Finite Group Databasebeta

← Group #13147003

Character table — Group #13147003

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11111111111122222266666666666666121212121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636727272727272
order1222336666664412121212344666121212121212121241212121212121212121212121212333666666666121212121212121212121212888824242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ4111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
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
χ6222222222222222222-122-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ7222222222222222222-122-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-122-1-1-12-1-1-1-1-12222-1-1-1-1000000000000000000
χ8222222222222222222-122-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-12-1-1-1-1-1-1-1-12222000000000000000000
χ9222222222222-2-2-2-2-2-222222222-2-2-2-222-2-2-2222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000
χ10222222222222-2-2-2-2-2-2-122-1-1-122111122-2-2-2-1-1-1-1-1-11111112-1-122-1-1-1-12-1-1-2-2-2-211111111000000000000000000
χ11222222222222-2-2-2-2-2-2-122-1-1-122111122-2-2-2-1-1-1-1-1-1111111-12-1-1-122-1-1-12-11111-2-2-2-21111000000000000000000
χ12222222222222-2-2-2-2-2-2-122-1-1-122111122-2-2-2-1-1-1-1-1-1111111-1-12-1-1-1-122-1-1211111111-2-2-2-2000000000000000000
χ1322-2-22222-2-2-2-200000022-2-22-2220000-2-2000222-2-2-20000002222-22-22-2-2-2-2000000000000000000000000000000
χ1422-2-22222-2-2-2-200000022-2-22-2220000-2-2000222-2-2-2000000-1-1-1-11-11-1111133−3−333−3−333−3−3000000000000000000
χ1522-2-22222-2-2-2-200000022-2-22-2220000-2-2000222-2-2-2000000-1-1-1-11-11-11111−3−333−3−333−3−333000000000000000000
χ1622-2-22222-2-2-2-2000000-12-21-112233−3−3-2-2000-1-1-1111333−3−3−32-1-12-2-11-11-211000033−3−3−3−333000000000000000000
χ1722-2-22222-2-2-2-2000000-12-21-112233−3−3-2-2000-1-1-1111333−3−3−3-12-1-112-2-111-21−3−333000033−3−3000000000000000000
χ1822-2-22222-2-2-2-2000000-12-21-112233−3−3-2-2000-1-1-1111333−3−3−3-1-12-11-112-211-233−3−3−3−3330000000000000000000000
χ1922-2-22222-2-2-2-2000000-12-21-1122−3−333-2-2000-1-1-1111−3−3−33332-1-12-2-11-11-2110000−3−33333−3−3000000000000000000
χ2022-2-22222-2-2-2-2000000-12-21-1122−3−333-2-2000-1-1-1111−3−3−3333-12-1-112-2-111-2133−3−30000−3−333000000000000000000
χ2122-2-22222-2-2-2-2000000-12-21-1122−3−333-2-2000-1-1-1111−3−3−3333-1-12-11-112-211-2−3−33333−3−30000000000000000000000
χ222-2-2222-2-2-2-2222i−2i2i2i−2i−2i200-2-22002i−2i2i−2i00000000000000000-1-1-11-11-11-1111i−ii−ii−ii−ii−ii−i2−2−i2i222−2−2−i2−i2i2i2000000
χ232-2-2222-2-2-2-2222i−2i2i2i−2i−2i200-2-22002i−2i2i−2i00000000000000000-1-1-11-11-11-1111i−ii−ii−ii−ii−ii−i−22i2−i2−2−222i2i2−i2−i2000000
χ242-2-2222-2-2-2-222−2i2i−2i−2i2i2i200-2-2200−2i2i−2i2i00000000000000000-1-1-11-11-11-1111−ii−ii−ii−ii−ii−ii2−2i2−i222−2−2i2i2−i2−i2000000
χ252-2-2222-2-2-2-222−2i2i−2i−2i2i2i200-2-2200−2i2i−2i2i00000000000000000-1-1-11-11-11-1111−ii−ii−ii−ii−ii−ii−22−i2i2−2−222−i2−i2i2i2000000
χ263333333333333333333-1-1333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000111111111111-1-1-1-1-1-1
χ273333333333333333333-1-1333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1111111
χ28333333333333-3-3-3-3-3-33-1-1333-1-1-3-3-3-3-1-1111-1-1-1-1-1-111111100000000000000000000000011-1-11111-1-1-1-1-11-1-111
χ29333333333333-3-3-3-3-3-33-1-1333-1-1-3-3-3-3-1-1111-1-1-1-1-1-1111111000000000000000000000000-1-111-1-1-1-111111-111-1-1
