Finite Group Databasebeta

← Group #13164549

Character table — Group #13164549

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111133333366666666666666121212121212121212121212121212363636363636363636363636727272727272969696969696
order12336622666634466666661212121241212121212121212121212121212888824242424242424244412121212333666
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ322222222222222222222222222222222222222222000000000000000000-1-1-1-1-1-1
χ4222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002-1-12-1-1
χ5222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-12-1-12-1
χ6222222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-1-12-1-12
χ72-222-2-22-222-2-2200222-2-2-2-2000000000000000000022−2−22222−2−2−2−2000000-1-1-1111
χ82-222-2-22-222-2-2200222-2-2-2-20000000000000000000−2−222−2−2−2−22222000000-1-1-1111
χ93333333333333-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1000000
χ103333333333333-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111000000
χ11333333-1-1-1-1-1-133-1-1-1-1-1-1-1333-1-1-1-1-1333-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11-111-1-1000000
χ12333333-1-1-1-1-1-133-1-1-1-1-1-1-1333-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-11-1-111000000
χ13333333-1-1-1-1-1-13-13-1-1-1-1-1-13-1-133-1-1-1-1-1-1333-1-1-1-1-1-11-11-111-1-111-1-1-11-1-111000000
χ14333333-1-1-1-1-1-13-13-1-1-1-1-1-13-1-133-1-1-1-1-1-1333-1-1-1-1-1-1-11-11-1-111-1-1111-111-1-1000000
χ1533−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320330000000−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i320000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32000000
χ1633−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320330000000−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32000000
χ1733−3−3i32−3+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+i322−1−i3−1−i3−1+i3−1+i31111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32000000
χ1833−3−3i32−3+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+i322−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32000000
χ1933−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i3203-12−1−i3−1+i32−1−i3−1+i30−3−3i32−3+3i321+i321−i32-11+i321−i320002−1−i3−1+i3−1−i3−1+i32−1+i32−1−i31-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i32000000
χ2033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i3203-12−1−i3−1+i32−1−i3−1+i30−3−3i32−3+3i321+i321−i32-11+i321−i320002−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32000000
χ2133−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320-132−1−i3−1+i32−1−i3−1+i301+i321−i32−3−3i32−3+3i32-11+i321−i322−1−i3−1+i3000−1+i3−1−i3−1+i32−1−i321-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32-111+i321−i32−1−i32−1+i32000000
χ2233−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320-132−1−i3−1+i32−1−i3−1+i301+i321−i32−3−3i32−3+3i32-11+i321−i322−1−i3−1+i3000−1+i3−1−i3−1+i32−1−i32-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i32000000
χ2333−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320330000000−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i320000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32000000
χ2433−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320330000000−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32000000
χ2533−3+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−i322−1+i3−1+i3−1−i3−1−i31111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32000000
χ2633−3+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−i322−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32000000
χ2733−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i3203-12−1+i3−1−i32−1+i3−1−i30−3+3i32−3−3i321−i321+i32-11−i321+i320002−1+i3−1−i3−1+i3−1−i32−1−i32−1+i31-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i32000000
χ2833−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i3203-12−1+i3−1−i32−1+i3−1−i30−3+3i32−3−3i321−i321+i32-11−i321+i320002−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32000000
χ2933−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320-132−1+i3−1−i32−1+i3−1−i301−i321+i32−3+3i32−3−3i32-11−i321+i322−1+i3−1−i3000−1−i3−1+i3−1−i32−1+i321-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32-111−i321+i32−1+i32−1−i32000000
χ3033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320-132−1+i3−1−i32−1+i3−1−i301−i321+i32−3+3i32−3−3i32-11−i321+i322−1+i3−1−i3000−1−i3−1+i3−1−i32−1+i32-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i321-1−1+i32−1−i321−i321+i32000000
χ314-444-4-44-444-4-4400444-4-4-4-40000000000000000000000000000000000000111-1-1-1
