000000000000000-2-2-2-22222-2-222000000000000002-2000000000000
χ252222222222222-2-2-2-2-2-2-2-22-2-22222-20000222-2000022-2-2-2-20000000000000000-2-2220000000000002-200000000000000
χ262222222222222-2-2-2-2-2-2-2-22-2-22222-20000-2-22-20000-2-222220000000000000000-2-222000000000000-2200000000000000
χ272222222222222-2-2-2-2-2-2-2-22-2-2222-22000022-22000022-2-2-2-2000000000000000022-2-2000000000000-2200000000000000
χ282222222222222-2-2-2-2-2-2-2-22-2-2222-220000-2-2-220000-2-22222000000000000000022-2-20000000000002-200000000000000
χ29222222222-2-2-2-22222-2-22-222-22-2-20022000000220000000022-2-222-2-2000000000000-2-2-2-20000000000000000002-20000
χ30222222222-2-2-2-22222-2-22-222-22-2-200220000002200000000-2-222-2-222000000000000-2-2-2-2000000000000000000-220000
χ31222222222-2-2-2-22222-2-22-222-22-2-200-2-2000000-2-20000000022-2-222-2-20000000000002222000000000000000000-220000
χ32222222222-2-2-2-22222-2-22-222-22-2-200-2-2000000-2-200000000-2-222-2-22200000000000022220000000000000000002-20000
χ33222222222-2-2-2-22222-2-2-22-2-22-2220000220000002200000022-2-2-2-2220000000000000000-2-2-2-200000000000000002-200
χ34222222222-2-2-2-22222-2-2-22-2-22-22200002200000022000000-2-22222-2-20000000000000000-2-2-2-20000000000000000-2200
χ35222222222-2-2-2-22222-2-2-22-2-22-2220000-2-2000000-2-200000022-2-2-2-222000000000000000022220000000000000000-2200
χ36222222222-2-2-2-22222-2-2-22-2-22-2220000-2-2000000-2-2000000-2-22222-2-20000000000000000222200000000000000002-200
χ3722-2-222-2-2222-2-222-2-22-2222-2-2-2-22000022000000-2-2000000000000002i2i−2i−2i2i2i−2i−2i0000000022-2-20000000000002i−2i000000
χ3822-2-222-2-2222-2-222-2-22-2222-2-2-2-22000022000000-2-200000000000000−2i−2i2i2i−2i−2i2i2i0000000022-2-2000000000000−2i2i000000
χ3922-2-222-2-2222-2-222-2-22-2222-2-2-2-220000-2-200000022000000000000002i2i−2i−2i2i2i−2i−2i00000000-2-222000000000000−2i2i000000
χ4022-2-222-2-2222-2-222-2-22-2222-2-2-2-220000-2-20000002200000000000000−2i−2i2i2i−2i−2i2i2i00000000-2-2220000000000002i−2i000000
χ4122-2-222-2-2222-2-2-2-222-2222-2-2-222-2002-20000002-200000000000000002i2i−2i−2i−2i−2i2i2i000022-2-2000000000000002i−2i00000000
χ4222-2-222-2-2222-2-2-2-222-2222-2-2-222-2002-20000002-20000000000000000−2i−2i2i2i2i2i−2i−2i000022-2-200000000000000−2i2i00000000
χ4322-2-222-2-2222-2-2-2-222-2222-2-2-222-200-22000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000-2-22200000000000000−2i2i00000000
χ4422-2-222-2-2222-2-2-2-222-2222-2-2-222-200-22000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000-2-222000000000000002i−2i00000000
χ4522-2-222-2-22-2-22222-2-2-22-22-22-22-220000222-20000-2-22-222-2-2000000000000000000000000-2-2220000000000000000002-2
χ4622-2-222-2-22-2-22222-2-2-22-22-22-22-22000022-220000-2-2-22-2-222000000000000000000000000-2-222000000000000000000-22
χ4722-2-222-2-22-2-22222-2-2-22-22-22-22-220000-2-22-20000222-222-2-200000000000000000000000022-2-2000000000000000000-22
χ4822-2-222-2-22-2-22222-2-2-22-22-22-22-220000-2-2-22000022-22-2-22200000000000000000000000022-2-20000000000000000002-2
χ4922-2-222-2-22-2-222-2-2222-22-2-2-222-22002-2002-2002-2002-2-2-22200000000000000000000-2-2220000000000002-20000000000
χ5022-2-222-2-22-2-222-2-2222-22-2-2-222-22002-200-22002-200-2222-2-200000000000000000000-2-222000000000000-220000000000
χ5122-2-222-2-22-2-222-2-2222-22-2-2-222-2200-22002-200-22002-2-2-2220000000000000000000022-2-2000000000000-220000000000
χ5222-2-222-2-22-2-222-2-2222-22-2-2-222-2200-2200-2200-2200-2222-2-20000000000000000000022-2-20000000000002-20000000000
χ53444444444-4-4-4-4-4-4-4-4444-4-44-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ54444444444-4-4-4-4-4-4-4-444-444-444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ5544444-4-4-4-400004-44-400000000000000002-2000000-222-22-20000004i−4i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ5644444-4-4-4-400004-44-400000000000000002-2000000-222-22-2000000−4i4i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ5744444-4-4-4-400004-44-40000000000000000-220000002-2-22-220000004i−4i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ5844444-4-4-4-400004-44-40000000000000000-220000002-2-22-22000000−4i4i