Finite Group Databasebeta

← Group #13147262

Character table — Group #13147262

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111222222222233336666666666666666666666666666666666666666661212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order124423466612121212224423466666666666666666661212121212121212121212121212121212121212336612121212888833666666661212121212121212121288882424242424242424
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
χ71111-11-1-1-1111-1-11111-11-111-1-1111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ81111-11-1-1-1111-1-11111-11-111-1-1111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-111
χ91111-11-1-1-1111-1-11111-11-111-1-1111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ101111-11-1-1-1111-1-11111-11-111-1-1111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ111111-11-1-1-1111-1-11111-11-111-1-1111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ121111-11-1-1-1111-1-11111-11-111-1-1111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-111-1111-1-1-1-111-1-111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−i1111111111-1-1-1-1-1-1-1-1-1-1i−ii−ii−ii−ii−ii−i
χ1411-1-111-1111-1-1-1-111-1-111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii1111111111-1-1-1-1-1-1-1-1-1-1−ii−ii−ii−ii−ii−ii
χ1511-1-111-1111-1-1-1-111-1-111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32i−ii−i−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32i−ii−iζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ1611-1-111-1111-1-1-1-111-1-111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ii−ii−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−ii−ii−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ1711-1-111-1111-1-1-1-111-1-111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32i−ii−i−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32i−ii−iζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ1811-1-111-1111-1-1-1-111-1-111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ii−ii−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−ii−ii−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ1911-1-1-111-1-11-1-11111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1i−i−ii11-1-1-1-1-1-11111-1-111-1-111i−i−iii−i−iii−i−ii
χ2011-1-1-111-1-11-1-11111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1−iii−i11-1-1-1-1-1-11111-1-111-1-111−iii−i−iii−i−iii−i
χ2111-1-1-111-1-11-1-11111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32i−i−ii−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32i−i−iiζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ2211-1-1-111-1-11-1-11111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−iii−i−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−iii−i−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ2311-1-1-111-1-11-1-11111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32i−i−ii−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32i−i−iiζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ2411-1-1-111-1-11-1-11111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−iii−i−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−iii−i−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ252222222222222222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ262222222222222222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300001+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i32−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ272222222222222222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300001−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i32−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ282222-22-2-2-2222-2-22222-2-1-222-2-2-1-1-1-1-1-111111111-122-2-2-1-1-1-1-1-1-1-111111111222222220000-1-1-2-21111-1-1-2-2-1-111-1-111000000000000
χ292222-22-2-2-2222-2-22222-2-1-222-2-2-1-1-1-1-1-111111111-122-2-2-1-1-1-1-1-1-1-111111111−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300001+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321+i321−i321+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000
χ302222-22-2-2-2222-2-22222-2-1-222-2-2-1-1-1-1-1-111111111-122-2-2-1-1-1-1-1-1-1-111111111−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300001−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i321+i321−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000
χ3122-2-222-2222-2-2-2-222-2-22-1-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111111112222-2-2-2-20000-1-122-1-1-1-1-1-1-2-211111111000000000000
