Finite Group Databasebeta

← Group #72313657

Character table — Group #72313657

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size111122222222224444444444444444448888888888888888888888881616161616161616161616161616161616161616161616161616161616163232323232323232
order12222244448888222222444444444488224444444444448888888888444444444444881616161616161616161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-111-1-11111-1-111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-111-1-11111-1-111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ171-1-111-1-1-11111-1-11-111-1-11-11111-1-1-1-11-11-11-11-1iiii−i−i−i−i11-1-11-1-1-111ii−i−iii−i−iii−i−i1-111-1-111-1-111-1-111-1-1i−ii−ii−ii−i
χ181-1-111-1-1-11111-1-11-111-1-11-11111-1-1-1-11-11-11-11-1iiii−i−i−i−i11-1-11-1-1-111ii−i−iii−i−iii−i−i1-1-1-111-1-111-1-111-1-111−ii−ii−ii−ii
χ191-1-111-1-1-11111-1-11-111-1-11-11111-1-1-1-11-11-11-11-1−i−i−i−iiiii11-1-11-1-1-111−i−iii−i−iii−i−iii1-111-1-111-1-111-1-111-1-1−ii−ii−ii−ii
χ201-1-111-1-1-11111-1-11-111-1-11-11111-1-1-1-11-11-11-11-1−i−i−i−iiiii11-1-11-1-1-111−i−iii−i−iii−i−iii1-1-1-111-1-111-1-111-1-111i−ii−ii−ii−i
χ211-1-111-1-1-11111-1-11-111-1-11-111-1-111-1-11-1-11-11-11iiii−i−i−i−i-1-1111-1-1-111−i−iiiii−i−i−i−iii-1111-1-111-1-1-1-111-1-111i−ii−i−ii−ii
χ221-1-111-1-1-11111-1-11-111-1-11-111-1-111-1-11-1-11-11-11iiii−i−i−i−i-1-1111-1-1-111−i−iiiii−i−i−i−iii-11-1-111-1-11111-1-111-1-1−ii−iii−ii−i
χ231-1-111-1-1-11111-1-11-111-1-11-111-1-111-1-11-1-11-11-11−i−i−i−iiiii-1-1111-1-1-111ii−i−i−i−iiiii−i−i-1111-1-111-1-1-1-111-1-111−ii−iii−ii−i
χ241-1-111-1-1-11111-1-11-111-1-11-111-1-111-1-11-1-11-11-11−i−i−i−iiiii-1-1111-1-1-111ii−i−i−i−iiiii−i−i-11-1-111-1-11111-1-111-1-1i−ii−i−ii−ii
χ251-1-111-1-1-11111-1-11-1-1-1111-1-1-111-1-1111-1-11-111-1iiii−i−i−i−i11-1-11-111-1-1ii−i−i−i−iii−i−iii-11ii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ261-1-111-1-1-11111-1-11-1-1-1111-1-1-111-1-1111-1-11-111-1iiii−i−i−i−i11-1-11-111-1-1ii−i−i−i−iii−i−iii-11−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ271-1-111-1-1-11111-1-11-1-1-1111-1-1-111-1-1111-1-11-111-1−i−i−i−iiiii11-1-11-111-1-1−i−iiiii−i−iii−i−i-11ii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ281-1-111-1-1-11111-1-11-1-1-1111-1-1-111-1-1111-1-11-111-1−i−i−i−iiiii11-1-11-111-1-1−i−iiiii−i−iii−i−i-11−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ291-1-111-1-1-11111-1-11-1-1-1111-1-1-1-1-111111-11-11-1-11iiii−i−i−i−i-1-1111-111-1-1−i−iii−i−iiiii−i−i1-1ii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ301-1-111-1-1-11111-1-11-1-1-1111-1-1-1-1-111111-11-11-1-11iiii−i−i−i−i-1-1111-111-1-1−i−iii−i−iiiii−i−i1-1−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ311-1-111-1-1-11111-1-11-1-1-1111-1-1-1-1-111111-11-11-1-11−i−i−i−iiiii-1-1111-111-1-1ii−i−iii−i−i−i−iii1-1ii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ321-1-111-1-1-11111-1-11-1-1-1111-1-1-1-1-111111-11-11-1-11−i−i−i−iiiii-1-1111-111-1-1ii−i−iii−i−i−i−iii1-1−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ3322222222222222-2-22-22-2-2-22-200002-22200000022-2-222-2-20000-2-22-22-200002-22-2000000000000000000000000000000
χ3422222222222222-2-22-22-2-2-22-200002-222000000-2-222-2-2220000-2-22-22-20000-22-22000000000000000000000000000000
χ3522222222222222-2-2-22-22-2-2-220000-222200000022-2-222-2-20000-2-2-22-220000-22-22000000000000000000000000000000
