Finite Group Databasebeta

← Group #72342454

Character table — Group #72342454

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size11112222222244444444444444444448888888888888888888816161616161616161616161616161616161616161616161616161616161616163232323232323232
order1222224444442244444444488888888222444448888888888882244444488888888888888881616161616161616444416161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-11-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ7111111111111111111-1-1-1-1111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ8111111111111111111-1-1-1-1111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ9111111111111-1-111-1-11111111111111-111-1111111-1-1-1-1111111-1-11-1-11-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ10111111111111-1-111-1-11111111111111-111-1111111-1-1-1-1111111-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111-1-111-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ12111111111111-1-111-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ13111111111111-1-111-1-1-1-1-1-1111-1-1-1-111-111-111-1-1-1-11111-1-1-1-111-1-11-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ14111111111111-1-111-1-1-1-1-1-1111-1-1-1-111-111-111-1-1-1-11111-1-1-1-111-1-11-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ15111111111111-1-111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-111-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111-1-111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-111-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171111-1-1111-11-1111-1-1-1ii−i−i-11-1ii−i−i1-1-1111-1-1i−ii−iii−i−iii−i−i1-111-1-1-11i−i1-1i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i1-1i−i1-1i−i
χ181111-1-1111-11-1111-1-1-1ii−i−i-11-1ii−i−i1-1-1111-1-1i−ii−iii−i−iii−i−i1-111-1-1-11i−i1-1i−i-1-111ii−i−i−i−iii-1-111−i−iii-11−ii-11−ii
χ191111-1-1111-11-1111-1-1-1ii−i−i-11-1ii−i−i1-1-1-1-1111i−ii−iii−i−i−i−iii1-1-1-1111-1i−i1-1−ii11-1-1−i−iiiii−i−i-1-111−i−iii1-1i−i-11−ii
χ201111-1-1111-11-1111-1-1-1ii−i−i-11-1ii−i−i1-1-1-1-1111i−ii−iii−i−i−i−iii1-1-1-1111-1i−i1-1−ii-1-111−i−iii−i−iii11-1-1ii−i−i-11−ii1-1i−i
χ211111-1-1111-11-1111-1-1-1−i−iii-11-1−i−iii1-1-1111-1-1−ii−ii−i−iii−i−iii1-111-1-1-11−ii1-1−ii11-1-1−i−iii−i−iii11-1-1−i−iii1-1−ii1-1−ii
χ221111-1-1111-11-1111-1-1-1−i−iii-11-1−i−iii1-1-1111-1-1−ii−ii−i−iii−i−iii1-111-1-1-11−ii1-1−ii-1-111−i−iiiii−i−i-1-111ii−i−i-11i−i-11i−i
χ231111-1-1111-11-1111-1-1-1−i−iii-11-1−i−iii1-1-1-1-1111−ii−ii−i−iiiii−i−i1-1-1-1111-1−ii1-1i−i11-1-1ii−i−i−i−iii-1-111ii−i−i1-1−ii-11i−i
χ241111-1-1111-11-1111-1-1-1−i−iii-11-1−i−iii1-1-1-1-1111−ii−ii−i−iiiii−i−i1-1-1-1111-1−ii1-1i−i-1-111ii−i−iii−i−i11-1-1−i−iii-11i−i1-1−ii
χ251111-1-1111-11-1-1-11-111ii−i−i-11-1ii−i−i1-1111-1-1-1i−ii−i−i−iiiii−i−i1-1-1-1-1111−ii-11i−i11-1-1−i−iiiii−i−i11-1-1ii−i−i-11−ii-11−ii
χ261111-1-1111-11-1-1-11-111ii−i−i-11-1ii−i−i1-1111-1-1-1i−ii−i−i−iiiii−i−i1-1-1-1-1111−ii-11i−i-1-111−i−iii−i−iii-1-111−i−iii1-1i−i1-1i−i
χ271111-1-1111-11-1-1-11-111ii−i−i-11-1ii−i−i1-11-1-1-111i−ii−i−i−iii−i−iii1-1111-1-1-1−ii-11−ii11-1-1ii−i−iii−i−i-1-111−i−iii-11−ii1-1i−i
χ281111-1-1111-11-1-1-11-111ii−i−i-11-1ii−i−i1-11-1-1-111i−ii−i−i−iii−i−iii1-1111-1-1-1−ii-11−ii-1-111ii−i−i−i−iii11-1-1ii−i−i1-1i−i-11−ii
χ291111-1-1111-11-1-1-11-111−i−iii-11-1−i−iii1-1111-1-1-1−ii−iiii−i−i−i−iii1-1-1-1-1111i−i-11−ii11-1-1ii−i−i−i−iii11-1-1−i−iii-11i−i-11i−i
χ301111-1-1111-11-1-1-11-111−i−iii-11-1−i−iii1-1111-1-1-1−ii−iiii−i−i−i−iii1-1-1-1-1111i−i-11−ii-1-111ii−i−iii−i−i-1-111ii−i−i1-1−ii1-1−ii
χ311111-1-1111-11-1-1-11-111−i−iii-11-1−i−iii1-11-1-1-111−ii−iiii−i−iii−i−i1-1111-1-1-1i−i-11i−i11-1-1−i−iii−i−iii-1-111ii−i−i-11i−i1-1−ii
