Finite Group Databasebeta

← Group #11723662

Character table — Group #11723662

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222224444444444444444444444181818181818363636363636112222222224444444444444444444444181818181818363636363636
order1233346661212333336666612121212121212121212121288242424242466121222666466612126666666666121212121212121212121212882424242424661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-11-111-1-1111111111111111111111111111111111-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-11-1-111111111111111111111111111111111111-1-1-1-1-1-1-11-1-111
χ522222-2222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000022222-2222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000
χ62222-122-12222-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-100000020-1-1002222-122-12222-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-100000020-1-100
χ72222-122-12222-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1000000-2011002222-122-12222-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1000000-201100
χ82222-1-22-12-2-22-1-1-1-12-1-1-1-11-2-2-21111111100000000−i3i3002222-1-22-12-2-22-1-1-1-12-1-1-1-11-2-2-21111111100000000−i3i300
χ92222-1-22-12-2-22-1-1-1-12-1-1-1-11-2-2-21111111100000000i3−i3002222-1-22-12-2-22-1-1-1-12-1-1-1-11-2-2-21111111100000000i3−i300
χ10222-12222-122-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000000200-1-1222-12222-122-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000000200-1-1
χ11222-12222-122-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000000-20011222-12222-122-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000000-20011
χ12222-12-222-1-2-2-12-1-1-1-12-1-1-1-2111-2-21111110000000000−i3i3222-12-222-1-2-2-12-1-1-1-12-1-1-1-2111-2-21111110000000000−i3i3
χ13222-12-222-1-2-2-12-1-1-1-12-1-1-1-2111-2-21111110000000000i3−i3222-12-222-1-2-2-12-1-1-1-12-1-1-1-2111-2-21111110000000000i3−i3
χ1422-1222-122-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-100000022-1222-122-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1000000
χ1522-1222-122-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2111100000022-1222-122-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-21111000000
χ1622-122-2-12211-1-12-1-1-1-12-1-1-2-21111-2-211110033−3−300000022-122-2-12211-1-12-1-1-1-12-1-1-2-21111-2-211110033−3−3000000
χ1722-122-2-12211-1-12-1-1-1-12-1-1-2-21111-2-2111100−3−33300000022-122-2-12211-1-12-1-1-1-12-1-1-2-21111-2-2111100−3−333000000
χ182-22220-2-2-20022222-2-2-2-2-2000000000000−i2i2−i2i2−i2i20000002-22220-2-2-20022222-2-2-2-2-2000000000000−i2i2−i2i2−i2i2000000
χ192-22220-2-2-20022222-2-2-2-2-2000000000000i2−i2i2−i2i2−i20000002-22220-2-2-20022222-2-2-2-2-2000000000000i2−i2i2−i2i2−i2000000
χ202-2-12201-2-23−3-1-12-1-111-211003−33−30033−3−3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000002-2-12201-2-23−3-1-12-1-111-211003−33−30033−3−3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ212-2-12201-2-23−3-1-12-1-111-211003−33−30033−3−3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000002-2-12201-2-23−3-1-12-1-111-211003−33−30033−3−3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ222-2-12201-2-2−33-1-12-1-111-21100−33−3300−3−333−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000002-2-12201-2-2−33-1-12-1-111-21100−33−3300−3−333−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ232-2-12201-2-2−33-1-12-1-111-21100−33−3300−3−333i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000002-2-12201-2-2−33-1-12-1-111-21100−33−3300−3−333i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ24444-2-244-2-244-2-2111-2-2111-2-2-2-2-2-2111111000000000000444-2-244-2-244-2-2111-2-2111-2-2-2-2-2-2111111000000000000
