Finite Group Databasebeta

← Group #13164498

Character table — Group #13164498

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111122266666666661212121212122424242424242424242424243636363636363636363636361111112226666666666121212121212242424242424242424242424363636363636363636363636
order1233664121223466612121212666121212333666121212121212226666882424242422666641212264666121212126661212126666661212121212122266668824242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-111-1-11-1-111-1-1-1111111111-1-1-1-1-1-11-111-1-11-111-1-1111111-1-1-1-111-1-11-1-111-1-1-1111111111-1-1-1-1-1-11-111-1-11-111-1-1
χ4111111-1-1-1-111-1-11-1-111-1-1-1111111111-1-1-1-1-1-1-11-1-111-11-1-111111111-1-1-1-111-1-11-1-111-1-1-1111111111-1-1-1-1-1-1-11-1-111-11-1-111
χ52222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000002222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ62222222222-1222-1-1-122-1-1-1-1-1-12-1-12-1-122-1-1-1-10000000000002222222222-1222-1-1-122-1-1-1-1-1-12-1-12-1-122-1-1-1-1000000000000
χ72222222222-1222-1-1-122-1-1-1-1-1-1-12-1-12-1-1-122-1-10000000000002222222222-1222-1-1-122-1-1-1-1-1-1-12-1-12-1-1-122-1-1000000000000
χ82222222222-1222-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-1220000000000002222222222-1222-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-122000000000000
χ9222222-2-2-2-222-2-22-2-222-2-2-2222-1-1-1-1-1-1111111000000000000222222-2-2-2-222-2-22-2-222-2-2-2222-1-1-1-1-1-1111111000000000000
χ10222222-2-2-2-2-12-2-2-11122111-1-1-12-1-12-1-1-2-21111000000000000222222-2-2-2-2-12-2-2-11122111-1-1-12-1-12-1-1-2-21111000000000000
χ11222222-2-2-2-2-12-2-2-11122111-1-1-1-12-1-12-111-2-211000000000000222222-2-2-2-2-12-2-2-11122111-1-1-1-12-1-12-111-2-211000000000000
χ12222222-2-2-2-2-12-2-2-11122111-1-1-1-1-12-1-121111-2-2000000000000222222-2-2-2-2-12-2-2-11122111-1-1-1-1-12-1-121111-2-2000000000000
χ13333333333-13-1-1-1333-1-1-1-1-1-1-1-1000000000000111111-1-1-1-1-1-1333333333-13-1-1-1333-1-1-1-1-1-1-1-1000000000000111111-1-1-1-1-1-1
χ14333333333-13-1-1-1333-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1111111333333333-13-1-1-1333-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1111111
χ15333333-3-3-313-1113-3-3-1-1111-1-1-10000000000001-111-1-1-11-1-111333333-3-3-313-1113-3-3-1-1111-1-1-10000000000001-111-1-1-11-1-111
χ16333333-3-3-313-1113-3-3-1-1111-1-1-1000000000000-11-1-1111-111-1-1333333-3-3-313-1113-3-3-1-1111-1-1-1000000000000-11-1-1111-111-1-1
χ1733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i3200000000000000000011−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i3200000000000000000011−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ1833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i32000000000000000000-1-11+i321−i321+i321−i32-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32303−3−3i32−3+3i32000−3−3i32−3+3i32000000000000000000-1-11+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ1933−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i300000000000011−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i300000000000011−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ2033−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i3000000000000-1-11+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-10-11+i321−i320001+i321−i322−1−i3−1+i32−1−i3−1+i3000000000000-1-11+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ2133−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i30000000000001-1−1−i32−1+i321+i321−i32-111+i321−i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i30000000000001-1−1−i32−1+i321+i321−i32-111+i321−i32−1−i32−1+i32
