Finite Group Databasebeta

← Group #72252792

Character table — Group #72252792

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size111122222222444444444444444444444444444488888888888888888888888818183636363636363636363636363636363636363636363636363636363636363636363636363636363636363636162162162162
order1222336666663333333666666666666666666666333333666666666666666666444444121212121212121212121212121212121212121212121212121212121212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-111-1-111-1-11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11i−ii−i11-1-1ii−i−iii−i−i11-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-1
χ611-1-111-1-111-1-11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11i−i−ii11-1-1ii−i−i−i−iii11-1-1iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-111
χ711-1-111-1-111-1-11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11−iii−i11-1-1−i−iiiii−i−i11-1-1−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-111
χ811-1-111-1-111-1-11111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11−ii−ii11-1-1−i−iii−i−iii11-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii11-1-1
χ92222222222222222222222222222222222222222222222222222222222222222-2-20000-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ1022222-12-12-12-12222-1-1-12222-1-12222-1-1-1-1-12222-1-12-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12200222-12-10000-1-1-1-1-1-1-1-100000000000022-1-1-1-122-1-1-1-10000
χ1122222-12-12-12-12222-1-1-12222-1-12222-1-1-1-1-12222-1-12-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12200-2-22-12-100001111-1-1-1-1000000000000-2-21111-2-211110000
χ1222222-12-12-12-12222-1-1-12222-1-12222-1-1-1-1-12222-1-12-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-20000-21-210000−i3i3−i3i3111100000000000000−i3−i3i3i300−i3−i3i3i30000
χ1322222-12-12-12-12222-1-1-12222-1-12222-1-1-1-1-12222-1-12-1-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-20000-21-210000i3−i3i3−i3111100000000000000i3i3−i3−i300i3i3−i3−i30000
χ142222-12-12-12-1222-1-122-122-1-12222-1-122-1-1-122-1-122-12-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1222200-12-12-1-1-1-10000-1-1-1-122-1-1-1-122-1-1-1-10000000000000000
χ152222-12-12-12-1222-1-122-122-1-12222-1-122-1-1-122-1-122-12-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-200-12-1211110000-1-1-1-1-2-21111-2-211110000000000000000
χ162222-12-12-12-1222-1-122-122-1-12222-1-122-1-1-122-1-122-12-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200001-21-2−i3i3−i3i30000111100−i3−i3i3i300−i3−i3i3i30000000000000000
χ172222-12-12-12-1222-1-122-122-1-12222-1-122-1-1-122-1-122-12-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200001-21-2i3−i3i3−i30000111100i3i3−i3−i300i3i3−i3−i30000000000000000
χ1822-2-222-2-222-2-22222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22-20000-2-22200000000-2-2220000000000000000000000000000