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ5944444-4-4-4-40000-44-4400000000000000002-2000000-22-22-2200004i−4i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6044444-4-4-4-40000-44-4400000000000000002-2000000-22-22-220000−4i4i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6144444-4-4-4-40000-44-440000000000000000-220000002-22-22-200004i−4i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6244444-4-4-4-40000-44-440000000000000000-220000002-22-22-20000−4i4i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ63444-4-4-44-444-44-40000000000000000222-20000-2-22-20000000000000000000000004-42-22-22-22-200000000000000000000
χ64444-4-4-44-444-44-4000000000000000022-220000-2-2-22000000000000000000000000-442-22-2-22-2200000000000000000000
χ65444-4-4-44-444-44-40000000000000000-2-22-20000222-2000000000000000000000000-44-22-222-22-200000000000000000000
χ66444-4-4-44-444-44-40000000000000000-2-2-22000022-220000000000000000000000004-4-22-22-22-2200000000000000000000
χ67444-4-4-44-44-44-440000000000000000222-20000-2-22-200000000000000000000004-400-22-22-22-2200000000000000000000
χ68444-4-4-44-44-44-44000000000000000022-220000-2-2-220000000000000000000000-4400-22-222-22-200000000000000000000
χ69444-4-4-44-44-44-440000000000000000-2-22-20000222-20000000000000000000000-44002-22-2-22-2200000000000000000000
χ70444-4-4-44-44-44-440000000000000000-2-2-22000022-2200000000000000000000004-4002-22-22-22-200000000000000000000
χ7144-44-4-4-4444-4-4400000000000000042-22-2000-4-22-22000000000000000000000000002-2-222-2-2200000000000000000000
χ7244-44-4-4-4444-4-440000000000000004-22-22000-42-22-200000000000000000000000000-222-2-222-200000000000000000000
χ7344-44-4-4-4444-4-44000000000000000-42-2-220004-222-2000000000000000000000000002-2-22-222-200000000000000000000
χ7444-44-4-4-4444-4-44000000000000000-4-222-200042-2-2200000000000000000000000000-222-22-2-2200000000000000000000
χ7544-44-4-4-444-444-400000000000000402-22-200-40-22-2200000000000000000000000000-222-2-222-200000000000000000000
χ7644-44-4-4-444-444-40000000000000040-22-2200-402-22-2000000000000000000000000002-2-222-2-2200000000000000000000
χ7744-44-4-4-444-444-400000000000000-402-2-220040-222-200000000000000000000000000-222-22-2-2200000000000000000000
χ7844-44-4-4-444-444-400000000000000-40-222-200402-2-22000000000000000000000000002-2-22-222-200000000000000000000
χ7944-4-444-4-4444-4-444-4-44-4-4-4-44444-400000000000000000000000000000000000000000000000000000000000000000000
χ8044-4-444-4-4444-4-4-4-444-44-4-4444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ8144-4-444-4-44-4-44444-4-4-444-44-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ8244-4-444-4-44-4-444-4-4444-4-4444-4-44-400000000000000000000000000000000000000000000000000000000000000000000
χ8344-4-44-444-400004-4-44000000000000000022000000-2-22-2-224-40000002-2-222-2-2200000000000000000000000000000000
χ8444-4-44-444-400004-4-44000000000000000022000000-2-22-2-22-44000000-222-2-222-200000000000000000000000000000000
χ8544-4-44-444-400004-4-440000000000000000-2-200000022-222-24-4000000-222-2-222-200000000000000000000000000000000
χ8644-4-44-444-400004-4-440000000000000000-2-200000022-222-2-440000002-2-222-2-2200000000000000000000000000000000
χ8744-4-44-444-40000-444-4000000000000000022000000-2-2-222-2004-400002-2-22-222-200000000000000000000000000000000
χ8844-4-44-444-40000-444-4000000000000000022000000-2-2-222-200-440000-222-22-2-2200000000000000000000000000000000
χ8944-4-44-444-40000-444-40000000000000000-2-2000000222-2-22004-40000-222-22-2-2200000000000000000000000000000000
χ9044-4-44-444-40000-444-40000000000000000-2-2000000222-2-2200-4400002-2-22-222-200000000000000000000000000000000
χ91888-8-88-88-80000000000000000000000000000000000000000000000000000000000000000004-4000000000000000000
χ92888-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000-44000000000000000000
χ9388-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000004-40000000000000000
χ9488-88-888-8-800000000000000000000000000000000000000000000000000000000000000000000-440000000000000000
χ9532-32000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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