χ324-444-4-44-444-4-4-200-2-2-22222000000000000000000000000000000000000011-2-1-12
χ334-444-4-44-444-4-4-200-2-2-2222200000000000000000000000000000000000001-21-12-1
χ344-444-4-44-444-4-4-200-2-2-222220000000000000000000000000000000000000-2112-1-1
χ35666666666666-3-2-2-3-3-3-3-3-3-3-2-2-2-2-2-2-2111111111111000000000000000000000000
χ36666666-2-2-2-2-2-26-2-2-2-2-2-2-2-26-2-2-2-2222-2-2-2-2-2-2222222000000000000000000000000
χ37666666-2-2-2-2-2-2-36-2111111-366-2-2-2-2-2-3-3-3111111111000000000000000000000000
χ38666666-2-2-2-2-2-2-3-26111111-3-2-266-2-2-2111-3-3-3111111000000000000000000000000
χ39666666-2-2-2-2-2-2-3-2-2111111-3-2-2-2-2222111111−1−2i3−1+2i3−1+2i3−1−2i3−1−2i3−1+2i3000000000000000000000000
χ40666666-2-2-2-2-2-2-3-2-2111111-3-2-2-2-2222111111−1+2i3−1−2i3−1−2i3−1+2i3−1+2i3−1−2i3000000000000000000000000
χ4166−3−3i3−3+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−i3-2-21+i31+i31−i31−i3000000000000000000000000
χ4266−3−3i3−3+3i3−3−3i3−3+3i3-2-21+i31−i31+i31−i306-2-21+i31−i3-21+i31−i30−3−3i3−3+3i31+i31−i3-21+i31−i3000-21+i31−i31+i31−i3-21−i3-21+i3000000000000000000000000
χ4366−3−3i3−3+3i3−3−3i3−3+3i3-2-21+i31−i31+i31−i30-26-21+i31−i3-21+i31−i301+i31−i3−3−3i3−3+3i3-21+i31−i3-21+i31−i30001−i31+i31−i3-21+i3-2000000000000000000000000
χ4466−3−3i3−3+3i3−3−3i3−3+3i3-2-21+i31−i31+i31−i30-2-24−2−2i3−2+2i34−2−2i3−2+2i301+i31−i31+i31−i32−1−i3−1+i3-21+i31−i3-21+i31−i322−1−i3−1−i3−1+i3−1+i3000000000000000000000000
χ4566−3−3i3−3+3i3−3−3i3−3+3i3-2-21+i31−i31+i31−i30-2-2-21+i31−i3-21+i31−i301+i31−i31+i31−i32−1−i3−1+i34−2−2i3−2+2i3-21+i31−i3−1−i3−1+i32−1+i32−1−i3000000000000000000000000
χ4666−3−3i3−3+3i3−3−3i3−3+3i3-2-21+i31−i31+i31−i30-2-2-21+i31−i3-21+i31−i301+i31−i31+i31−i32−1−i3−1+i3-21+i31−i34−2−2i3−2+2i3−1+i3−1−i3−1+i32−1−i32000000000000000000000000
χ4766−3+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+i3-2-21−i31−i31+i31+i3000000000000000000000000
χ4866−3+3i3−3−3i3−3+3i3−3−3i3-2-21−i31+i31−i31+i306-2-21−i31+i3-21−i31+i30−3+3i3−3−3i31−i31+i3-21−i31+i3000-21−i31+i31−i31+i3-21+i3-21−i3000000000000000000000000
χ4966−3+3i3−3−3i3−3+3i3−3−3i3-2-21−i31+i31−i31+i30-26-21−i31+i3-21−i31+i301−i31+i3−3+3i3−3−3i3-21−i31+i3-21−i31+i30001+i31−i31+i3-21−i3-2000000000000000000000000
χ5066−3+3i3−3−3i3−3+3i3−3−3i3-2-21−i31+i31−i31+i30-2-24−2+2i3−2−2i34−2+2i3−2−2i301−i31+i31−i31+i32−1+i3−1−i3-21−i31+i3-21−i31+i322−1+i3−1+i3−1−i3−1−i3000000000000000000000000
χ5166−3+3i3−3−3i3−3+3i3−3−3i3-2-21−i31+i31−i31+i30-2-2-21−i31+i3-21−i31+i301−i31+i31−i31+i32−1+i3−1−i34−2+2i3−2−2i3-21−i31+i3−1+i3−1−i32−1−i32−1+i3000000000000000000000000
χ5266−3+3i3−3−3i3−3+3i3−3−3i3-2-21−i31+i31−i31+i30-2-2-21−i31+i3-21−i31+i301−i31+i31−i31+i32−1+i3−1−i3-21−i31+i34−2+2i3−2−2i3−1−i3−1+i3−1−i32−1+i32000000000000000000000000
χ536-666-6-6-22-2-222600-2-2-2222-600000000000000000002−2−2222−2−2−2−222000000000000
χ546-666-6-6-22-2-222600-2-2-2222-60000000000000000000−222−2−2−22222−2−2000000000000
χ556-6−3−3i3−3+3i33+3i33−3i36-6−3−3i3−3+3i33+3i33−3i30000000000000000000000000000022−2−2−ζ7+ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23000000000000
χ566-6−3−3i3−3+3i33+3i33−3i36-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000000−2−222ζ7−ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23000000000000
χ576-6−3−3i3−3+3i33+3i33−3i3-221+i31−i3−1−i3−1+i30004−2−2i3−2+2i3-42+2i32−2i3000000000000000000002−2−22−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23000000000000
χ586-6−3−3i3−3+3i33+3i33−3i3-221+i31−i3−1−i3−1+i30004−2−2i3−2+2i3-42+2i32−2i300000000000000000000−222−2ζ7−ζ13−ζ5+ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000000000000
χ596-6−3+3i3−3−3i33−3i33+3i36-6−3+3i3−3−3i33−3i33+3i30000000000000000000000000000022−2−2ζ5−ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13000000000000
χ606-6−3+3i3−3−3i33−3i33+3i36-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000000−2−222−ζ5+ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13000000000000
χ616-6−3+3i3−3−3i33−3i33+3i3-221−i31+i3−1+i3−1−i30004−2+2i3−2−2i3-42−2i32+2i3000000000000000000002−2−22ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000000000
χ626-6−3+3i3−3−3i33−3i33+3i3-221−i31+i3−1+i3−1−i30004−2+2i3−2−2i3-42−2i32+2i300000000000000000000−222−2−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000000000
χ6312-121212-12-12-44-4-444-600222-2-2-260000000000000000000000000000000000000000000
χ6412-12−6−6i3−6+6i36+6i36−6i3-442+2i32−2i3−2−2i3−2+2i3000-42+2i32−2i34−2−2i3−2+2i300000000000000000000000000000000000000000000
χ6512-12−6+6i3−6−6i36−6i36+6i3-442−2i32+2i3−2+2i3−2−2i3000-42−2i32+2i34−2+2i3−2−2i300000000000000000000000000000000000000000000

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