χ1922-2-22-1-212-1-212222-1-1-12222-1-1-2-2-2-21111-1-2-2-2-2112-1-1-1-1-12-1-1-1-1-1-2-211111111112-20000-212-100003−3−3311-1-10000000000000033−3−300−3−3330000
χ2022-2-22-1-212-1-212222-1-1-12222-1-1-2-2-2-21111-1-2-2-2-2112-1-1-1-1-12-1-1-1-1-1-2-211111111112-20000-212-10000−333−311-1-100000000000000−3−3330033−3−30000
χ2122-2-22-1-212-1-212222-1-1-12222-1-1-2-2-2-21111-1-2-2-2-2112-1-1-1-1-12-1-1-1-1-1-2-21111111111-22002i−2i2-1-210000−i−iii-1-1110000000000002i2i−i−i−i−i−2i−2iiiii0000
χ2222-2-22-1-212-1-212222-1-1-12222-1-1-2-2-2-21111-1-2-2-2-2112-1-1-1-1-12-1-1-1-1-1-2-21111111111-2200−2i2i2-1-210000ii−i−i-1-111000000000000−2i−2iiiii2i2i−i−i−i−i0000
χ2322-2-2-121-2-121-222-1-122-122-1-122-2-211-2-211-1-2-211-2-2-12-1-1-1-1-12-1-1-1-111-2-2111111112-200001-2-123−3−33000011-1-10033−3−300−3−3330000000000000000
χ2422-2-2-121-2-121-222-1-122-122-1-122-2-211-2-211-1-2-211-2-2-12-1-1-1-1-12-1-1-1-111-2-2111111112-200001-2-12−333−3000011-1-100−3−3330033−3−30000000000000000
χ2522-2-2-121-2-121-222-1-122-122-1-122-2-211-2-211-1-2-211-2-2-12-1-1-1-1-12-1-1-1-111-2-211111111-222i−2i00-121-2−i−iii0000-1-1112i2i−i−i−i−i−2i−2iiiii0000000000000000
χ2622-2-2-121-2-121-222-1-122-122-1-122-2-211-2-211-1-2-211-2-2-12-1-1-1-1-12-1-1-1-111-2-211111111-22−2i2i00-121-2ii−i−i0000-1-111−2i−2iiiii2i2i−i−i−i−i0000000000000000
χ272-22-2222-2-2-2-222222222-2-2-2-2-2-22-222-2-22-2-22-2-2-222222222-2-2-2-2-2-22-22-22222-2-2-2-20000000000000000000000000000000000000000000000−i2i2−i2i2
χ282-22-2222-2-2-2-222222222-2-2-2-2-2-22-222-2-22-2-22-2-2-222222222-2-2-2-2-2-22-22-22222-2-2-2-20000000000000000000000000000000000000000000000i2−i2i2−i2
χ292-2-2222-22-2-22-22222222-2-2-2-2-2-2-22-2-222-22-2-2222-2-2222222-2-2-2-2-2-2-22-22-2-2-2-222220000000000000000000000000000000000000000000000−i2i2i2−i2
χ302-2-2222-22-2-22-22222222-2-2-2-2-2-2-22-2-222-22-2-2222-2-2222222-2-2-2-2-2-2-22-22-2-2-2-222220000000000000000000000000000000000000000000000i2−i2−i2i2
χ314444444444441-211-2-241-211-2-21-211-2-2444-2111-2-2-2111-2-2-2111-2-2-2-21111-2-211-2-20022000000222200000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ324444444444441-211-2-241-211-2-21-211-2-2444-2111-2-2-2111-2-2-2111-2-2-2-21111-2-211-2-200-2-2000000-2-2-2-2000000001111111111110000000000000000
χ33444444444444-21-2-2114-21-2-211-21-2-2114441-2-2-2111-2-2-2111-2-2-21111-2-2-2-211-2-2110000220000000022220000000000000000-1-1-1-1-1-1-1-1-1-1-1-10000
χ34444444444444-21-2-2114-21-2-211-21-2-2114441-2-2-2111-2-2-2111-2-2-21111-2-2-2-211-2-2110000-2-200000000-2-2-2-200000000000000001111111111110000
χ3544444-24-24-24-2-21-2-2−1−3i32−1+3i32-2-21-2-2−1−3i32−1+3i32-21-2-2−1−3i32−1+3i32-2-2-21-2-2-2−1−3i32−1+3i321111−1−3i32−1+3i321111−1−3i32−1+3i32111111−1−3i32−1+3i3211−1−3i32−1+3i3200002200000000−1−i3−1+i3−1−i3−1+i30000000000000000-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000
χ3644444-24-24-24-2-21-2-2−1−3i32−1+3i32-2-21-2-2−1−3i32−1+3i32-21-2-2−1−3i32−1+3i32-2-2-21-2-2-2−1−3i32−1+3i321111−1−3i32−1+3i321111−1−3i32−1+3i32111111−1−3i32−1+3i3211−1−3i32−1+3i320000-2-2000000001+i31−i31+i31−i3000000000000000011−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000