χ25444-2-2-44-2-2-4-4-2-2111-2-2111222222-1-1-1-1-1-1000000000000444-2-2-44-2-2-4-4-2-2111-2-2111222222-1-1-1-1-1-1000000000000
χ2644-24-24-2-24-2-2-21-211-21-211-24-2-211-2-2111100000000000044-24-24-2-24-2-2-21-211-21-211-24-2-211-2-21111000000000000
χ2744-24-2-4-2-2422-21-211-21-2112-422-1-122-1-1-1-100000000000044-24-2-4-2-2422-21-211-21-2112-422-1-122-1-1-1-1000000000000
χ2844-2-244-24-2-2-21-2-2111-2-2114-211-2-2-2-2111100000000000044-2-244-24-2-2-21-2-2111-2-2114-211-2-2-2-21111000000000000
χ2944-2-24-4-24-2221-2-2111-2-211-42-1-12222-1-1-1-100000000000044-2-24-4-24-2221-2-2111-2-211-42-1-12222-1-1-1-1000000000000
χ3044-2-2-24-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i3200000000000044-2-2-24-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000
χ3144-2-2-24-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i3200000000000044-2-2-24-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000
χ3244-2-2-2-4-2-2-222111−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i3200000000000044-2-2-2-4-2-2-222111−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000
χ3344-2-2-2-4-2-2-222111−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i3200000000000044-2-2-2-4-2-2-222111−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000
χ344-444-20-42-4004-2-2-2-2-422220000000000000000000000004-444-20-42-4004-2-2-2-2-42222000000000000000000000000
χ354-44-240-4-4200-24-2-2-22-42220000000000000000000000004-44-240-4-4200-24-2-2-22-4222000000000000000000000000
χ364-44-2-20-42200-2-211122-1-1-10000003i−3i3i−3i−3i3i0000000000004-44-2-20-42200-2-211122-1-1-10000003i−3i3i−3i−3i3i000000000000
χ374-44-2-20-42200-2-211122-1-1-1000000−3i3i−3i3i3i−3i0000000000004-44-2-20-42200-2-211122-1-1-1000000−3i3i−3i3i3i−3i000000000000
χ384-4-24-2022-423−23-21-2112-12-1-10023−23−3300−3−3330000000000004-4-24-2022-423−23-21-2112-12-1-10023−23−3300−3−333000000000000
χ394-4-24-2022-4−2323-21-2112-12-1-100−23233−30033−3−30000000000004-4-24-2022-4−2323-21-2112-12-1-100−23233−30033−3−3000000000000
χ404-4-2-2402-4223−231-2-211-122-1-100−3323−2300−3−3330000000000004-4-2-2402-4223−231-2-211-122-1-100−3323−2300−3−333000000000000
χ414-4-2-2402-42−23231-2-211-122-1-1003−3−23230033−3−30000000000004-4-2-2402-42−23231-2-211-122-1-1003−3−23230033−3−3000000000000
χ424-4-2-2-2022223−23111−1−3i32−1+3i32-1-1-11+3i321−3i3200−33−333i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ220000000000004-4-2-2-2022223−23111−1−3i32−1+3i32-1-1-11+3i321−3i3200−33−333i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22000000000000
χ434-4-2-2-2022223−23111−1+3i32−1−3i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ220000000000004-4-2-2-2022223−23111−1+3i32−1−3i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22000000000000
χ444-4-2-2-20222−2323111−1−3i32−1+3i32-1-1-11+3i321−3i32003−33−3−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ220000000000004-4-2-2-20222−2323111−1−3i32−1+3i32-1-1-11+3i321−3i32003−33−3−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22000000000000
χ454-4-2-2-20222−2323111−1+3i32−1−3i32-1-1-11−3i321+3i32003−33−33i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ220000000000004-4-2-2-20222−2323111−1+3i32−1−3i32-1-1-11−3i321+3i32003−33−33i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22000000000000
