Finite Group Databasebeta

← Group #72257457

Character table — Group #72257457

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size111122222222222222222244444444448888881616161616161616161616161616161616161616161616161616161616161616323232323232323232323232
order12222222224444444488882222888888448888444444444444888816161616161616161616161616161616444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ91111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ121111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ131111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ141111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ151111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ161111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2222200000000-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2-2-2-2-20000000022220000000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000-2-2220000000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000022-2-20000000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-200002222000000-2-200000000000000002i−2i2i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i2000000000000
χ222222222222-2-2-2-2-2-2-2-200002222000000-2-200000000000000002i−2i2i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i2000000000000
χ232222222222-2-2-2-2-2-2-2-200002222000000-2-20000000000000000−2i2i−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i2000000000000
χ242222222222-2-2-2-2-2-2-2-200002222000000-2-20000000000000000−2i2i−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i2000000000000
χ252222222222-2-2-2-2-2-2-2-20000-2-2-2-20000002200000000000000002i−2i−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ262222222222-2-2-2-2-2-2-2-20000-2-2-2-20000002200000000000000002i−2i−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ272222222222-2-2-2-2-2-2-2-20000-2-2-2-2000000220000000000000000−2i2i2i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ282222222222-2-2-2-2-2-2-2-20000-2-2-2-2000000220000000000000000−2i2i2i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ29222222-2-2-2-22-2222-2-2-2222200002-2-2-22-2000000000000002i2i−2i−2i000000002-22-20000000000000000002i−2i
χ30222222-2-2-2-22-2222-2-2-2222200002-2-2-22-2000000000000002i2i−2i−2i00000000-22-22000000000000000000−2i2i
χ31222222-2-2-2-22-2222-2-2-2222200002-2-2-22-200000000000000−2i−2i2i2i000000002-22-2000000000000000000−2i2i
χ32222222-2-2-2-22-2222-2-2-2222200002-2-2-22-200000000000000−2i−2i2i2i00000000-22-220000000000000000002i−2i
χ332222-2-22-22-2-2-222-222-2-2-2-2-20000222-22-200000000002i2i−2i−2i000000002i−2i2i−2i0000000000002-20000000000
χ342222-2-22-22-2-2-222-222-2-2-2-2-20000222-22-200000000002i2i−2i−2i00000000−2i2i−2i2i000000000000-220000000000
χ352222-2-22-22-2-2-222-222-2-2-2-2-20000222-22-20000000000−2i−2i2i2i000000002i−2i2i−2i000000000000-220000000000
χ362222-2-22-22-2-2-222-222-2-2-2-2-20000222-22-20000000000−2i−2i2i2i00000000−2i2i−2i2i0000000000002-20000000000
χ3722-2-22-222-2-2-22-2222-2-222-2-222-2-222-22-2-22-222-2-20000000000000000000000000000000000002-22-20000
χ3822-2-22-222-2-2-22-2222-2-222-2-222-2-222-22-2-22-222-2-2000000000000000000000000000000000000-22-220000
χ3922-2-22-222-2-2-22-2222-2-222-2-2-2-22222-22-2-2-22-2-2220000000000000000000000000000000000002-2-220000
χ4022-2-22-222-2-2-22-2222-2-222-2-2-2-22222-22-2-2-22-2-222000000000000000000000000000000000000-222-20000
χ4122-2-22-222-2-2-22-2222-2-2-2-22222-2-2-2-22-2222-2-2-22200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ4222-2-22-222-2-2-22-2222-2-2-2-22222-2-2-2-22-2222-2-2-2220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ4322-2-22-222-2-2-22-2222-2-2-2-222-2-222-2-22-222-2222-2-200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ4422-2-22-222-2-2-22-2222-2-2-2-222-2-222-2-22-222-2222-2-20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ4522-2-22-2-2-222-2-2-222-222-2-2220000-22-222-2000000000000002-2-2200000000000000002-22-2000000002-200
