Finite Group Databasebeta

← Group #72281740

Character table — Group #72281740

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size112222222224444444444444448888881616161616161616161616161616161616161616161616161616161616161616323232323232323232323232
order12222444488222222444444888888888444444444444888816161616161616161616161616161616444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11iiii−i−i−i−i11-1-111-1-111-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−i
χ10111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11iiii−i−i−i−i11-1-111-1-1-1-111-1-111-1-1-1-11111i−ii−i−i−iii−i−iii
χ11111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11iiii−i−i−i−i-1-111-1-11111-1-111-1-1-1-1-1-11111−ii−iiii−i−i−i−iii
χ12111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11iiii−i−i−i−i-1-111-1-111-1-111-1-1111111-1-1-1-1−ii−ii−i−iiiii−i−i
χ13111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11−i−i−i−iiiii11-1-111-1-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ14111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11−i−i−i−iiiii11-1-111-1-1-1-111-1-111-1-1-1-11111−ii−iiii−i−iii−i−i
χ15111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11−i−i−i−iiiii-1-111-1-11111-1-111-1-1-1-1-1-11111i−ii−i−i−iiiii−i−i
χ16111-1-111-1-11111-1-11-111-1-1-11-1-1111-1-1-11−i−i−i−iiiii-1-111-1-111-1-111-1-1111111-1-1-1-1i−ii−iii−i−i−i−iii
χ17222222222222-22-2-2-22-22-2-2-2222-2-22-2-2200000000000000000000000000000000000000002-22-2
χ18222222222222-22-2-2-22-22-2-2-2222-2-22-2-220000000000000000000000000000000000000000-22-22
χ1922222222222-22-2-2-22-22-22-2-22222-2-22-2-200000000000000002222-2-2-2-200000000000000000000
χ2022222222222-22-2-2-22-22-22-2-22222-2-22-2-20000000000000000-2-2-2-2222200000000000000000000
χ2122222222222-2-2-222-2-2-2-2-222222-22-2-22-20000000000000000000000000000000022-2-200000000
χ2222222222222-2-2-222-2-2-2-2-222222-22-2-22-200000000000000000000000000000000-2-22200000000
χ23222222222-2-2222222222222-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000000000000000
χ24222222222-2-2222222222222-2-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ25222222222-2-22-22-2-2-22-22-2-2-2-2-2-222-222-20000000000000000000000000000000000002i−2i2i−2i0000
χ26222222222-2-22-22-2-2-22-22-2-2-2-2-2-222-222-2000000000000000000000000000000000000−2i2i−2i2i0000
χ27222222222-2-2-22-2-2-22-22-22-2-2-2-2-2-222-22200000000000000000000000022-2-222-2-2000000000000
χ28222222222-2-2-22-2-2-22-22-22-2-2-2-2-2-222-222000000000000000000000000-2-222-2-222000000000000
χ29222222222-2-2-2-2-222-2-2-2-2-222-2-2-22-222-2222-2-222-2-2000000000000000000000000000000000000
χ30222222222-2-2-2-2-222-2-2-2-2-222-2-2-22-222-22-2-222-2-222000000000000000000000000000000000000
χ3122222-2-2-2-2002-2222-2-22-22-2-2000000000000000002-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3222222-2-2-2-2002-2222-2-22-22-2-2000000000000000002-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3322222-2-2-2-2002-2222-2-22-22-2-200000000000000000-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3422222-2-2-2-2002-2222-2-22-22-2-200000000000000000-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3522222-2-2-2-200-2-2-2-2-2-22222220000000000000000000002-22-2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ3622222-2-2-2-200-2-2-2-2-2-22222220000000000000000000002-22-2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ3722222-2-2-2-200-2-2-2-2-2-2222222000000000000000000000-22-22i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ3822222-2-2-2-200-2-2-2-2-2-2222222000000000000000000000-22-22−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ39222-2-222-2-2222-2-22-222-2-222-2-2-22-2-2-222200000000000000000000000000000000000000002i−2i−2i2i
