Finite Group Databasebeta

← Group #72343566

Character table — Group #72343566

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111111122222222222244444444444488888888888888888888888888161616161616161616161616161616161616161616161616161616161616161616161616161632323232
order12222222444444444444444488888888448888888888888888888888882222444444448888888888161616161616161616161616161616162488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ911111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1311111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1411111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ1511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1
χ17111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i111111-1-1-1-1-1-1i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-11-1i−i
χ18111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-111-1-1-1-111i−iii−i−i−i−iii−i−iii−i−iii-1-111-1-111-11−ii
χ19111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111-1-11111-1-1i−i−i−iiiii−i−i−i−iii−i−iii-1-111-1-1111-1i−i
χ20111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-1-1-1-1-1111111i−i−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-11−ii
χ21111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111-1-11111-1-1−iiii−i−i−i−iiiii−i−iii−i−i-1-111-1-1111-1−ii
χ22111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-1-1-1-1-1111111−iiii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-11i−i
χ23111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii111111-1-1-1-1-1-1−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-11-1−ii
χ24111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-111-1-1-1-111−ii−i−iiiii−i−iii−i−iii−i−i-1-111-1-111-11i−i
χ25111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−iii−i−i-1-11111-1-111-1-1−ii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-11−ii
χ26111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−iii−i−i-1-1-1-111-1-11111−ii−i−iii−i−iii−i−iiiii−i−i-1-11111-1-11-1i−i
χ27111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111ii−i−i−i−iii−i−i−i−iiiiiii−i−i1111-1-111-1-1-1-1−iiii−i−iii−i−i−i−iiiii−i−i-1-11111-1-1-11−ii
χ28111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111ii−i−i−i−iii−i−i−i−iiiiiii−i−i11-1-1-1-111-1-111−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-1111-1i−i
χ29111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111−i−iiiii−i−iiiii−i−i−i−i−i−iii1111-1-111-1-1-1-1i−i−i−iii−i−iiiii−i−i−i−iii-1-11111-1-1-11i−i
χ30111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111−i−iiiii−i−iiiii−i−i−i−i−i−iii11-1-1-1-111-1-111i−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-1111-1−ii
χ31111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111−i−iiiii−i−i−i−i−i−iiiii−i−iii-1-11111-1-111-1-1i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-11i−i
χ32111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-111−i−iiiii−i−i−i−i−i−iiiii−i−iii-1-1-1-111-1-11111i−iii−i−iii−i−iii−i−i−i−iii-1-11111-1-11-1−ii
χ33222222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22222222200000000-2-2-2-2000000000000-2-20000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000220000000000000000000000000000
χ3522222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000-2-2-2-2000000000000220000000000000000000000000000
χ3622222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000002222000000000000-2-20000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2222-2-2-2222i2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i000000000000−2i2i0000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2222-2-2-222−2i−2i2i2i−2i−2i2i2i000000002i2i−2i−2i0000000000002i−2i0000000000000000000000000000
χ39222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2222-2-22i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i0000000000002i−2i0000000000000000000000000000
χ40222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2222-2-2−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i000000000000−2i2i0000000000000000000000000000
χ41222-22-2-2-222-2-22i−2i2i2i−2i−2i2i−2i00002-22i−2i2-22i−2i000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000002-20000002i−2i00000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ42222-22-2-2-222-2-22i−2i2i2i−2i−2i2i−2i00002-22i−2i2-22i−2i000000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000-22000000−2i2i0000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ43222-22-2-2-222-2-22i−2i2i2i−2i−2i2i−2i00002-22i−2i2-22i−2i00000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000002-20000002i−2i0000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ44222-22-2-2-222-2-22i−2i2i2i−2i−2i2i−2i00002-22i−2i2-22i−2i00000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000-22000000−2i2i00000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ45222-22-2-2-222-2-2−2i2i−2i−2i2i2i−2i2i00002-2−2i2i2-2−2i2i000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000002-2000000−2i2i00000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ46222-22-2-2-222-2-2−2i2i−2i−2i2i2i−2i2i00002-2−2i2i2-2−2i2i000000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000-220000002i−2i0000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ47222-22-2-2-222-2-2−2i2i−2i−2i2i2i−2i2i00002-2−2i2i2-2−2i2i00000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000002-2000000−2i2i0000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ48222-22-2-2-222-2-2−2i2i−2i−2i2i2i−2i2i00002-2−2i2i2-2−2i2i00000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000-220000002i−2i00000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ4922-22-22-2-22-22-22i−2i2i−2i2i−2i−2i2i00002-2−2i2i-222i−2i000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000002ζ3−2ζ32ζ−2ζ000000002-22i−2i00000000
χ5022-22-22-2-22-22-22i−2i2i−2i2i−2i−2i2i00002-2−2i2i-222i−2i000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000−2ζ32ζ3−2ζ2ζ00000000-22−2i2i00000000
χ5122-22-22-2-22-22-22i−2i2i−2i2i−2i−2i2i00002-2−2i2i-222i−2i00000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000002ζ3−2ζ32ζ−2ζ00000000-22−2i2i00000000
χ5222-22-22-2-22-22-22i−2i2i−2i2i−2i−2i2i00002-2−2i2i-222i−2i00000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000−2ζ32ζ3−2ζ2ζ000000002-22i−2i00000000
χ5322-22-22-2-22-22-2−2i2i−2i2i−2i2i2i−2i00002-22i−2i-22−2i2i000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000002ζ−2ζ2ζ3−2ζ3000000002-2−2i2i00000000
χ5422-22-22-2-22-22-2−2i2i−2i2i−2i2i2i−2i00002-22i−2i-22−2i2i000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000−2ζ2ζ−2ζ32ζ300000000-222i−2i00000000
χ5522-22-22-2-22-22-2−2i2i−2i2i−2i2i2i−2i00002-22i−2i-22−2i2i00000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000002ζ−2ζ2ζ3−2ζ300000000-222i−2i00000000
χ5622-22-22-2-22-22-2−2i2i−2i2i−2i2i2i−2i00002-22i−2i-22−2i2i00000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000−2ζ2ζ−2ζ32ζ3000000002-2−2i2i00000000
χ5722-2-2-2-2222-2-22222-2-22-2-2000022-2-2-2-2220000002i−2i2i−2i00002-2-222-2-222i−2i2i−2i00002i−2i2i−2i0000000000000000000000000000000000
χ5822-2-2-2-2222-2-22222-2-22-2-2000022-2-2-2-2220000002i−2i2i−2i0000-222-2-222-22i−2i2i−2i0000−2i2i−2i2i0000000000000000000000000000000000
χ5922-2-2-2-2222-2-22222-2-22-2-2000022-2-2-2-222000000−2i2i−2i2i00002-2-222-2-22−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000000000000000
χ6022-2-2-2-2222-2-22222-2-22-2-2000022-2-2-2-222000000−2i2i−2i2i0000-222-2-222-2−2i2i−2i2i00002i−2i2i−2i0000000000000000000000000000000000
χ6122-2-2-2-2222-2-22222-2-22-2-20000-2-22222-2-20000002i−2i2i−2i000000000000−2i2i−2i2i2-20000002-200002i−2i2i−2i000000000000000000000000
χ6222-2-2-2-2222-2-22222-2-22-2-20000-2-22222-2-20000002i−2i2i−2i000000000000−2i2i−2i2i-22000000-220000−2i2i−2i2i000000000000000000000000
χ6322-2-2-2-2222-2-22222-2-22-2-20000-2-22222-2-2000000−2i2i−2i2i0000000000002i−2i2i−2i2-20000002-20000−2i2i−2i2i000000000000000000000000
χ6422-2-2-2-2222-2-22222-2-22-2-20000-2-22222-2-2000000−2i2i−2i2i0000000000002i−2i2i−2i-22000000-2200002i−2i2i−2i000000000000000000000000
χ6522-2-2-2-2222-2-22-2-2-222-22200002222-2-2-2-20000002-2-2200002i−2i−2i2i−2i2i2i−2i2-2-220000−2i2i2i−2i0000000000000000000000000000000000
χ6622-2-2-2-2222-2-22-2-2-222-22200002222-2-2-2-20000002-2-220000−2i2i2i−2i2i−2i−2i2i2-2-2200002i−2i−2i2i0000000000000000000000000000000000
χ6722-2-2-2-2222-2-22-2-2-222-22200002222-2-2-2-2000000-222-200002i−2i−2i2i−2i2i2i−2i-222-200002i−2i−2i2i0000000000000000000000000000000000
χ6822-2-2-2-2222-2-22-2-2-222-22200002222-2-2-2-2000000-222-20000−2i2i2i−2i2i−2i−2i2i-222-20000−2i2i2i−2i0000000000000000000000000000000000
χ6922-2-2-2-2222-2-22-2-2-222-2220000-2-2-2-222220000002-2-22000000000000-222-22-2000000-2200002-2-22000000000000000000000000
χ7022-2-2-2-2222-2-22-2-2-222-2220000-2-2-2-222220000002-2-22000000000000-222-2-220000002-20000-222-2000000000000000000000000
χ7122-2-2-2-2222-2-22-2-2-222-2220000-2-2-2-22222000000-222-20000000000002-2-222-2000000-220000-222-2000000000000000000000000
χ7222-2-2-2-2222-2-22-2-2-222-2220000-2-2-2-22222000000-222-20000000000002-2-22-220000002-200002-2-22000000000000000000000000
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χ9244-4-4-4-444-444-4-4-44-4-44440000000000000000000000-444-4000000000000000000000000000000000000000000000000000000
χ938-888-8-88-8000000000000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-888-8-88-800000000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000
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χ998-8-8-8888-80000000000008-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-8-8888-8000000000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.