χ46111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ47111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ48111111111111111111111111111111111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-111
χ49111111111111111111111111111111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1
χ5022222-2222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-2-2-2-2-22-2-2-222-2-2-2-2-2-2-2-2-2-2222222222222000000000000
χ512222-122-12222-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-100000020-1-100-2-2-2-21-2-21-2-2-2-21111-211111-2-2-211111111000000-201100
χ522222-122-12222-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1000000-201100-2-2-2-21-2-21-2-2-2-21111-211111-2-2-21111111100000020-1-100
χ532222-1-22-12-2-22-1-1-1-12-1-1-1-11-2-2-21111111100000000−i3i300-2-2-2-212-21-222-21111-21111-1222-1-1-1-1-1-1-1-100000000i3−i300
χ542222-1-22-12-2-22-1-1-1-12-1-1-1-11-2-2-21111111100000000i3−i300-2-2-2-212-21-222-21111-21111-1222-1-1-1-1-1-1-1-100000000−i3i300
χ55222-12222-122-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000000200-1-1-2-2-21-2-2-2-21-2-21-21111-2111-2111-2-21111110000000-20011
χ56222-12222-122-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000000-20011-2-2-21-2-2-2-21-2-21-21111-2111-2111-2-21111110000000200-1-1
χ57222-12-222-1-2-2-12-1-1-1-12-1-1-1-2111-2-21111110000000000−i3i3-2-2-21-22-2-21221-21111-21112-1-1-122-1-1-1-1-1-10000000000i3−i3
χ58222-12-222-1-2-2-12-1-1-1-12-1-1-1-2111-2-21111110000000000i3−i3-2-2-21-22-2-21221-21111-21112-1-1-122-1-1-1-1-1-10000000000−i3i3
χ5922-1222-122-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1000000-2-21-2-2-21-2-21111-21111-211-2-21111-2-21111-2-21111000000
χ6022-1222-122-1-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-21111000000-2-21-2-2-21-2-21111-21111-211-2-21111-2-2111122-1-1-1-1000000
χ6122-122-2-12211-1-12-1-1-1-12-1-1-2-21111-2-211110033−3−3000000-2-21-2-221-2-2-1-111-21111-21122-1-1-1-122-1-1-1-100−3−333000000
χ6222-122-2-12211-1-12-1-1-1-12-1-1-2-21111-2-2111100−3−333000000-2-21-2-221-2-2-1-111-21111-21122-1-1-1-122-1-1-1-10033−3−3000000
χ632-22220-2-2-20022222-2-2-2-2-2000000000000−i2i2−i2i2−i2i2000000-22-2-2-2022200-2-2-2-2-222222000000000000i2−i2i2−i2i2−i2000000
χ642-22220-2-2-20022222-2-2-2-2-2000000000000i2−i2i2−i2i2−i2000000-22-2-2-2022200-2-2-2-2-222222000000000000−i2i2−i2i2−i2i2000000
χ652-2-12201-2-23−3-1-12-1-111-211003−33−30033−3−3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000-221-2-20-122−3311-211-1-12-1-100−33−3300−3−333i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ662-2-12201-2-23−3-1-12-1-111-211003−33−30033−3−3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000-221-2-20-122−3311-211-1-12-1-100−33−3300−3−333−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ672-2-12201-2-2−33-1-12-1-111-21100−33−3300−3−333−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000-221-2-20-1223−311-211-1-12-1-1003−33−30033−3−3i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ682-2-12201-2-2−33-1-12-1-111-21100−33−3300−3−333i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000-221-2-20-1223−311-211-1-12-1-1003−33−30033−3−3−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ69444-2-244-2-244-2-2111-2-2111-2-2-2-2-2-2111111000000000000-4-4-422-4-422-4-422-1-1-122-1-1-1222222-1-1-1-1-1-1000000000000