χ321111-1-1111-11-1-1-11-111−i−iii-11-1−i−iii1-11-1-1-111−ii−iiii−i−iii−i−i1-1111-1-1-1i−i-11i−i-1-111−i−iiiii−i−i11-1-1−i−iii1-1−ii-11i−i
χ3322222222222222222222222-2-2-2-2-2-2-2-220020022-2-2-2-2-2-20000-2-200000022-2-2000000000000000000000000000000
χ34222222222222222222-2-2-2-22-2-22222-2-2200200-2-22222220000-2-2000000-2-2-2-2000000000000000000000000000000
χ35222222222222-2-222-2-222222-2-2-2-2-2-2-2-2-200-20022-2-222220000-2-2000000-2-222000000000000000000000000000000
χ36222222222222-2-222-2-2-2-2-2-22-2-22222-2-2-200-200-2-222-2-2-2-20000-2-20000002222000000000000000000000000000000
χ37222222-2222-2200-2-2002222-222222222022022-2-2-2-200002222-2-200-200-20000-2-20000000000000000000000000000
χ38222222-2222-2200-2-2002222-2222222220-2-20-2-2-2-2-2-20000-2-2-2-2-2-20020020000220000000000000000000000000000
χ39222222-2222-2200-2-2002222-2-2-2-2-2-2-2-2-2000000-2-22200000000222-202-2000000000002-22-200000000000000000000
χ40222222-2222-2200-2-2002222-2-2-2-2-2-2-2-2-2000000-2-2220000000022-220-2200000000000-22-2200000000000000000000
χ41222222-2222-2200-2-200-2-2-2-2-222-2-2-2-22202202222220000-2-2-2-2-2-200-200-20000220000000000000000000000000000
χ42222222-2222-2200-2-200-2-2-2-2-222-2-2-2-2220-2-20-2-2222200002222-2-20020020000-2-20000000000000000000000000000
χ43222222-2222-2200-2-200-2-2-2-2-2-2-22222-2-200000022-2-200000000222-202-200000000000-22-2200000000000000000000
χ44222222-2222-2200-2-200-2-2-2-2-2-2-22222-2-200000022-2-20000000022-220-22000000000002-22-200000000000000000000
χ452222-2-2222-22-2222-2-2-22i2i−2i−2i-2-22−2i−2i2i2i-22-2002002i−2i−2i2i−2i−2i2i2i0000-220000002i−2i-22000000000000000000000000000000
χ462222-2-2222-22-2222-2-2-2−2i−2i2i2i-2-222i2i−2i−2i-22-200200−2i2i2i−2i2i2i−2i−2i0000-22000000−2i2i-22000000000000000000000000000000
χ472222-2-2222-22-2-2-22-2222i2i−2i−2i-2-22−2i−2i2i2i-22200-2002i−2i−2i2i2i2i−2i−2i0000-22000000−2i2i2-2000000000000000000000000000000
χ482222-2-2222-22-2-2-22-222−2i−2i2i2i-2-222i2i−2i−2i-22200-200−2i2i2i−2i−2i−2i2i2i0000-220000002i−2i2-2000000000000000000000000000000
χ492222-2-2-222-2-2-200-22002i2i−2i−2i22-22i2i−2i−2i2-20220-2-2−2i2i−2i2i00002i2i−2i−2i-2200200-20000−2i2i0000000000000000000000000000
χ502222-2-2-222-2-2-200-22002i2i−2i−2i22-22i2i−2i−2i2-20-2-2022−2i2i−2i2i0000−2i−2i2i2i-2200-200200002i−2i0000000000000000000000000000
χ512222-2-2-222-2-2-200-22002i2i−2i−2i2-22−2i−2i2i2i-22000000−2i2i2i−2i000000002-22-20-22000000000002i−2i−2i2i00000000000000000000
χ522222-2-2-222-2-2-200-22002i2i−2i−2i2-22−2i−2i2i2i-22000000−2i2i2i−2i000000002-2-2202-200000000000−2i2i2i−2i00000000000000000000
χ532222-2-2-222-2-2-200-2200−2i−2i2i2i22-2−2i−2i2i2i2-20220-2-22i−2i2i−2i0000−2i−2i2i2i-2200200-200002i−2i0000000000000000000000000000
χ542222-2-2-222-2-2-200-2200−2i−2i2i2i22-2−2i−2i2i2i2-20-2-20222i−2i2i−2i00002i2i−2i−2i-2200-20020000−2i2i0000000000000000000000000000
χ552222-2-2-222-2-2-200-2200−2i−2i2i2i2-222i2i−2i−2i-220000002i−2i−2i2i000000002-22-20-2200000000000−2i2i2i−2i00000000000000000000
χ562222-2-2-222-2-2-200-2200−2i−2i2i2i2-222i2i−2i−2i-220000002i−2i−2i2i000000002-2-2202-2000000000002i−2i−2i2i00000000000000000000