χ4622-2-22-2-2-222-2-2-222-222-2-2220000-22-222-2000000000000002-2-220000000000000000-22-2200000000-2200
χ4722-2-22-2-2-222-2-2-222-222-2-2220000-22-222-200000000000000-222-200000000000000002-22-200000000-2200
χ4822-2-22-2-2-222-2-2-222-222-2-2220000-22-222-200000000000000-222-20000000000000000-22-22000000002-200
χ4922-2-2-222-2-222-2-22-22-2222-2-20000-2-2222-200000000002-2-2200000000000000002i−2i2i−2i0000002i−2i00000000
χ5022-2-2-222-2-222-2-22-22-2222-2-20000-2-2222-200000000002-2-220000000000000000−2i2i−2i2i000000−2i2i00000000
χ5122-2-2-222-2-222-2-22-22-2222-2-20000-2-2222-20000000000-222-200000000000000002i−2i2i−2i000000−2i2i00000000
χ5222-2-2-222-2-222-2-22-22-2222-2-20000-2-2222-20000000000-222-20000000000000000−2i2i−2i2i0000002i−2i00000000
χ53444444-4-4-4-44-4444-4-4-4-4-4-4-40000-4444-4400000000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-44-4-4-444400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ55444444-4-4-4-4-44-4-4-44440000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ564444-4-44-44-444-4-44-4-440000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ574444-4-44-44-444-4-44-4-44000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ584444-4-44-44-4-4-444-444-444440000-4-4-44-4400000000000000000000000000000000000000000000000000
χ594444-4-4-44-444-4-4-4444-4000000000000000000004-4000000000000000000000000000000000000000000
χ604444-4-4-44-444-4-4-4444-400000000000000000000-44000000000000000000000000000000000000000000
χ614444-4-4-44-44-4444-4-4-4444440000-444-4-4-400000000000000000000000000000000000000000000000000
χ624444-4-4-44-44-4444-4-4-44-4-4-4-400004-4-444400000000000000000000000000000000000000000000000000
χ6344-4-44-444-4-44-44-4-4-444000044-4-4000000-44000000000000000000000000000000000000000000000000
χ6444-4-44-444-4-44-44-4-4-4440000-4-4440000004-4000000000000000000000000000000000000000000000000
χ6544-4-44-4-4-444444-4-44-4-40000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ6644-4-44-4-4-444444-4-44-4-4000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ6744-4-44-4-4-444-4-4-444-44444-4-400004-44-4-4400000000000000000000000000000000000000000000000000
χ6844-4-4-444-4-444-4-44-44-44-4-444000044-4-4-4400000000000000000000000000000000000000000000000000
χ6944-4-4-444-4-44-444-44-44-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ7044-4-4-444-4-44-444-44-44-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ7144-4-4-44-444-444-44-4-44-444-4-40000-44-4-44400000000000000000000000000000000000000000000000000
χ7244-4-4-44-444-444-44-4-44-4-4-44400004-444-4-400000000000000000000000000000000000000000000000000
χ7344-4-4-44-444-4-4-44-444-4400000000000000000000004i−4i0000000000000000000000000000000000000000
χ7444-4-4-44-444-4-4-44-444-440000000000000000000000−4i4i0000000000000000000000000000000000000000
χ758-88-8000000000000004i2−4i24i2−4i24-44-4000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ768-88-8000000000000004i2−4i24i2−4i2-44-4400000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ778-88-800000000000000−4i24i2−4i24i24-44-400000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ788-88-800000000000000−4i24i2−4i24i2-44-44000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ798-8-88000000000000004i2−4i2−4i24i24-4-44000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ808-8-88000000000000004i2−4i2−4i24i2-444-400000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ818-8-8800000000000000−4i24i24i2−4i24-4-4400000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ828-8-8800000000000000−4i24i24i2−4i2-444-4000000002i2−2i2−2i22i200000000000000000000000000000000000000000000

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