Finite Group Databasebeta

← Group #72342536

Character table — Group #72342536

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size1111222222222222222222444444444444444444444444448888888888888888888888161616161616161616161616161616161616161616161616161616163232323232323232
order12222222444444444488882222244444444444888888888844444444444488888888884444444444441616161616161616161616161616161688888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-1-1111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-1-1-1111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111-1-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-11111-1-1-111-11111-111-1-1111-1-1-111-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ10111111-1-11111-1-1-111-11111-111-1-1111-1-1-111-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−i-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii
χ11111111-1-11111-1-1-111-11111-111-1-1111-1-1-111-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ12111111-1-11111-1-1-111-11111-111-1-1111-1-1-111-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i
χ13111111-1-11111-1-1-111-11111-1-1-111111-1-1-1-1-111-11111-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ14111111-1-11111-1-1-111-11111-1-1-111111-1-1-1-1-111-11111-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ15111111-1-11111-1-1-111-11111-1-1-111111-1-1-1-1-111-11111-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ16111111-1-11111-1-1-111-11111-1-1-111111-1-1-1-1-111-11111-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ171111-1-11111-1-11-1-11111111-111111-1-11-1-1-1-1-1-11-1-1-1-111-1-1111-11-111-1-111-1-11-111-1-111-1-11-11-111-1-111-1-111-1-111-1-111-1-111-1-11-11-11-11-1
χ181111-1-11111-1-11-1-11111111-111111-1-11-1-1-1-1-1-11-1-1-1-111-1-1111-11-111-1-111-1-11-111-1-111-1-11-11-111-1-111-1-1-1-111-1-111-1-111-1-111-11-11-11-11
χ191111-1-11111-1-11-1-11111111-111111-1-11-1-1-1-1-1-11-1-1-1-111-1-1111-11-1-1-111-1-1111-111-1-111-1-1-11-11-1-111-1-11111-1-111-1-111-1-111-1-1-11-11-11-11
χ201111-1-11111-1-11-1-11111111-111111-1-11-1-1-1-1-1-11-1-1-1-111-1-1111-11-1-1-111-1-1111-111-1-111-1-1-11-11-1-111-1-111-1-111-1-111-1-111-1-1111-11-11-11-1
χ211111-1-11111-1-11-1-11111111-1-1-1-1-11-1-11-1-111111-1-1-1-111-1-111-11-1111-1-111-1-11-1-1-111-1-1111-11-1-1-111-1-11111-1-111-1-1-1-111-1-1111-11-1-11-11
χ221111-1-11111-1-11-1-11111111-1-1-1-1-11-1-11-1-111111-1-1-1-111-1-111-11-1111-1-111-1-11-1-1-111-1-1111-11-1-1-111-1-111-1-111-1-11111-1-111-1-1-11-111-11-1
χ231111-1-11111-1-11-1-11111111-1-1-1-1-11-1-11-1-111111-1-1-1-111-1-111-11-11-1-111-1-1111-1-1-111-1-111-11-1111-1-111-1-111-1-111-1-1-1-111-1-111-11-111-11-1
χ241111-1-11111-1-11-1-11111111-1-1-1-1-11-1-11-1-111111-1-1-1-111-1-111-11-11-1-111-1-1111-1-1-111-1-111-11-1111-1-111-1-1-1-111-1-11111-1-111-1-11-11-1-11-11
χ251111-1-1-1-111-1-1-11111-11111111-1-11-1-1-111-1-111-1-1-1-1-1-1-111111-1-11ii−i−i−i−iii-1111-1-1-1-111i−i−iiii−i−i−i−iii11-1-1-1-11111-1-1-1-111i−i−iii−i−ii
χ261111-1-1-1-111-1-1-11111-11111111-1-11-1-1-111-1-111-1-1-1-1-1-1-111111-1-11ii−i−i−i−iii-1111-1-1-1-111i−i−iiii−i−i−i−iii-1-11111-1-1-1-11111-1-1−iii−i−iii−i
χ271111-1-1-1-111-1-1-11111-11111111-1-11-1-1-111-1-111-1-1-1-1-1-1-111111-1-11−i−iiiii−i−i-1111-1-1-1-111−iii−i−i−iiiii−i−i11-1-1-1-11111-1-1-1-111−iii−i−iii−i
χ281111-1-1-1-111-1-1-11111-11111111-1-11-1-1-111-1-111-1-1-1-1-1-1-111111-1-11−i−iiiii−i−i-1111-1-1-1-111−iii−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1i−i−iii−i−ii
χ291111-1-1-1-111-1-1-11111-111111-1-1111-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1ii−i−i−i−iii-11-1-11111-1-1i−i−ii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1i−i−ii−iii−i
χ301111-1-1-1-111-1-1-11111-111111-1-1111-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1ii−i−i−i−iii-11-1-11111-1-1i−i−ii−i−iiiii−i−i-1-11111-1-111-1-1-1-111−iii−ii−i−ii
χ311111-1-1-1-111-1-1-11111-111111-1-1111-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1−i−iiiii−i−i-11-1-11111-1-1−iii−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1−iii−ii−i−ii
χ321111-1-1-1-111-1-1-11111-111111-1-1111-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1−i−iiiii−i−i-11-1-11111-1-1−iii−iii−i−i−i−iii-1-11111-1-111-1-1-1-111i−i−ii−iii−i
χ33222222222222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ34222222222222222222-2-2-2-22-2-2-2-2222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222222222000000000000000000000000000000000000