χ40222-2-222-2-2222-2-22-222-2-222-2-2-22-2-2-22220000000000000000000000000000000000000000−2i2i2i−2i
χ41222-2-222-2-222-2222-2-2-222-22-2-2-222-22-22-2000000000000000022-2-2-2-22200000000000000000000
χ42222-2-222-2-222-2222-2-2-222-22-2-2-222-22-22-20000000000000000-2-22222-2-200000000000000000000
χ43222-2-222-2-222-2-22-222-2-222-22-2-22-2222-2-2000000000000000000000000000000002i−2i−2i2i00000000
χ44222-2-222-2-222-2-22-222-2-222-22-2-22-2222-2-200000000000000000000000000000000−2i2i2i−2i00000000
χ45222-2-222-2-2-2-222-2-22-222-2-2-2222-2-2-2222-20000000022-2-2-2-2220000000000000000000000000000
χ46222-2-222-2-2-2-222-2-22-222-2-2-2222-2-2-2222-200000000-2-22222-2-20000000000000000000000000000
χ47222-2-222-2-2-2-22-2-22-222-2-222-222-2222-2-2-20000000000000000000000000000000000002-2-220000
χ48222-2-222-2-2-2-22-2-22-222-2-222-222-2222-2-2-2000000000000000000000000000000000000-222-20000
χ49222-2-222-2-2-2-2-2222-2-2-222-22-222-2-22-22-2200000000000000000000000022-2-2-2-222000000000000
χ50222-2-222-2-2-2-2-2222-2-2-222-22-222-2-22-22-22000000000000000000000000-2-22222-2-2000000000000
χ51222-2-222-2-2-2-2-2-22-222-2-222-2222-22-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ52222-2-222-2-2-2-2-2-22-222-2-222-2222-22-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ53222-2-2-2-222002-2-2-222-222-22-2000000000000000002-2-220000i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ54222-2-2-2-222002-2-2-222-222-22-2000000000000000002-2-220000−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ55222-2-2-2-222002-2-2-222-222-22-200000000000000000-222-20000i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ56222-2-2-2-222002-2-2-222-222-22-200000000000000000-222-20000−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ57222-2-2-2-22200-2-222-2222-2-2-220000000000000000000002-2-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ58222-2-2-2-22200-2-222-2222-2-2-220000000000000000000002-2-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ59222-2-2-2-22200-2-222-2222-2-2-22000000000000000000000-222-2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ60222-2-2-2-22200-2-222-2222-2-2-22000000000000000000000-222-2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ6144444-4-4-4-400444-4-44-4-4-4-44400000000000000000000000000000000000000000000000000000
χ6244444-4-4-4-400-44-44444-44-4-4-400000000000000000000000000000000000000000000000000000
χ63444-4-4-4-4440044-44-4-4-4-444-4400000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44400-444-44-44-4-444-400000000000000000000000000000000000000000000000000000
χ6544-44-4-444-4440000000000004-4-40000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ6644-44-4-444-4440000000000004-4-4000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ6744-44-4-444-4-4-4000000000000-4440000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ6844-44-4-444-4-4-4000000000000-444000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ6944-4-44-44-4444000000000000-44-40000002-22-2-22-22000000000000000000000000000000000000
χ7044-4-44-44-4444000000000000-44-4000000-22-222-22-2000000000000000000000000000000000000
χ7144-4-44-44-44-4-40000000000004-440000002-2-22-222-2000000000000000000000000000000000000
χ7244-4-44-44-44-4-40000000000004-44000000-222-22-2-22000000000000000000000000000000000000
χ7388-88-88-8-880000000000000000000000000000000000000000000000000000000000000000000
χ7488-8-888-88-80000000000000000000000000000000000000000000000000000000000000000000
χ7516-1600000008i2−8i200000000000000000000000000000000000000000000000000000000000000000
χ7616-160000000−8i28i200000000000000000000000000000000000000000000000000000000000000000

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