χ3744444-24-24-24-2-21-2-2−1+3i32−1−3i32-2-21-2-2−1+3i32−1−3i32-21-2-2−1+3i32−1−3i32-2-2-21-2-2-2−1+3i32−1−3i321111−1+3i32−1−3i321111−1+3i32−1−3i32111111−1+3i32−1−3i3211−1+3i32−1−3i3200002200000000−1+i3−1−i3−1+i3−1−i30000000000000000-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000
χ3844444-24-24-24-2-21-2-2−1+3i32−1−3i32-2-21-2-2−1+3i32−1−3i32-21-2-2−1+3i32−1−3i32-2-2-21-2-2-2−1+3i32−1−3i321111−1+3i32−1−3i321111−1+3i32−1−3i32111111−1+3i32−1−3i3211−1+3i32−1−3i320000-2-2000000001−i31+i31−i31+i3000000000000000011−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000
χ394444-24-24-24-241-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32-2-21-2−1−3i32−1+3i32-2-2-2-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1+3i321111−1−3i32−1+3i32111111−1−3i32−1+3i3211−1−3i32−1+3i32110022000000−1−i3−1+i3−1−i3−1+i300000000-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000000
χ404444-24-24-24-241-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32-2-21-2−1−3i32−1+3i32-2-2-2-2-2-21−1−3i32−1+3i32-2-211−1−3i32−1+3i321111−1−3i32−1+3i32111111−1−3i32−1+3i3211−1−3i32−1+3i321100-2-20000001+i31−i31+i31−i30000000011−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000000
χ414444-24-24-24-241-2−1+3i32−1−3i32-2-2-21-2−1+3i32−1−3i32-2-21-2−1+3i32−1−3i32-2-2-2-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1−3i321111−1+3i32−1−3i32111111−1+3i32−1−3i3211−1+3i32−1−3i32110022000000−1+i3−1−i3−1+i3−1−i300000000-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000000000
χ424444-24-24-24-241-2−1+3i32−1−3i32-2-2-21-2−1+3i32−1−3i32-2-21-2−1+3i32−1−3i32-2-2-2-2-2-21−1+3i32−1−3i32-2-211−1+3i32−1−3i321111−1+3i32−1−3i32111111−1+3i32−1−3i3211−1+3i32−1−3i321100-2-20000001−i31+i31−i31+i30000000011−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000000000
χ434444-2-2-2-2-2-2-2-244-2-2-2-2144-2-2-2-244-2-2-2-211144-2-2-2-2-2-21111-2-21111-2-2-2-211111111440000-2-2-2-20000000011110000000000000000000000000000
χ444444-2-2-2-2-2-2-2-244-2-2-2-2144-2-2-2-244-2-2-2-211144-2-2-2-2-2-21111-2-21111-2-2-2-211111111-4-40000222200000000-1-1-1-10000000000000000000000000000
χ4544-4-444-4-444-4-41-211-2-241-211-2-2-12-1-122-4-442-1-1-122-2111-2-2-2111-2-222-1-1-1-122-1-122002i−2i0000002i2i−2i−2i00000000−i−i−i−i−i−iiiiiii0000000000000000
χ4644-4-444-4-444-4-41-211-2-241-211-2-2-12-1-122-4-442-1-1-122-2111-2-2-2111-2-222-1-1-1-122-1-12200−2i2i000000−2i−2i2i2i00000000iiiiii−i−i−i−i−i−i0000000000000000
χ4744-4-444-4-444-4-4-21-2-2114-21-2-2112-122-1-1-4-44-1222-1-11-2-2-2111-2-2-211-1-12222-1-122-1-100002i−2i000000002i2i−2i−2i0000000000000000−i−i−i−i−i−iiiiiii0000
χ4844-4-444-4-444-4-4-21-2-2114-21-2-2112-122-1-1-4-44-1222-1-11-2-2-2111-2-2-211-1-12222-1-122-1-10000−2i2i00000000−2i−2i2i2i0000000000000000iiiiii−i−i−i−i−i−i0000