χ2233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i3000000000000-111+i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i3210-1−1−i32−1+i320001+i321−i32-21+i31−i32−1−i3−1+i3000000000000-111+i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ2333−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i320000000000000000001-1−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i320000000000000000001-1−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i32
χ2433−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i32000000000000000000-111+i321−i32−1−i32−1+i32-111+i321−i32−1−i32−1+i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-3033+3i323−3i32000−3−3i32−3+3i32000000000000000000-111+i321−i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ2533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i3200000000000000000011−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i3200000000000000000011−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ2633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i32000000000000000000-1-11−i321+i321−i321+i32-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32303−3+3i32−3−3i32000−3+3i32−3−3i32000000000000000000-1-11−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ2733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i300000000000011−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i300000000000011−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ2833−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i3000000000000-1-11−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-10-11−i321+i320001−i321+i322−1+i3−1−i32−1+i3−1−i3000000000000-1-11−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ2933−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i30000000000001-1−1+i32−1−i321−i321+i32-111−i321+i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i30000000000001-1−1+i32−1−i321−i321+i32-111−i321+i32−1+i32−1−i32
χ3033−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i3000000000000-111−i321+i32−1+i32−1−i321-1−1+i32−1−i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i3210-1−1+i32−1−i320001−i321+i32-21−i31+i32−1+i3−1−i3000000000000-111−i321+i32−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ3133−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i320000000000000000001-1−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i320000000000000000001-1−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i32
χ3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i32000000000000000000-111−i321+i32−1+i32−1−i32-111−i321+i32−1+i32−1−i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-3033−3i323+3i32000−3+3i32−3−3i32000000000000000000-111−i321+i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ334-444-4-400004000-40000000000111-1-1-13−33−33−30000000000004-444-4-400004000-40000000000111-1-1-13−33−33−3000000000000
χ344-444-4-400004000-40000000000111-1-1-1−33−33−330000000000004-444-4-400004000-40000000000111-1-1-1−33−33−33000000000000
χ354-444-4-400004000-40000000000-2-2-22220000000000000000004-444-4-400004000-40000000000-2-2-2222000000000000000000
χ364-444-4-40000-2000223−230000000011-2-1-123−3−33000000000000004-444-4-40000-2000223−230000000011-2-1-123−3−3300000000000000
χ374-444-4-40000-2000223−23000000001-21-12-1−33003−30000000000004-444-4-40000-2000223−23000000001-21-12-1−33003−3000000000000
χ384-444-4-40000-2000223−2300000000-2112-1-1003−3−330000000000004-444-4-40000-2000223−2300000000-2112-1-1003−3−33000000000000
χ394-444-4-40000-20002−23230000000011-2-1-12−333−3000000000000004-444-4-40000-20002−23230000000011-2-1-12−333−300000000000000
χ404-444-4-40000-20002−2323000000001-21-12-13−300−330000000000004-444-4-40000-20002−2323000000001-21-12-13−300−33000000000000
χ414-444-4-40000-20002−232300000000-2112-1-100−333−30000000000004-444-4-40000-20002−232300000000-2112-1-100−333−3000000000000
χ42666666666-2-3-2-2-2-3-3-3-2-2111111000000000000000000000000666666666-2-3-2-2-2-3-3-3-2-2111111000000000000000000000000
χ43666666-6-6-62-3-222-333-2-2-1-1-1111000000000000000000000000666666-6-6-62-3-222-333-2-2-1-1-1111000000000000000000000000