χ70444-2-2-44-2-2-4-4-2-2111-2-2111222222-1-1-1-1-1-1000000000000-4-4-4224-4224422-1-1-122-1-1-1-2-2-2-2-2-2111111000000000000
χ7144-24-24-2-24-2-2-21-211-21-211-24-2-211-2-21111000000000000-4-42-42-422-4222-12-1-12-12-1-12-422-1-122-1-1-1-1000000000000
χ7244-24-2-4-2-2422-21-211-21-2112-422-1-122-1-1-1-1000000000000-4-42-42422-4-2-22-12-1-12-12-1-1-24-2-211-2-21111000000000000
χ7344-2-244-24-2-2-21-2-2111-2-2114-211-2-2-2-21111000000000000-4-422-4-42-4222-122-1-1-122-1-1-42-1-12222-1-1-1-1000000000000
χ7444-2-24-4-24-2221-2-2111-2-211-42-1-12222-1-1-1-1000000000000-4-422-442-42-2-2-122-1-1-122-1-14-211-2-2-2-21111000000000000
χ7544-2-2-24-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000-4-4222-422222-1-1-11+3i321−3i32-1-1-11+3i321−3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000
χ7644-2-2-24-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000-4-4222-422222-1-1-11−3i321+3i32-1-1-11−3i321+3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000
χ7744-2-2-2-4-2-2-222111−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000-4-42224222-2-2-1-1-11+3i321−3i32-1-1-11+3i321−3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000
χ7844-2-2-2-4-2-2-222111−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000-4-42224222-2-2-1-1-11−3i321+3i32-1-1-11−3i321+3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000
χ794-444-20-42-4004-2-2-2-2-42222000000000000000000000000-44-4-4204-2400-422224-2-2-2-2000000000000000000000000
χ804-44-240-4-4200-24-2-2-22-4222000000000000000000000000-44-42-4044-2002-4222-24-2-2-2000000000000000000000000
χ814-44-2-20-42200-2-211122-1-1-10000003i−3i3i−3i−3i3i000000000000-44-42204-2-20022-1-1-1-2-2111000000−3i3i−3i3i3i−3i000000000000
χ824-44-2-20-42200-2-211122-1-1-1000000−3i3i−3i3i3i−3i000000000000-44-42204-2-20022-1-1-1-2-21110000003i−3i3i−3i−3i3i000000000000
χ834-4-24-2022-423−23-21-2112-12-1-10023−23−3300−3−333000000000000-442-420-2-24−23232-12-1-1-21-21100−23233−30033−3−3000000000000
χ844-4-24-2022-4−2323-21-2112-12-1-100−23233−30033−3−3000000000000-442-420-2-2423−232-12-1-1-21-2110023−23−3300−3−333000000000000
χ854-4-2-2402-4223−231-2-211-122-1-100−3323−2300−3−333000000000000-4422-40-24-2−2323-122-1-11-2-211003−3−23230033−3−3000000000000
χ864-4-2-2402-42−23231-2-211-122-1-1003−3−23230033−3−3000000000000-4422-40-24-223−23-122-1-11-2-21100−3323−2300−3−333000000000000
χ874-4-2-2-2022223−23111−1−3i32−1+3i32-1-1-11+3i321−3i3200−33−333i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22000000000000-442220-2-2-2−2323-1-1-11+3i321−3i32111−1−3i32−1+3i32003−33−3−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22000000000000
χ884-4-2-2-2022223−23111−1+3i32−1−3i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22000000000000-442220-2-2-2−2323-1-1-11−3i321+3i32111−1+3i32−1−3i32003−33−33i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22000000000000
χ894-4-2-2-20222−2323111−1−3i32−1+3i32-1-1-11+3i321−3i32003−33−3−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22000000000000-442220-2-2-223−23-1-1-11+3i321−3i32111−1−3i32−1+3i3200−33−333i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22000000000000
χ904-4-2-2-20222−2323111−1+3i32−1−3i32-1-1-11−3i321+3i32003−33−33i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22000000000000-442220-2-2-223−23-1-1-11−3i321+3i32111−1+3i32−1−3i3200−33−33−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22000000000000

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