χ4944-4-44-2-424-2-42-21-2-2−1−3i32−1+3i32-2-21-2-2−1−3i32−1+3i322-1221+3i321−3i3222-2-12221+3i321−3i321111−1−3i32−1+3i321111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i32-1-11+3i321−3i3200002i−2i000000002ζ222ζ14−2ζ22−2ζ140000000000000000−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ140000
χ5044-4-44-2-424-2-42-21-2-2−1−3i32−1+3i32-2-21-2-2−1−3i32−1+3i322-1221+3i321−3i3222-2-12221+3i321−3i321111−1−3i32−1+3i321111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i32-1-11+3i321−3i320000−2i2i00000000−2ζ22−2ζ142ζ222ζ140000000000000000iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ140000
χ5144-4-44-2-424-2-42-21-2-2−1+3i32−1−3i32-2-21-2-2−1+3i32−1−3i322-1221−3i321+3i3222-2-12221−3i321+3i321111−1+3i32−1−3i321111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i32-1-11−3i321+3i3200002i−2i000000002ζ142ζ22−2ζ14−2ζ220000000000000000−i−i−ζ14−ζ14−ζ22−ζ22iiζ14ζ14ζ22ζ220000
χ5244-4-44-2-424-2-42-21-2-2−1+3i32−1−3i32-2-21-2-2−1+3i32−1−3i322-1221−3i321+3i3222-2-12221−3i321+3i321111−1+3i32−1−3i321111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i32-1-11−3i321+3i320000−2i2i00000000−2ζ14−2ζ222ζ142ζ220000000000000000iiζ14ζ14ζ22ζ22−i−i−ζ14−ζ14−ζ22−ζ220000
χ5344-4-4-242-4-242-41-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32-2-2-121+3i321−3i322222-22-11+3i321−3i322211−1−3i32−1+3i321111−1−3i32−1+3i3211-1-1-1-11+3i321−3i32-1-11+3i321−3i32-1-1002i−2i0000002ζ222ζ14−2ζ22−2ζ1400000000−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ140000000000000000
χ5444-4-4-242-4-242-41-2−1−3i32−1+3i32-2-2-21-2−1−3i32−1+3i32-2-2-121+3i321−3i322222-22-11+3i321−3i322211−1−3i32−1+3i321111−1−3i32−1+3i3211-1-1-1-11+3i321−3i32-1-11+3i321−3i32-1-100−2i2i000000−2ζ22−2ζ142ζ222ζ1400000000iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ140000000000000000
χ5544-4-4-242-4-242-41-2−1+3i32−1−3i32-2-2-21-2−1+3i32−1−3i32-2-2-121−3i321+3i322222-22-11−3i321+3i322211−1+3i32−1−3i321111−1+3i32−1−3i3211-1-1-1-11−3i321+3i32-1-11−3i321+3i32-1-1002i−2i0000002ζ142ζ22−2ζ14−2ζ2200000000−i−i−ζ14−ζ14−ζ22−ζ22iiζ14ζ14ζ22ζ220000000000000000
χ5644-4-4-242-4-242-41-2−1+3i32−1−3i32-2-2-21-2−1+3i32−1−3i32-2-2-121−3i321+3i322222-22-11−3i321+3i322211−1+3i32−1−3i321111−1+3i32−1−3i3211-1-1-1-11−3i321+3i32-1-11−3i321+3i32-1-100−2i2i000000−2ζ14−2ζ222ζ142ζ2200000000iiζ14ζ14ζ22ζ22−i−i−ζ14−ζ14−ζ22−ζ220000000000000000
χ5744-4-4-2-222-2-22244-2-2-2-2144-2-2-2-2-4-42222-1-11-4-42222-2-21111-2-211112222-1-1-1-1-1-1-1-14-4000022-2-200000000-1-1110000000000000000000000000000
χ5844-4-4-2-222-2-22244-2-2-2-2144-2-2-2-2-4-42222-1-11-4-42222-2-21111-2-211112222-1-1-1-1-1-1-1-1-440000-2-2220000000011-1-10000000000000000000000000000
χ594-44-4444-4-4-4-441-211-2-24-12-1-1221211224-4-4-2-1-1-1-2-2-2111-2-22-1-1-122-221-111-2-2-1-12200000000000000000000003−33−33−33−33−33−30000000000000000
χ604-44-4444-4-4-4-441-211-2-24-12-1-1221211224-4-4-2-1-1-1-2-2-2111-2-22-1-1-122-221-111-2-2-1-1220000000000000000000000−33−33−33−33−33−330000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.