χ572-22-22-20-22-2020000002-22-20222-22-2-2-202-202-2000000002-22-200000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ582-22-22-20-22-2020000002-22-20222-22-2-2-202-202-2000000002-22-200000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ592-22-22-20-22-2020000002-22-20222-22-2-2-20-220-2200000000-22-2200000000000000i2−i2i2−i20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ602-22-22-20-22-2020000002-22-20222-22-2-2-20-220-2200000000-22-2200000000000000−i2i2−i2i20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ612-22-22-20-22-202000000-22-22022-22-22-2-202-202-200000000-22-2200000000000000i2−i2i2−i20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ622-22-22-20-22-202000000-22-22022-22-22-2-202-202-200000000-22-2200000000000000−i2i2−i2i20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ632-22-22-20-22-202000000-22-22022-22-22-2-20-220-22000000002-22-200000000000000i2−i2i2−i20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ642-22-22-20-22-202000000-22-22022-22-22-2-20-220-22000000002-22-200000000000000−i2i2−i2i20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ652-22-2-220-2220-20000002i−2i−2i2i02-22i−2i−2i2i-2202-20-22000000002i−2i−2i2i00000000000000i2−i2−i2i20000−222−2i2−i2−i2i2−222−200000000
χ662-22-2-220-2220-20000002i−2i−2i2i02-22i−2i−2i2i-2202-20-22000000002i−2i−2i2i00000000000000−i2i2i2−i200002−2−22−i2i2i2−i22−2−2200000000
χ672-22-2-220-2220-20000002i−2i−2i2i02-22i−2i−2i2i-220-2202-200000000−2i2i2i−2i00000000000000i2−i2−i2i20000−222−2−i2i2i2−i22−2−2200000000
χ682-22-2-220-2220-20000002i−2i−2i2i02-22i−2i−2i2i-220-2202-200000000−2i2i2i−2i00000000000000−i2i2i2−i200002−2−22i2−i2−i2i2−222−200000000
χ692-22-2-220-2220-2000000−2i2i2i−2i02-2−2i2i2i−2i-2202-20-2200000000−2i2i2i−2i00000000000000i2−i2−i2i200002−2−22i2−i2−i2i22−2−2200000000
χ702-22-2-220-2220-2000000−2i2i2i−2i02-2−2i2i2i−2i-2202-20-2200000000−2i2i2i−2i00000000000000−i2i2i2−i20000−222−2−i2i2i2−i2−222−200000000
χ712-22-2-220-2220-2000000−2i2i2i−2i02-2−2i2i2i−2i-220-2202-2000000002i−2i−2i2i00000000000000i2−i2−i2i200002−2−22−i2i2i2−i2−222−200000000
χ722-22-2-220-2220-2000000−2i2i2i−2i02-2−2i2i2i−2i-220-2202-2000000002i−2i−2i2i00000000000000−i2i2i2−i20000−222−2i2−i2−i2i22−2−2200000000
χ734444444-4-4-44-444-4-4-4-40000400000000400-400000000000000000000000000000000000000000000000000000000
χ744444444-4-4-44-4-4-4-4-4440000400000000-400400000000000000000000000000000000000000000000000000000000
χ75444444-4-4-4-4-4-40044000000-40000000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ76444444-4-4-4-4-4-40044000000-4000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ774444-4-44-4-444444-44440000-400000000-400-400000000000000000000000000000000000000000000000000000000
χ784444-4-44-4-4444-4-4-44-4-40000-400000000400400000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-44-44004-400000040000000000000000004-4-440000000000000000000000000000000000000000000000
χ804444-4-4-4-4-44-44004-40000004000000000000000000-444-40000000000000000000000000000000000000000000000
χ814-44-44-40-44-4040000004-44-40-4-4-44-4444000000000000000000000000000000000000000000000000000000000000
χ824-44-44-40-44-404000000-44-440-4-44-44-444000000000000000000000000000000000000000000000000000000000000
χ834-44-4-440-4440-40000004i−4i−4i4i0-44−4i4i4i−4i4-4000000000000000000000000000000000000000000000000000000000000
χ844-44-4-440-4440-4000000−4i4i4i−4i0-444i−4i−4i4i4-4000000000000000000000000000000000000000000000000000000000000
χ858-88-88-808-880-80000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-8808-8-8080000000000000000000000000000000000000000000000000000000000000000000000000000000
χ878-8-88008000-8000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88008000-800000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-8000808-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800-800080-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ911616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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