Finite Group Databasebeta

← Group #72318985

Character table — Group #72318985

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111111122222222222244444444444444448888888888888888888888888888161616161616161616161616161616161616161616161616161616163232323232323232
order1222222244444444444444448888888888884488888888881616161616161616161616161616161622224444888888888888161616161616161622448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-11-1111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111111-11-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ17111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−iii−i−i11-1-111-1-11-1-11i−ii−i
χ18111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii−i−iii11-1-111-1-1-111-1−ii−ii
χ19111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i−i−iii-1-111-1-11111-1-1i−i−ii
χ20111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iiiii−i−i-1-111-1-111-1-111−iii−i
χ21111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111−i−iii−i−iiiii−i−i-1-111-1-11111-1-1−iii−i
χ22111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i−i−iii-1-111-1-111-1-111i−i−ii
χ23111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii−i−iii11-1-111-1-11-1-11−ii−ii
χ24111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−iii−i−i11-1-111-1-1-111-1i−ii−i
χ25111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−iii−i−i11-1-1-1-111-111-1−ii−ii
χ26111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii−i−iii−i−iii11-1-1-1-1111-1-11i−ii−i
χ27111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i−i−iii-1-11111-1-1-1-111−iii−i
χ28111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−i−iii−i−iiiii−i−i-1-11111-1-111-1-1i−i−ii
χ29111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iiiii−i−i-1-11111-1-1-1-111i−i−ii
χ30111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i−i−iii-1-11111-1-111-1-1−iii−i
χ31111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iii−i−iii11-1-1-1-111-111-1i−ii−i
χ32111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−iii−i−iii−i−i11-1-1-1-1111-1-11−ii−ii
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-20000000000000000000000002-22-2000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-222000000000000000000000000-22-22000000000000000000000000
χ3522222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000-22-22000000000000000000000000
χ3622222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-222-2-2220000000000000000000000002-22-2000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000002i−2i−2i2i000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000−2i2i2i−2i000000000000000000000000
χ39222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i000000000000000000000000
χ40222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i−2i2i000000000000000000000000
χ412222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i0000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000002-2002i−2i00000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ422222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i0000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000-2200−2i2i0000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ432222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000002-2002i−2i0000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ442222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000-2200−2i2i00000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ452222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i0000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000002-200−2i2i00000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ462222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i0000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000-22002i−2i0000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ472222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000002-200−2i2i0000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ482222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000-22002i−2i00000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ4922-2-222-2-22-22-22i2i−2i−2i−2i−2i2i2i000000002-22-22i−2i2i−2i0000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000002-2002i−2i00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5022-2-222-2-22-22-22i2i−2i−2i−2i−2i2i2i000000002-22-22i−2i2i−2i0000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000-2200−2i2i0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5122-2-222-2-22-22-22i2i−2i−2i−2i−2i2i2i000000002-22-22i−2i2i−2i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000002-2002i−2i0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5222-2-222-2-22-22-22i2i−2i−2i−2i−2i2i2i000000002-22-22i−2i2i−2i000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000-2200−2i2i00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5322-2-222-2-22-22-2−2i−2i2i2i2i2i−2i−2i000000002-22-2−2i2i−2i2