χ3222-2-222-2222-2-2-2-222-2-22-1-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i300001+i321−i32−1−i3−1+i31+i321+i321−i321−i321+i321−i321+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3322-2-222-2222-2-2-2-222-2-22-1-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i300001−i321+i32−1+i3−1−i31−i321−i321+i321+i321−i321+i321−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3422-2-2-222-2-22-2-22222-2-2-2-1222-2-2-1-1-1-1-1-111111111-1-2-22211111111-1-1-1-1-1-1-1-12222-2-2-2-20000-1-1-2-21111-1-12211-1-111-1-1000000000000
χ3522-2-2-222-2-22-2-22222-2-2-2-1222-2-2-1-1-1-1-1-111111111-1-2-22211111111-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i300001+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000
χ3622-2-2-222-2-22-2-22222-2-2-2-1222-2-2-1-1-1-1-1-111111111-1-2-22211111111-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i300001−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000
χ372-22i−2i02000-22i−2i002-22i−2i0202-200222-2-2-200000000-22i−2i002i2i2i2i−2i−2i−2i−2i0000000022-2-22i−2i2i−2i000022000000-2-2002i−2i002i−2i00000000000000
χ382-22i−2i02000-22i−2i002-22i−2i0202-200222-2-2-200000000-22i−2i002i2i2i2i−2i−2i−2i−2i00000000−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ70000−1−i3−1+i30000001+i31−i3002ζ11−2ζ11002ζ7−2ζ700000000000000
χ392-22i−2i02000-22i−2i002-22i−2i0202-200222-2-2-200000000-22i−2i002i2i2i2i−2i−2i−2i−2i00000000−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ110000−1+i3−1−i30000001−i31+i3002ζ7−2ζ7002ζ11−2ζ1100000000000000
χ402-22i−2i02000-22i−2i002-22i−2i0-102-200-1-1-1111−i3−i3−i3−i3i3i3i3i312i−2i00−i−i−i−iiiii3333−3−3−3−322-2-22i−2i2i−2i0000-1-100−i3i3−i3i31100−ii3−3−ii3−3000000000000
χ412-22i−2i02000-22i−2i002-22i−2i0-102-200-1-1-1111−i3−i3−i3−i3i3i3i3i312i−2i00−i−i−i−iiiii3333−3−3−3−3−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ700001+i321−i3200−3+i323−i323+i32−3−i32−1−i32−1+i3200−ζ11ζ112ζ7+ζ11−2ζ7−ζ11−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11000000000000
χ422-22i−2i02000-22i−2i002-22i−2i0-102-200-1-1-1111−i3−i3−i3−i3i3i3i3i312i−2i00−i−i−i−iiiii3333−3−3−3−3−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ1100001−i321+i32003+i32−3−i32−3+i323−i32−1+i32−1−i3200−ζ7ζ7−ζ7−2ζ11ζ7+2ζ11−ζ11ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ432-22i−2i02000-22i−2i002-22i−2i0-102-200-1-1-1111i3i3i3i3−i3−i3−i3−i312i−2i00−i−i−i−iiiii−3−3−3−3333322-2-22i−2i2i−2i0000-1-100i3−i3i3−i31100−ii−33−ii−33000000000000
χ442-22i−2i02000-22i−2i002-22i−2i0-102-200-1-1-1111i3i3i3i3−i3−i3−i3−i312i−2i00−i−i−i−iiiii−3−3−3−33333−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ700001+i321−i32003−i32−3+i32−3−i323+i32−1−i32−1+i3200−ζ11ζ11−2ζ7−ζ112ζ7+ζ11−ζ7ζ7ζ7+2ζ11−ζ7−2ζ11000000000000
χ452-22i−2i02000-22i−2i002-22i−2i0-102-200-1-1-1111i3i3i3i3−i3−i3−i3−i312i−2i00−i−i−i−iiiii−3−3−3−33333−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ1100001−i321+i3200−3−i323+i323−i32−3+i32−1+i32−1−i3200−ζ7ζ7ζ7+2ζ11−ζ7−2ζ11−ζ11ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ462-2−2i2i02000-2−2i2i002-2−2i2i0202-200222-2-2-200000000-2−2i2i00−2i−2i−2i−2i2i2i2i2i0000000022-2-2−2i2i−2i2i000022000000-2-200−2i2i00−2i2i00000000000000
χ472-2−2i2i02000-2−2i2i002-2−2i2i0202-200222-2-2-200000000-2−2i2i00−2i−2i−2i−2i2i2i2i2i00000000−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ70000−1−i3−1+i30000001+i31−i300−2ζ112ζ1100−2ζ72ζ700000000000000
χ482-2−2i2i02000-2−2i2i002-2−2i2i0202-200222-2-2-200000000-2−2i2i00−2i−2i−2i−2i2i2i2i2i00000000−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ110000−1+i3−1−i30000001−i31+i300−2ζ72ζ700−2ζ112ζ1100000000000000
χ492-2−2i2i02000-2−2i2i002-2−2i2i0-102-200-1-1-1111−i3−i3−i3−i3i3i3i3i31−2i2i00iiii−i−i−i−i−3−3−3−3333322-2-2−2i2i−2i2i0000-1-100−i3i3−i3i31100i−i−33i−i−33000000000000
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χ1016-6−6i6i0-303i3−3i333i−3i33−336-6−6i6i000-333i3−3i30000000000000003i−3i33−33000000000000000000000000000000000000000000000000000000000000
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χ1036-6−6i6i0-303i3−3i333i−3i33−33-222i−2i0001-1−i3i3-24-22-420−2i302i302i30−2i30−ii−3302i−4i2i0−2i4i−2i0−230230230−2300000000000000000000000000000000000000000000
χ1046-6−6i6i0-303i3−3i333i−3i33−33-222i−2i0001-1−i3i3-2-2422-402i3−2i300−2i32i300−ii−3302i2i−4i0−2i−2i4i023−2300−2323000000000000000000000000000000000000000000000

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