χ303333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32033000−3−3i32−3+3i320000−3−3i32−3+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+3i32033000−3−3i32−3+3i320000−3−3i32−3+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+3i320-1-10001+i321−i3200001+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+3i320-1-10001+i321−i3200001+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+3i323−3i32033000−3−3i32−3+3i320000−3−3i32−3+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+3i323−3i32033000−3−3i32−3+3i320000−3−3i32−3+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+3i323−3i320-1-10001+i321−i3200001+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+3i323−3i320-1-10001+i321−i3200001+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+3i32−3−3i32033000−3+3i32−3−3i320000−3+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+3i32−3−3i32033000−3+3i32−3−3i320000−3+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+3i32−3−3i320-1-10001−i321+i3200001−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+3i32−3−3i320-1-10001−i321+i3200001−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+3i32033000−3+3i32−3−3i320000−3+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+3i32033000−3+3i32−3−3i320000−3+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+3i320-1-10001−i321+i3200001−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+3i320-1-10001−i321+i3200001−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
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χ666666−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3-6-63+3i33−3i33+3i33−3i30-2-20001+i31−i300001+i31−i32−1−i3−1+i3-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000000000000000000000
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χ686666−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3−3+3i3−3−3i3-6-63−3i33+3i33−3i33+3i30-2-20001−i31+i300001−i31+i32−1+i3−1−i3-21−i31+i3-21−i31+i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000000000000000000000
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χ7666-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i300000006-6000−3+3i3−3−3i300003−3i33+3i3000000000000000000000000000000000000000000000000000000000
χ7766-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i30000000-220001−i31+i30000−1+i3−1−i30004−2+2i3−2−2i3-42−2i32+2i3000000000000000000000000000000000000000000000000
χ7866-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i30000000-220001−i31+i30000−1+i3−1−i3000-21−i31+i32−1+i3−1−i323−2ζ14−4ζ224ζ14+2ζ22−232ζ14+4ζ22−4ζ14−2ζ22000000000000000000000000000000000000000000
χ7966-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i30000000-220001−i31+i30000−1+i3−1−i3000-21−i31+i32−1+i3−1−i3−232ζ14+4ζ22−4ζ14−2ζ2223−2ζ14−4ζ224ζ14+2ζ22000000000000000000000000000000000000000000
χ806-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i36i−6i6ζ226ζ14−6ζ22−6ζ14000000000000000000000000000000000000000000000000000002−2−i2i2−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000
χ816-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i36i−6i6ζ226ζ14−6ζ22−6ζ1400000000000000000000000000000000000000000000000000000−22i2−i2ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000
χ826-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i3−6i6i−6ζ22−6ζ146ζ226ζ14000000000000000000000000000000000000000000000000000002−2i2−i2−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23−ζ7−ζ13−ζ5−ζ23ζ7+ζ13ζ5+ζ23000000
χ836-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i3−6i6i−6ζ22−6ζ146ζ226ζ1400000000000000000000000000000000000000000000000000000−22−i2i2ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23ζ7+ζ13ζ5+ζ23−ζ7−ζ13−ζ5−ζ23000000
χ846-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i36i−6i6ζ146ζ22−6ζ14−6ζ22000000000000000000000000000000000000000000000000000002−2−i2i2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000000
χ856-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i36i−6i6ζ146ζ22−6ζ14−6ζ2200000000000000000000000000000000000000000000000000000−22i2−i2−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000
χ866-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3−6i6i−6ζ14−6ζ226ζ146ζ22000000000000000000000000000000000000000000000000000002−2i2−i2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13000000
χ876-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3−6i6i−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000000000000000000000000−22−i2i2−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13000000
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.