χ35222222222222-222-2-2-2000022222-2-2-22-2-22222-20000000000-2-2-2-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ36222222222222-222-2-2-2000022222-2-2-22-2-22222-20000000000-2-2-2-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ37222222222222-222-2-2-200002-2-2-2-2-2-2-22-2-2-2-2-2-2-200000000002222000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ38222222222222-222-2-2-200002-2-2-2-2-2-2-22-2-2-2-2-2-2-200000000002222000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3922222222-2-2-2-22-2-2222222220000-22-2-22-20000-222-2-222-2-2-2-2000022-2-222-2-2-2200000000-22-2200000000000000000000000000000000
χ4022222222-2-2-2-22-2-2222222220000-22-2-22-20000-222-2-222-2-2-2-20000-2-222-2-222-22000000002-22-200000000000000000000000000000000
χ4122222222-2-2-2-22-2-2222-2-2-2-220000-22-2-22-20000-2-2-222-2-222220000000000002-20000000000002-22-22-22-2000000000000000000000000
χ4222222222-2-2-2-22-2-2222-2-2-2-220000-22-2-22-20000-2-2-222-2-222220000000000002-2000000000000-22-22-22-22000000000000000000000000
χ43222222-2-222222-2-2-2-220000-222-2-2-2-2-2-22222-2-220000000000-2-222000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ44222222-2-222222-2-2-2-220000-222-2-2-2-2-2-22222-2-220000000000-2-222000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ45222222-2-222222-2-2-2-220000-2-2-222-2-2-2-222-2-2222000000000022-2-2000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ46222222-2-222222-2-2-2-220000-2-2-222-2-2-2-222-2-2222000000000022-2-2000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ47222222-2-22222-2-2-222-2-2-2-2-2-222-2-2222-2-2-222-2-2-2-2-2-2-22222-2-222-2-20000000022-2-2-2-22222000000000000000000000000000000000000
χ48222222-2-22222-2-2-222-2-2-2-2-2-2-2-222222-2-2-2-2-222-2-2-2-2-22222-2-2-2-22200000000222222-2-2-2-2000000000000000000000000000000000000
χ49222222-2-2-2-2-2-2-22222-22222-20000-22-22-220000222-2-2-2-222-2-200002i2i−2i−2i−2i−2i2i2i2-200000000−2i2i2i−2i00000000000000000000000000000000
χ50222222-2-2-2-2-2-2-22222-22222-20000-22-22-220000222-2-2-2-222-2-20000−2i−2i2i2i2i2i−2i−2i2-2000000002i−2i−2i2i00000000000000000000000000000000
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χ52222222-2-2-2-2-2-2-22222-2-2-2-2-2-20000-22-22-2200002-2-22222-2-222000000000000-22000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ532222-2-22222-2-22-2-2222-2-2-2-2-222222-2-22-2-2-2-2-2-222222-2-222-2-22-22-200000000-22-2-222-2-222000000000000000000000000000000000000
χ542222-2-22222-2-22-2-2222-2-2-2-2-2-2-2-2-22-2-22-2-2222222222-2-222-2-2-22-2200000000-2222-2-222-2-2000000000000000000000000000000000000
χ552222-2-22222-2-2-2-2-2-2-2-20000-22222-222222-2-2-2-2-20000000000-22-22000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
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χ682222-2-2-2-222-2-2-22222-2-2-2-2-22-2-2222-2-2-22222-2-2-2222222-2-2-2-2-222-2000000002-222-2-2-2-222000000000000000000000000000000000000
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χ954-44-4-44004-4-44000000−2i22i2−2i22i20004-400000000-4402i2−2i22i2−2i20000−2i22i2000000000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ964-44-4-44004-4-44000000−2i22i2−2i22i2000-44000000004-402i2−2i22i2−2i20000−2i22i20000000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ974-44-4-4400-444-40000002i2−2i22i2−2i204-400000000-44000−2i22i22i2−2i20000−2i22i2000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ984-44-4-4400-444-40000002i2−2i22i2−2i20-44000000004-4000−2i22i22i2−2i20000−2i22i200000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ994-44-4-4400-444-4000000−2i22i2−2i22i204-400000000-440002i2−2i2−2i22i200002i2−2i200000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ1004-44-4-4400-444-4000000−2i22i2−2i22i20-44000000004-40002i2−2i2−2i22i200002i2−2i2000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ10188-8-8008-80000-800-8880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-800-880000800-88-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-880000000008i−8i0004i2−4i2−4i24i2000000000000000000000042−42000000000000000000000000000000000000000000000000000000000000
χ1048-8-880000000008i−8i000−4i24i24i2−4i20000000000000000000000−4242000000000000000000000000000000000000000000000000000000000000
χ1058-8-88000000000−8i8i0004i2−4i2−4i24i20000000000000000000000−4242000000000000000000000000000000000000000000000000000000000000
χ1068-8-88000000000−8i8i000−4i24i24i2−4i2000000000000000000000042−42000000000000000000000000000000000000000000000000000000000000

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