Finite Group Databasebeta

← Group #13147060

Character table — Group #13147060

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11111111111122222266666666666666121212121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636727272727272
order12223366666622666634466666661212121241212121212121212121212121212333666666666666666666666888824242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-111111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ4111111111111-1-1-1-1-1-111111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ522222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ6222222222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ7222222222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-12222-1-1-1-1000000000000000000
χ8222222222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222000000000000000000
χ9222222222222-2-2-2-2-2-222222-2-2-2-222222-2-2-2222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000
χ10222222222222-2-2-2-2-2-2-122-1-11111-12222-2-2-2-1-1-1-1-1-11111112-1-1222-1-1-1-1-1-1-2-2-2-211111111000000000000000000
χ11222222222222-2-2-2-2-2-2-122-1-11111-12222-2-2-2-1-1-1-1-1-1111111-12-1-1-1-1222-1-1-11111-2-2-2-21111000000000000000000
χ12222222222222-2-2-2-2-2-2-122-1-11111-12222-2-2-2-1-1-1-1-1-1111111-1-12-1-1-1-1-1-122211111111-2-2-2-2000000000000000000
χ1322-2-22222-2-2-2-22-222-2-22002-222-2-2-20000000000000000000-1-1-111-111-111-111-1-111-1-111-1-12−22−222−2−222−2−2000000
χ1422-2-22222-2-2-2-22-222-2-22002-222-2-2-20000000000000000000-1-1-111-111-111-111-1-111-1-111-1-1−22−22−2−222−2−222000000
χ1522-2-22222-2-2-2-2-22-2-2222002-2-2-222-20000000000000000000-1-1-111-111-111-1-1-111-1-111-1-1112−2−2222−2−2−2−222000000
χ1622-2-22222-2-2-2-2-22-2-2222002-2-2-222-20000000000000000000-1-1-111-111-111-1-1-111-1-111-1-111−222−2−2−22222−2−2000000
χ172-2-2222-2-2-2-22200000022-2-2-20000222-2-2000222-2-2-20000002222-2-22-2-22-2-2000000000000000000000000000000
χ182-2-2222-2-2-2-22200000022-2-2-20000222-2-2000222-2-2-2000000-1-1-1-111-111-111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ192-2-2222-2-2-2-22200000022-2-2-20000222-2-2000222-2-2-2000000-1-1-1-111-111-111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ202-2-2222-2-2-2-222000000-12-211−i3i3−i3i3-122-2-2000-1-1-1111−i3−i3−i3i3i3i32-1-12-2-2-111-1110000−i3i3−i3i3i3−i3i3−i3000000000000000000
χ212-2-2222-2-2-2-222000000-12-211−i3i3−i3i3-122-2-2000-1-1-1111−i3−i3−i3i3i3i3-12-1-1112-2-2-111i3−i3i3−i30000−i3i3−i3i3000000000000000000
χ222-2-2222-2-2-2-222000000-12-211−i3i3−i3i3-122-2-2000-1-1-1111−i3−i3−i3i3i3i3-1-12-111-1112-2-2−i3i3−i3i3i3−i3i3−i30000000000000000000000
χ232-2-2222-2-2-2-222000000-12-211i3−i3i3−i3-122-2-2000-1-1-1111i3i3i3−i3−i3−i32-1-12-2-2-111-1110000i3−i3i3−i3−i3i3−i3i3000000000000000000
χ242-2-2222-2-2-2-222000000-12-211i3−i3i3−i3-122-2-2000-1-1-1111i3i3i3−i3−i3−i3-12-1-1112-2-2-111−i3i3−i3i30000i3−i3i3−i3000000000000000000
χ252-2-2222-2-2-2-222000000-12-211i3−i3i3−i3-122-2-2000-1-1-1111i3i3i3−i3−i3−i3-1-12-111-1112-2-2i3−i3i3−i3−i3i3−i3i30000000000000000000000
χ263333333333333333333-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000111111111111-1-1-1-1-1-1
χ273333333333333333333-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1111111
χ28333333333333-3-3-3-3-3-33-1-133-3-3-3-33-1-1-1-1111-1-1-1-1-1-111111100000000000000000000000011-1-11111-1-1-1-1-11-1-111
χ29333333333333-3-3-3-3-3-33-1-133-3-3-3-33-1-1-1-1111-1-1-1-1-1-1111111000000000000000000000000-1-111-1-1-1-111111-111-1-1
χ303333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320330000000−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i320000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ313333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320330000000−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320-1-100000001+i321−i321+i321−i32-11+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i30000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320-1-100000001+i321−i321+i321−i32-11+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ343333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320330000000−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i3200000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−1−i32−1+i321+i321−i32
χ353333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320330000000−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ363333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-1-100000001+i321−i321+i321−i321−1−i32−1+i322−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i300000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-111+i321−i32−1−i32−1+i32
χ373333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320-1-100000001+i321−i321+i321−i321−1−i32−1+i322−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i3000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ383333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320330000000−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i320000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ393333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320330000000−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ403333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320-1-100000001−i321+i321−i321+i32-11−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i30000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ413333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320-1-100000001−i321+i321−i321+i32-11−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ423333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320330000000−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3200000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1−1+i32−1−i321−i321+i32