χ3622222222222222-2-2-22-22-2-2-220000-2222000000-2-222-2-2220000-2-2-22-2200002-22-2000000000000000000000000000000
χ372222222222-2-2-2-22222222222222222-2-222222200000000-2-2-2-2-2-2-2-2-2-2000000000000-2-2000000000000000000000000
χ382222222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-2-2-2000000002222-2-2-2-2-2-200000000000022000000000000000000000000
χ392222222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-2-2-2-2-22200000000-2-2-2-2-2-2222200000000000022000000000000000000000000
χ402222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222-2-2000000002222-2-22222000000000000-2-2000000000000000000000000
χ412222222222-2-2-2-2-2-22-22-2-2-22-200002-2-2-200000000000000000022-22-222-22-200002-22-200000000000000000000000000
χ422222222222-2-2-2-2-2-22-22-2-2-22-200002-2-2-200000000000000000022-22-22-22-220000-22-2200000000000000000000000000
χ432222222222-2-2-2-2-2-2-22-22-2-2-220000-22-2-2000000000000000000222-22-22-22-20000-22-2200000000000000000000000000
χ442222222222-2-2-2-2-2-2-22-22-2-2-220000-22-2-2000000000000000000222-22-2-22-2200002-22-200000000000000000000000000
χ45222222-2-2-2-20000-2-2222222-2-22222-2-20022-2-2-2-200000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ46222222-2-2-2-20000-2-2222222-2-22222-2-20022-2-2-2-200000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ47222222-2-2-2-20000-2-2222222-2-2-2-2-2-2-2-200-2-2222200000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ48222222-2-2-2-20000-2-2222222-2-2-2-2-2-2-2-200-2-2222200000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ49222222-2-2-2-20000-2-2-2-2-2-2222222222200-2-222-2-2000000000000000000000000000000002−22−2−22−222−22−2−22−2200000000
χ50222222-2-2-2-20000-2-2-2-2-2-2222222222200-2-222-2-200000000000000000000000000000000−22−222−22−2−22−222−22−200000000
χ51222222-2-2-2-20000-2-2-2-2-2-22222-2-2-2-2220022-2-222000000000000000000000000000000002−22−2−22−22−22−222−22−200000000
χ52222222-2-2-2-20000-2-2-2-2-2-22222-2-2-2-2220022-2-22200000000000000000000000000000000−22−222−22−22−22−2−22−2200000000
χ532-2-222-222-2-20000-2222-2-22-2-2-222-2-222002-2-22-2200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ542-2-222-222-2-20000-2222-2-22-2-2-222-2-222002-2-22-2200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ552-2-222-222-2-20000-2222-2-22-2-2-2-2-2222200-222-22-200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ562-2-222-222-2-20000-2222-2-22-2-2-2-2-2222200-222-22-200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ572-2-222-222-2-20000-22-2-2222-22222-2-2-2-200-222-2-22000000000000000000000000000000002−2−22−222−22−2−22−222−200000000
χ582-2-222-222-2-20000-22-2-2222-22222-2-2-2-200-222-2-2200000000000000000000000000000000−222−22−2−22−222−22−2−2200000000
χ592-2-222-222-2-20000-22-2-2222-222-2-222-2-2002-2-222-2000000000000000000000000000000002−2−22−222−2−222−22−2−2200000000
χ602-2-222-222-2-20000-22-2-2222-222-2-222-2-2002-2-222-200000000000000000000000000000000−222−22−2−222−2−22−222−200000000
χ612-2-222-2-2-22222-2-2-222-2-22-222-20000-222-20000002i2i−2i−2i−2i−2i2i2i0000-22-222-200002i−2i−2i2i000000000000000000000000000000
χ622-2-222-2-2-22222-2-2-222-2-22-222-20000-222-2000000−2i−2i2i2i2i2i−2i−2i0000-22-222-20000−2i2i2i−2i000000000000000000000000000000
χ632-2-222-2-2-22222-2-2-22-222-2-22-2200002-22-20000002i2i−2i−2i−2i−2i2i2i0000-222-2-220000−2i2i2i−2i000000000000000000000000000000
