Finite Group Databasebeta

← Group #13166267

Character table — Group #13166267

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222222244448888888888888888888888999999121218181818181818181818181818181818181818181818181818181818181818181848484848108108108108108108
order123468812122424242433663366121212121212242424242424242424242424448888242444466888812121212121212121212242424242424242424242424661212248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111-1-1ii−i−i11-1ii−i−i-1-1-1-1i−iiiii−i−i−i−i-1-1-1-1-1-1iiii−i−i−i−i1111-1-1ii−i−i
χ6111111111111111111111111111111111111111-1-1ii−i−i-1-1-1ii−i−i-1-1-1-1i−iiiii−i−i−i−i-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-111−i−iii
χ7111111111111111111111111111111111111111-1-1−i−iii11-1−i−iii-1-1-1-1−ii−i−i−i−iiiii-1-1-1-1-1-1−i−i−i−iiiii1111-1-1−i−iii
χ8111111111111111111111111111111111111111-1-1−i−iii-1-1-1−i−iii-1-1-1-1−ii−i−i−i−iiiii-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-111ii−i−i
χ911111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-11-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-111-11-1
χ1011111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1111-1-11-11
χ1111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11
χ1211111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-1
χ1311111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1-1-1−i−iii-1-111i−i−i−i−i−iiiii-1-11111iiii−i−i−i−i11-1-11-1i−i−ii
χ1411111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-11-1−i−iii-1-111i−i−i−i−i−iiiii-1-11111iiii−i−i−i−i-1-111-11−iii−i
χ1511111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1-1-1ii−i−i-1-111−iiiiii−i−i−i−i-1-11111−i−i−i−iiiii11-1-11-1−iii−i
χ1611111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-11-1ii−i−i-1-111−iiiiii−i−i−i−i-1-11111−i−i−i−iiiii-1-111-11i−i−ii
χ17222-2200-2-2000022222222-2-2-2-2-2-200000000000022222200-20000-2-200-2-20000000022000022-2-222-2-20000000000
χ18222-2200-2-2000022222222-2-2-2-2-2-200000000000022-2-2-2-200-20000-2-2002200000000220000-2-222-2-2220000000000
χ19222-2200-2-2000022222222-2-2-2-2-2-2000000000000-2-22i2i−2i−2i00200002200−2i2i00000000-2-200002i2i−2i−2i−2i−2i2i2i0000000000
χ20222-2200-2-2000022222222-2-2-2-2-2-2000000000000-2-2−2i−2i2i2i002000022002i−2i00000000-2-20000−2i−2i2i2i2i2i−2i−2i0000000000
χ2122-12-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222220022222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ2222-12-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-2-2-2-2002-2-2-2-2-1-122-2-211111111-1-1-1-1-1-1111111110000000000
χ2322-12-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-22i2i−2i−2i00-22i2i−2i−2i11-2-22i−2i−i−i−i−iiiii111111−i−i−i−iiiii0000000000
χ2422-12-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2−2i−2i2i2i00-2−2i−2i2i2i11-2-2−2i2iiiii−i−i−i−i111111iiii−i−i−i−i0000000000
χ2522-12-1-2-2-1-111112222-1-1-1-122-1-1-1-1-2-2-2-211111111222222002-2-2-2-2-1-1-2-22211111111-1-11111-1-1-1-1-1-1-1-10000000000
χ2622-12-1-2-2-1-111112222-1-1-1-122-1-1-1-1-2-2-2-21111111122-2-2-2-20022222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111110000000000
χ2722-12-1-2-2-1-111112222-1-1-1-122-1-1-1-1-2-2-2-211111111-2-22i2i−2i−2i00-2−2i−2i2i2i11222i−2iiiii−i−i−i−i11-1-1-1-1−i−i−i−iiiii0000000000
χ2822-12-1-2-2-1-111112222-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2−2i−2i2i2i00-22i2i−2i−2i1122−2i2i−i−i−i−iiiii11-1-1-1-1iiii−i−i−i−i0000000000
χ2922-1-2-1001133−3−32222-1-1-1-1-2-2111100003333−3−3−3−322222200-200001100-2-233−3−333−3−3-1-133−3−3-1-111-1-1110000000000
χ3022-1-2-1001133−3−32222-1-1-1-1-2-2111100003333−3−3−3−322-2-2-2-200-20000110022−3−333−3−333-1-133−3−311-1-111-1-10000000000
χ3122-1-2-1001133−3−32222-1-1-1-1-2-2111100003333−3−3−3−3-2-22i2i−2i−2i0020000-1-100−2i2ii3i3−i3−i3−i3−i3i3i311−3−333−i−iiiii−i−i0000000000
χ3222-1-2-1001133−3−32222-1-1-1-1-2-2111100003333−3−3−3−3-2-2−2i−2i2i2i0020000-1-1002i−2i−i3−i3i3i3i3i3−i3−i311−3−333ii−i−i−i−iii0000000000
χ3322-1-2-10011−3−3332222-1-1-1-1-2-211110000−3−3−3−3333322222200-200001100-2-2−3−333−3−333-1-1−3−333-1-111-1-1110000000000
χ3422-1-2-10011−3−3332222-1-1-1-1-2-211110000−3−3−3−3333322-2-2-2-200-2000011002233−3−333−3−3-1-1−3−33311-1-111-1-10000000000
χ3522-1-2-10011−3−3332222-1-1-1-1-2-211110000−3−3−3−33333-2-22i2i−2i−2i0020000-1-100−2i2i−i3−i3i3i3i3i3−i3−i31133−3−3−i−iiiii−i−i0000000000
χ3622-1-2-10011−3−3332222-1-1-1-1-2-211110000−3−3−3−33333-2-2−2i−2i2i2i0020000-1-1002i−2ii3i3−i3−i3−i3−i3i3i31133−3−3ii−i−i−i−iii0000000000