χ433333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320330000000−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ443333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320-1-100000001−i321+i321−i321+i321−1+i32−1−i322−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i300000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-111−i321+i32−1+i32−1−i32
χ453333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320-1-100000001−i321+i321−i321+i321−1+i32−1−i322−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i3000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ4644-4-44444-4-4-4-44-444-4-44004-444-4-4-40000000000000000000111-1-11-1-11-1-11-1-111-1-111-1-111000000000000000000
χ4744-4-44444-4-4-4-44-444-4-4-200-22-2-2222000000000000000000011-2-1-11-1-1122-2-1-111-1-11122-2-2000000000000000000
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χ4944-4-44444-4-4-4-44-444-4-4-200-22-2-22220000000000000000000-21122-2-1-11-1-1122-2-2-1-111-1-111000000000000000000
χ5044-4-44444-4-4-4-4-44-4-4444004-4-4-444-40000000000000000000111-1-11-1-11-1-1111-1-111-1-111-1-1000000000000000000
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χ656666−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i366−3−3i3−3+3i3−3−3i3−3+3i30-2-200000001+i31−i31+i31−i3-21+i31−i3-21+i31−i3-21+i31−i3-21+i31−i3-21+i31−i3000000000000000000000000000000000000000000
χ666666−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3-6-63+3i33−3i33+3i33−3i30-2-200000001+i31−i31+i31−i32−1−i3−1+i3-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000000000000000000000
χ676666−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i366−3+3i3−3−3i3−3+3i3−3−3i30-2-200000001−i31+i31−i31+i3-21−i31+i3-21−i31+i3-21−i31+i3-21−i31+i3-21−i31+i3000000000000000000000000000000000000000000
χ686666−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3-6-63−3i33+3i33−3i33+3i30-2-200000001−i31+i31−i31+i32−1+i3−1−i3-21−i31+i3-21−i31+i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000000000000000000000
χ6966-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i36-6−3−3i3−3+3i33+3i33−3i3000000000000000000000000000000000000000000000000000002−22−2−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000000
χ7066-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i36-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000000000000000000000−22−22ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23000000
χ7166-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3-663+3i33−3i3−3−3i3−3+3i3000000000000000000000000000000000000000000000000000002−2−22−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23000000
χ7266-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3-663+3i33−3i3−3−3i3−3+3i300000000000000000000000000000000000000000000000000000−222−2ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000000
χ7366-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i36-6−3+3i3−3−3i33−3i33+3i3000000000000000000000000000000000000000000000000000002−22−2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000
χ7466-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i36-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000000000000000000−22−22−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000
χ7566-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3-663−3i33+3i3−3+3i3−3−3i3000000000000000000000000000000000000000000000000000002−2−22ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000
χ7666-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3-663−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000−222−2−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000
χ776-6-6666-6-6-6-6660000006-22-6-600006-2-222000-2-2-2222000000000000000000000000000000000000000000000000
χ786-6-6666-6-6-6-666000000-3-2233−3i33i3−3i33i3-3-2-222000111-1-1-1i3i3i3−i3−i3−i3000000000000000000000000000000000000000000
χ796-6-6666-6-6-6-666000000-3-22333i3−3i33i3−3i3-3-2-222000111-1-1-1−i3−i3−i3i3i3i3000000000000000000000000000000000000000000
χ806-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i300000006-60000000−3−3i3−3+3i33+3i33−3i3000000000000000000000000000000000000000000000000000000000
χ816-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000-2200000001+i31−i3−1−i3−1+i30004−2−2i3−2+2i3-42+2i32−2i3000000000000000000000000000000000000000000000000
χ826-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000-2200000001+i31−i3−1−i3−1+i3000-21+i31−i32−1−i3−1+i3−2i3−3+i33+i32i33−i3−3−i3000000000000000000000000000000000000000000
χ836-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000-2200000001+i31−i3−1−i3−1+i3000-21+i31−i32−1−i3−1+i32i33−i3−3−i3−2i3−3+i33+i3000000000000000000000000000000000000000000
χ846-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i300000006-60000000−3+3i3−3−3i33−3i33+3i3000000000000000000000000000000000000000000000000000000000
χ856-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000-2200000001−i31+i3−1+i3−1−i30004−2+2i3−2−2i3-42−2i32+2i3000000000000000000000000000000000000000000000000
χ866-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000-2200000001−i31+i3−1+i3−1−i3000-21−i31+i32−1+i3−1−i3−2i33+i3−3+i32i3−3−i33−i3000000000000000000000000000000000000000000
χ876-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000-2200000001−i31+i3−1+i3−1−i3000-21−i31+i32−1+i3−1−i32i3−3−i33−i3−2i33+i3−3+i3000000000000000000000000000000000000000000
χ8812-1212-12−6−6i3−6+6i36+6i36−6i3−6−6i3−6+6i36+6i36−6i300000000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-1212-12−6+6i3−6−6i36−6i36+6i3−6+6i3−6−6i36−6i36+6i300000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.