Finite Group Databasebeta

← Group #13147306

Character table — Group #13147306

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111222222222233336666666666666666666666666666666666666666661212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order1222223666666622222236666666666666666666666666666666666666663366666644443366666666666666666644441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ4111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32
χ5111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ6111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32
χ71111-1-11111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1
χ81111-1-11111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-111-1-111
χ91111-1-11111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ101111-1-11111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ111111-1-11111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ121111-1-11111-1-1-1-11111-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-11-111-1-111-1-111-1-11-1111-1-111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−i111-11-11-1-111-1-11-1-111-1-1i−ii−ii−ii−ii−ii−i
χ1411-1-11-111-1-111-1-111-1-11-1111-1-111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii111-11-11-1-111-1-11-1-111-1-1−ii−ii−ii−ii−ii−ii
χ1511-1-11-111-1-111-1-111-1-11-1111-1-111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32i−ii−i−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32i−ii−iζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ1611-1-11-111-1-111-1-111-1-11-1111-1-111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ii−ii−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ii−ii−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ1711-1-11-111-1-111-1-111-1-11-1111-1-111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32i−ii−i−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32i−ii−iζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ1811-1-11-111-1-111-1-111-1-11-1111-1-111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ii−ii−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ii−ii−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ1911-1-1-1111-1-1-1-11111-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1i−i−ii11-11-111-1-1-1-1111-1-1-1-111i−i−iii−i−iii−i−ii
χ2011-1-1-1111-1-1-1-11111-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−iii−i11-11-111-1-1-1-1111-1-1-1-111−iii−i−iii−i−iii−i
χ2111-1-1-1111-1-1-1-11111-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32i−i−ii−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32i−i−iiζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ2211-1-1-1111-1-1-1-11111-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−iii−i−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−iii−i−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ2311-1-1-1111-1-1-1-11111-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32i−i−ii−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32i−i−iiζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ2411-1-1-1111-1-1-1-11111-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−iii−i−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−iii−i−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ2522222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2622222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i32000000000000
χ2722222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i32000000000000
χ282222-2-22222-2-2-2-22222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222222220000-1-1-2-2-2-2-1-1-11111-1-1-11111000000000000
χ292222-2-22222-2-2-2-22222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300001+i321−i321+i31+i31−i31−i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ302222-2-22222-2-2-2-22222-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300001−i321+i321−i31−i31+i31+i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3122-2-22-222-2-222-2-222-2-22-2-122-2-222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111112222-2-2-2-20000-1-12-22-2-111-1-111-111-1-111000000000000
χ3222-2-22-222-2-222-2-222-2-22-2-122-2-222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i300001+i321−i32−1−i31+i3−1+i31−i31+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32000000000000
χ3322-2-22-222-2-222-2-222-2-22-2-122-2-222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i300001−i321+i32−1+i31−i3−1−i31+i31−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32000000000000
χ3422-2-2-2222-2-2-2-22222-2-2-22-122-2-2-2-222-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-12222-2-2-2-20000-1-1-22-22-11111-1-1-11111-1-1000000000000
χ3522-2-2-2222-2-2-2-22222-2-2-22-122-2-2-2-222-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i300001+i321−i321+i3−1−i31−i3−1+i31+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32000000000000
χ3622-2-2-2222-2-2-2-22222-2-2-22-122-2-2-2-222-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i300001−i321+i321−i3−1+i31+i3−1−i31−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32000000000000
χ372-22-2002-22-200002-22-20022-22-20000222-2-2-2-22222-2-2-2-2000000000000000022-2-22-22-20000220000-22-20000-22-20000000000000000
χ382-22-2002-22-200002-22-20022-22-20000222-2-2-2-22222-2-2-2-20000000000000000−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000−1−i3−1+i300001+i3−1−i31+i300001−i3−1+i31−i30000000000000000
χ392-22-2002-22-200002-22-20022-22-20000222-2-2-2-22222-2-2-2-20000000000000000−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000−1+i3−1−i300001−i3−1+i31−i300001+i3−1−i31+i30000000000000000
χ402-22-2002-22-200002-22-200-12-22-20000-1-1-11111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-2-22-22-20000-1-100001-11−i3i3−i3i31-11−i3i3−i3i3000000000000
χ412-22-2002-22-200002-22-200-12-22-20000-1-1-11111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i300001+i321−i320000−1−i321+i32−1−i32−3+i323−i32−3+i323−i32−1+i321−i32−1+i323+i32−3−i323+i32−3−i32000000000000
χ422-22-2002-22-200002-22-200-12-22-20000-1-1-11111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i300001−i321+i320000−1+i321−i32−1+i323+i32−3−i323+i32−3−i32−1−i321+i32−1−i32−3+i323−i32−3+i323−i32000000000000
χ432-22-2002-22-200002-22-200-12-22-20000-1-1-11111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-2-22-22-20000-1-100001-11i3−i3i3−i31-11i3−i3i3−i3000000000000
χ442-22-2002-22-200002-22-200-12-22-20000-1-1-11111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i300001+i321−i320000−1−i321+i32−1−i323−i32−3+i323−i32−3+i32−1+i321−i32−1+i32−3−i323+i32−3−i323+i32000000000000
χ452-22-2002-22-200002-22-200-12-22-20000-1-1-11111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i300001−i321+i320000−1+i321−i32−1+i32−3−i323+i32−3−i323+i32−1−i321+i32−1−i323−i32−3+i323−i32−3+i32000000000000
χ462-2-22002-2-2200002-2-220022-2-220000222-2-2-2-2-2-2-2-22222000000000000000022-2-2-22-220000220000-2-220000-2-220000000000000000
χ472-2-22002-2-2200002-2-220022-2-220000222-2-2-2-2-2-2-2-222220000000000000000−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i30000−1−i3−1+i300001+i31+i3−1−i300001−i31−i3−1+i30000000000000000
χ482-2-22002-2-2200002-2-220022-2-220000222-2-2-2-2-2-2-2-222220000000000000000−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i30000−1+i3−1−i300001−i31−i3−1+i300001+i31+i3−1−i30000000000000000
χ492-2-22002-2-2200002-2-2200-12-2-220000-1-1-111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i322-2-2-22-220000-1-1000011-1−i3i3i3−i311-1−i3i3i3−i3000000000000
χ502-2-22002-2-2200002-2-2200-12-2-220000-1-1-111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i300001+i321−i320000−1−i32−1−i321+i32−3+i323−i323−i32−3+i32−1+i32−1+i321−i323+i32−3−i32−3−i323+i32000000000000
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χ1046-6-6600-333-33i3−3i3−3i33i3-222-20001-1-11−i3i3i3−i3-2-24022-4022-40-2-2402i3−2i300−2i32i300−2i32i3002i3−2i3000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.