i0000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000002-200−2i2i00002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5422-2-222-2-22-22-2−2i−2i2i2i2i2i−2i−2i000000002-22-2−2i2i−2i2i0000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000-22002i−2i0000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5522-2-222-2-22-22-2−2i−2i2i2i2i2i−2i−2i000000002-22-2−2i2i−2i2i000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000002-200−2i2i0000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5622-2-222-2-22-22-2−2i−2i2i2i2i2i−2i−2i000000002-22-2−2i2i−2i2i000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000-22002i−2i00002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5722-2-2-2-2222-2-222222-2-2-2-2000000002-2-222-2-2200002i−2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000002-22-2000000000000
χ5822-2-2-2-2222-2-222222-2-2-2-2000000002-2-222-2-2200002i−2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000-22-22000000000000
χ5922-2-2-2-2222-2-222222-2-2-2-2000000002-2-222-2-220000−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000-22-22000000000000
χ6022-2-2-2-2222-2-222222-2-2-2-2000000002-2-222-2-220000−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000002-22-2000000000000
χ6122-2-2-2-2222-2-222222-2-2-2-200000000-222-2-222-200002i−2i−2i2i2i−2i−2i2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-200000000
χ6222-2-2-2-2222-2-222222-2-2-2-200000000-222-2-222-200002i−2i−2i2i2i−2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-2200000000
χ6322-2-2-2-2222-2-222222-2-2-2-200000000-222-2-222-20000−2i2i2i−2i−2i2i2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-2200000000
χ6422-2-2-2-2222-2-222222-2-2-2-200000000-222-2-222-20000−2i2i2i−2i−2i2i2i−2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-200000000
χ6522-2-2-2-2222-2-22-2-2-2-22222000000002-2-22-222-200002-22-2-22-222-2-222-2-2200000000000000000000000000002-2-22000000000000
χ6622-2-2-2-2222-2-22-2-2-2-22222000000002-2-22-222-200002-22-2-22-22-222-2-222-20000000000000000000000000000-222-2000000000000
χ6722-2-2-2-2222-2-22-2-2-2-22222000000002-2-22-222-20000-22-222-22-22-2-222-2-220000000000000000000000000000-222-2000000000000
χ6822-2-2-2-2222-2-22-2-2-2-22222000000002-2-22-222-20000-22-222-22-2-222-2-222-200000000000000000000000000002-2-22000000000000
χ6922-2-2-2-2222-2-22-2-2-2-2222200000000-222-22-2-2200002-2-22-222-20000000022-2-2-2-2220000000000000000000000002-2-2200000000
χ7022-2-2-2-2222-2-22-2-2-2-2222200000000-222-22-2-2200002-2-22-222-200000000-2-22222-2-2000000000000000000000000-222-200000000
χ7122-2-2-2-2222-2-22-2-2-2-2222200000000-222-22-2-220000-222-22-2-220000000022-2-2-2-222000000000000000000000000-222-200000000
χ7222-2-2-2-2222-2-22-2-2-2-2222200000000-222-22-2-220000-222-22-2-2200000000-2-22222-2-20000000000000000000000002-2-2200000000
χ7344444444-4-4-4-44-44-44-44-444-4-40000000000004-400000000000000000000000000000000000000000000000000000000000000
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χ794444-4-4-4-4-4-4444i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000000000000000000000000000000
χ804444-4-4-4-4-4-4444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i000000000000000000000000000000000000
χ814444-4-4-4-4-4-444−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000000000000000000000000000000000000
χ824444-4-4-4-4-4-444−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000000000000000000000000000000
χ8344-4-444-4-44-44-44i4i−4i−4i−4i−4i4i4i00000000-44-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ8444-4-444-4-44-44-4−4i−4i4i4i4i4i−4i−4i00000000-44-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ8544-4-444-4-4-44-444i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000
χ8644-4-444-4-4-44-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000
χ8744-4-444-4-4-44-44−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000
χ8844-4-444-4-4-44-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000
χ8944-4-4-4-444-444-44-44-4-44-44000044-4-400000000004-4000000000000000000000000000000000000000000000000000000000000
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χ9244-4-4-4-444-444-4-44-444-44-40000-4-44400000000004-4000000000000000000000000000000000000000000000000000000000000
χ938-88-88-88-8000000000000000042−4242−42000000000000000000000000000000000000000000000000000000000000000000000000
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χ968-88-8-88-88000000000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ978-8-888-8-88000000000000008-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-888-8-8800000000000000-880000000000000000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-888-8000000000000000042−42−4242000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-888-80000000000000000−424242−42000000000000000000000000000000000000000000000000000000000000000000000000

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