χ642-2-222-2-2-22222-2-2-22-222-2-22-2200002-22-2000000−2i−2i2i2i2i2i−2i−2i0000-222-2-2200002i−2i−2i2i000000000000000000000000000000
χ652-2-222-2-2-222-2-2222-222-2-22-22222-2-2-2-2-222-22-22-200000000-2-222-2222-2-2000000000000-22000000000000000000000000
χ662-2-222-2-2-222-2-2222-222-2-22-222-2-222-2-2-22-22-22-220000000022-2-2-2222-2-20000000000002-2000000000000000000000000
χ672-2-222-2-2-222-2-2222-2-2-2222-2-2-222-2-222-22-22-222-200000000-2-222-22-2-2220000000000002-2000000000000000000000000
χ682-2-222-2-2-222-2-2222-2-2-2222-2-2-2-2-22222-222-22-2-220000000022-2-2-22-2-222000000000000-22000000000000000000000000
χ692-2-222-2-2-222-2-222-222-2-22-222-20000-22-220000000000000000002-22-2-222i−2i−2i2i00002i−2i−2i2i00000000000000000000000000
χ702-2-222-2-2-222-2-222-222-2-22-222-20000-22-220000000000000000002-22-2-22−2i2i2i−2i0000−2i2i2i−2i00000000000000000000000000
χ712-2-222-2-2-222-2-222-22-222-2-22-2200002-2-220000000000000000002-2-222-22i−2i−2i2i0000−2i2i2i−2i00000000000000000000000000
χ722-2-222-2-2-222-2-222-22-222-2-22-2200002-2-220000000000000000002-2-222-2−2i2i2i−2i00002i−2i−2i2i00000000000000000000000000
χ73444444-4-4-4-40000444-44-4-4-4-440000-440000000000000000000000000000000000000000000000000000000000000000
χ74444444-4-4-4-4000044-44-44-4-44-400004-40000000000000000000000000000000000000000000000000000000000000000
χ754444-4-44-4-4444440000000000000000-4-4000000004i−4i004i−4i000000000000000000000000000000000000000000000000
χ764444-4-44-4-4444440000000000000000-4-400000000−4i4i00−4i4i000000000000000000000000000000000000000000000000
χ774444-4-44-4-44-4-4-4-40000000000000000440000004i−4i004i−4i00000000000000000000000000000000000000000000000000
χ784444-4-44-4-44-4-4-4-4000000000000000044000000−4i4i00−4i4i00000000000000000000000000000000000000000000000000
χ794-4-444-444-4-400004-44-4-44-44-4400004-40000000000000000000000000000000000000000000000000000000000000000
χ804-4-444-444-4-400004-4-444-4-444-40000-440000000000000000000000000000000000000000000000000000000000000000
χ814-4-44-44-44-4444-4-40000000000000000-44000000004-400-44000000000000000000000000000000000000000000000000
χ824-4-44-44-44-4444-4-40000000000000000-4400000000-44004-4000000000000000000000000000000000000000000000000
χ834-4-44-44-44-44-4-44400000000000000004-40000004-400-4400000000000000000000000000000000000000000000000000
χ844-4-44-44-44-44-4-44400000000000000004-4000000-44004-400000000000000000000000000000000000000000000000000
χ858888-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-80000004i2−4i24i2−4i200000000004-44-40000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ8788-8-80000004i2−4i24i2−4i20000000000-44-44000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ8888-8-8000000−4i24i2−4i24i200000000004-44-4000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ8988-8-8000000−4i24i2−4i24i20000000000-44-440000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ908-88-80000004i2−4i2−4i24i200000000004-4-440000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ918-88-80000004i2−4i2−4i24i20000000000-444-4000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ928-88-8000000−4i24i24i2−4i200000000004-4-44000000000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ938-88-8000000−4i24i24i2−4i20000000000-444-40000000000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ948-8-88-888-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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