χ4466−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-20-21+i31−i30001+i31−i3-21+i31−i3-21+i31−i300000000000000000000000066−3−3i3−3+3i3−3−3i3−3+3i36−3−3i3−3+3i3-20-21+i31−i30001+i31−i3-21+i31−i3-21+i31−i3000000000000000000000000
χ4566−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i320-2−1−i3−1+i30001+i31−i32−1−i3−1+i3-21+i31−i300000000000000000000000066−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i320-2−1−i3−1+i30001+i31−i32−1−i3−1+i3-21+i31−i3000000000000000000000000
χ4666−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-20-21−i31+i30001−i31+i3-21−i31+i3-21−i31+i300000000000000000000000066−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-20-21−i31+i30001−i31+i3-21−i31+i3-21−i31+i3000000000000000000000000
χ4766−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i320-2−1+i3−1−i30001−i31+i32−1+i3−1−i3-21−i31+i300000000000000000000000066−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i320-2−1+i3−1−i30001−i31+i32−1+i3−1−i3-21−i31+i3000000000000000000000000
χ4812-12−6−6i3−6+6i36+6i36−6i3000000000000000000000000000000000000000000012-12−6−6i3−6+6i36+6i36−6i30000000000000000000000000000000000000000000
χ4912-12−6+6i3−6−6i36−6i36+6i3000000000000000000000000000000000000000000012-12−6+6i3−6−6i36−6i36+6i30000000000000000000000000000000000000000000
χ501111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ52111111-1-1-1-111-1-11-1-111-1-1-1111111111-1-1-1-1-1-11-111-1-11-111-1-1-1-1-1-1-1-11111-1-111-111-1-1111-1-1-1-1-1-1-1-1-1111111-11-1-111-11-1-111
χ53111111-1-1-1-111-1-11-1-111-1-1-1111111111-1-1-1-1-1-1-11-1-111-11-1-111-1-1-1-1-1-11111-1-111-111-1-1111-1-1-1-1-1-1-1-1-11111111-111-1-11-111-1-1
χ542222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000
χ552222222222-1222-1-1-122-1-1-1-1-1-12-1-12-1-122-1-1-1-1000000000000-2-2-2-2-2-2-2-2-2-21-2-2-2111-2-2111111-211-211-2-21111000000000000
χ562222222222-1222-1-1-122-1-1-1-1-1-1-12-1-12-1-1-122-1-1000000000000-2-2-2-2-2-2-2-2-2-21-2-2-2111-2-21111111-211-2111-2-211000000000000
χ572222222222-1222-1-1-122-1-1-1-1-1-1-1-12-1-12-1-1-1-122000000000000-2-2-2-2-2-2-2-2-2-21-2-2-2111-2-211111111-211-21111-2-2000000000000
χ58222222-2-2-2-222-2-22-2-222-2-2-2222-1-1-1-1-1-1111111000000000000-2-2-2-2-2-22222-2-222-222-2-2222-2-2-2111111-1-1-1-1-1-1000000000000
χ59222222-2-2-2-2-12-2-2-11122111-1-1-12-1-12-1-1-2-21111000000000000-2-2-2-2-2-222221-2221-1-1-2-2-1-1-1111-211-21122-1-1-1-1000000000000
χ60222222-2-2-2-2-12-2-2-11122111-1-1-1-12-1-12-111-2-211000000000000-2-2-2-2-2-222221-2221-1-1-2-2-1-1-11111-211-21-1-122-1-1000000000000
χ61222222-2-2-2-2-12-2-2-11122111-1-1-1-1-12-1-121111-2-2000000000000-2-2-2-2-2-222221-2221-1-1-2-2-1-1-111111-211-2-1-1-1-122000000000000
χ62333333333-13-1-1-1333-1-1-1-1-1-1-1-1000000000000111111-1-1-1-1-1-1-3-3-3-3-3-3-3-3-31-3111-3-3-311111111000000000000-1-1-1-1-1-1111111
χ63333333333-13-1-1-1333-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1111111-3-3-3-3-3-3-3-3-31-3111-3-3-311111111000000000000111111-1-1-1-1-1-1
χ64333333-3-3-313-1113-3-3-1-1111-1-1-10000000000001-111-1-1-11-1-111-3-3-3-3-3-3333-1-31-1-1-33311-1-1-1111000000000000-11-1-1111-111-1-1
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χ894-444-4-40000-20002−2323000000001-21-12-13−300−33000000000000-44-4-44400002000-223−2300000000-12-11-21−33003−3000000000000
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χ9566−3+3i3−3−3i3−3+3i3−3−3i36−3+3i3−3−3i3-20-21−i31+i30001−i31+i3-21−i31+i3-21−i31+i3000000000000000000000000-6-63−3i33+3i33−3i33+3i3-63−3i33+3i3202−1+i3−1−i3000−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000
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χ9812-12−6+6i3−6−6i36−6i36+6i30000000000000000000000000000000000000000000-12126−6i36+6i3−6+6i3−6−6i30000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).