Finite Group Databasebeta

← Group #13147371

Character table — Group #13147371

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1119999999991212111999999999121222218181818181818181824242221818181818181818182424222181818181818181818242444436363636363636363648484443636363636363636364848
order133244661212121233266244661212121266412124441212121212121212824248882424242424242424824248882424242424242424412124441212121212121212412124441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ3111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11
χ4111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11
χ53−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ2200
χ63−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ2200
χ73−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200
χ83−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200
χ93−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ1400
χ103−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ1400
χ113−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200
χ123−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200
χ134440000000001-24440000000001-24440000000001-24440000000001-24440000000001-24440000000001-24440000000001-2
χ14444000000000-21444000000000-21444000000000-21444000000000-21444000000000-21444000000000-21444000000000-21
χ151111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ17111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11-1-1-11−ii11−i−iii-1-1-1-1-11−ii11−i−iii-1-1
χ18111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11-1-1-11i−i11ii−i−i-1-1-1-1-11i−i11ii−i−i-1-1
χ193−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ2200-33+3i323−3i32-1−ii1+i321−i32−ζ14−ζ22ζ14ζ2200-33+3i323−3i32-1−ii1+i321−i32−ζ14−ζ22ζ14ζ2200
χ203−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ2200-33+3i323−3i32-1i−i1+i321−i32ζ14ζ22−ζ14−ζ2200-33+3i323−3i32-1i−i1+i321−i32ζ14ζ22−ζ14−ζ2200
χ213−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200
χ223−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200
χ233−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ1400-33−3i323+3i32-1−ii1−i321+i32−ζ22−ζ14ζ22ζ1400-33−3i323+3i32-1−ii1−i321+i32−ζ22−ζ14ζ22ζ1400
χ243−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ1400-33−3i323+3i32-1i−i1−i321+i32ζ22ζ14−ζ22−ζ1400-33−3i323+3i32-1i−i1−i321+i32ζ22ζ14−ζ22−ζ1400
χ253−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200
χ263−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200
χ274440000000001-24440000000001-24440000000001-24440000000001-24440000000001-2-4-4-4000000000-12-4-4-4000000000-12
χ28444000000000-21444000000000-21444000000000-21444000000000-21444000000000-21-4-4-40000000002-1-4-4-40000000002-1
χ29111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ301111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1
χ31111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11-1-1-11−ii11−i−iii-1-1-1-1-11−ii11−i−iii-1-1111-1i−i-1-1ii−i−i11-1-1-11−ii11−i−iii-1-1
χ32111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11-1-1-11i−i11ii−i−i-1-1-1-1-11i−i11ii−i−i-1-1111-1−ii-1-1−i−iii11-1-1-11i−i11ii−i−i-1-1
χ333−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ2200-33+3i323−3i32-1−ii1+i321−i32−ζ14−ζ22ζ14ζ2200-33+3i323−3i32-1−ii1+i321−i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321i−i−1−i32−1+i32ζ14ζ22−ζ14−ζ2200-33+3i323−3i32-1−ii1+i321−i32−ζ14−ζ22ζ14ζ2200
χ343−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ2200-33+3i323−3i32-1i−i1+i321−i32ζ14ζ22−ζ14−ζ2200-33+3i323−3i32-1i−i1+i321−i32ζ14ζ22−ζ14−ζ22003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ14−ζ22ζ14ζ2200-33+3i323−3i32-1i−i1+i321−i32ζ14ζ22−ζ14−ζ2200
χ353−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200
χ363−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200
χ373−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ1400-33−3i323+3i32-1−ii1−i321+i32−ζ22−ζ14ζ22ζ1400-33−3i323+3i32-1−ii1−i321+i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321i−i−1+i32−1−i32ζ22ζ14−ζ22−ζ1400-33−3i323+3i32-1−ii1−i321+i32−ζ22−ζ14ζ22ζ1400
χ383−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ1400-33−3i323+3i32-1i−i1−i321+i32ζ22ζ14−ζ22−ζ1400-33−3i323+3i32-1i−i1−i321+i32ζ22ζ14−ζ22−ζ14003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ22−ζ14ζ22ζ1400-33−3i323+3i32-1i−i1−i321+i32ζ22ζ14−ζ22−ζ1400
χ393−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200
χ403−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200
χ414440000000001-24440000000001-24440000000001-2-4-4-4000000000-12-4-4-4000000000-124440000000001-2-4-4-4000000000-12
χ42444000000000-21444000000000-21444000000000-21-4-4-40000000002-1-4-4-40000000002-1444000000000-21-4-4-40000000002-1
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.