χ372-220-2−i2i200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130001−i−1+i1+i−1−i002−2001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i2−22−22ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000
χ382-220-2−i2i200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−1+i1−i−1−i1+i002−200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i2−22−2−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000
χ392-220-2−i2i200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−1−i1+i−1+i1−i00−2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i−22−22−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000
χ402-220-2−i2i200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230001+i−1−i1−i−1+i00−22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i−22−222ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000
χ412-220-2i2−i200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−1+i1−i−1−i1+i00−2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i−22−222ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000
χ422-220-2i2−i200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130001−i−1+i1+i−1−i00−22001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i−22−22−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000
χ432-220-2i2−i200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230001+i−1−i1−i−1+i002−2001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i2−22−2−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000
χ442-220-2i2−i200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−1−i1+i−1+i1−i002−200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i2−22−22ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000
χ452-2-101−i2i23−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2322-2-2-1-1110033−3−3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130001−i−1+i1+i−1−i−i3i32−200−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000
χ462-2-101−i2i23−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2322-2-2-1-1110033−3−3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−1+i1−i−1−i1+i−i3i32−200ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000
χ472-2-101−i2i23−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2322-2-2-1-1110033−3−3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−1−i1+i−1+i1−ii3−i3−2200ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000
χ482-2-101−i2i23−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2322-2-2-1-1110033−3−3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230001+i−1−i1−i−1+ii3−i3−2200−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000
χ492-2-101−i2i2−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ722-2-2-1-11100−3−333−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130001−i−1+i1+i−1−ii3−i32−200−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ502-2-101−i2i2−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ722-2-2-1-11100−3−333−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−1+i1−i−1−i1+ii3−i32−200ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ512-2-101−i2i2−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ722-2-2-1-11100−3−333−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−1−i1+i−1+i1−i−i3i3−2200ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22i−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ522-2-101−i2i2−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ722-2-2-1-11100−3−333−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230001+i−1−i1−i−1+i−i3i3−2200−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22i−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ532-2-101i2−i23−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2322-2-2-1-1110033−3−3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−1+i1−i−1−i1+i−i3i3−2200ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000
χ542-2-101i2−i23−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2322-2-2-1-1110033−3−3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130001−i−1+i1+i−1−i−i3i3−2200−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000
χ552-2-101i2−i23−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2322-2-2-1-1110033−3−3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230001+i−1−i1−i−1+ii3−i32−200−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14i−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.