Finite Group Databasebeta

← Group #13167599

Character table — Group #13167599

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444488888888888888888888181818181818181818181818181818181818181818181818181818181818181818181818727272727272727272727272
order122222366666663366666633666666666666666666444488888888121212121212121224242424242424242424242424242424244466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ11222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ12222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000111111113333−3−3−3−33333−3−3−3−3000000000000
χ13222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000011111111−3−3−3−33333−3−3−3−33333000000000000
χ142222-2-2222-2-2-2-222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-222-200000000-2-22222-2-20000000000000000000000000000
χ152222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-222222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000
χ162222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-22-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1000000000000
χ172222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-222-20000000011-1-1-1-1113333−3−3−3−3−3−3−3−33333000000000000
χ182222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-222-20000000011-1-1-1-111−3−3−3−333333333−3−3−3−3000000000000
χ1922-2-20022-20000-222-22-22-2-222000022-2-2-2-20000000002i−2i022−2−2−i2−i2i2i2002i2i−2i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ2022-2-20022-20000-222-22-22-2-222000022-2-2-2-20000000002i−2i0−2−222i2i2−i2−i2002i2i−2i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ2122-2-20022-20000-222-22-22-2-222000022-2-2-2-2000000000−2i2i022−2−2i2i2−i2−i200−2i−2i2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ2222-2-20022-20000-222-22-22-2-222000022-2-2-2-2000000000−2i2i0−2−222−i2−i2i2i200−2i−2i2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ2322-2-200-1-11−i3−i3i3i3122-22-22-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i302i−2i022−2−2−i2−i2i2i23−3−i−iii3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ2422-2-200-1-11−i3−i3i3i3122-22-22-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i302i−2i0−2−222i2i2−i2−i23−3−i−iii3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ2522-2-200-1-11−i3−i3i3i3122-22-22-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i30−2i2i022−2−2i2i2−i2−i2−33ii−i−i−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2622-2-200-1-11−i3−i3i3i3122-22-22-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i30−2i2i0−2−222−i2−i2i2i2−33ii−i−i−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ2722-2-200-1-11i3i3−i3−i3122-22-22-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i302i−2i022−2−2−i2−i2i2i2−33−i−iii−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ2822-2-200-1-11i3i3−i3−i3122-22-22-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i302i−2i0−2−222i2i2−i2−i2−33−i−iii−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2922-2-200-1-11i3i3−i3−i3122-22-22-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i30−2i2i022−2−2i2i2−i2−i23−3ii−i−i3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ3022-2-200-1-11i3i3−i3−i3122-22-22-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i30−2i2i0−2−222−i2−i2i2i23−3ii−i−i3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ312-22-22-22-222-22-2-2222-2-2-2-22222-22-2-2-222-2-222-2-222-2-20000−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ322-22-22-22-222-22-2-2222-2-2-2-22222-22-2-2-222-2-222-2-222-2-20000i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ332-22-22-2-11-1-11-111222-2-2-2-22-1-12-22-211-1-111-1-111-1-1110000−i2i2−i2i2−i2i2−i2i23−33−33−3−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ342-22-22-2-11-1-11-111222-2-2-2-22-1-12-22-211-1-111-1-111-1-1110000−i2i2−i2i2−i2i2−i2i2−33−33−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ352-22-22-2-11-1-11-111222-2-2-2-22-1-12-22-211-1-111-1-111-1-1110000i2−i2i2−i2i2−i2i2−i23−33−33−3−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ362-22-22-2-11-1-11-111222-2-2-2-22-1-12-22-211-1-111-1-111-1-1110000i2−i2i2−i2i2−i2i2−i2−33−33−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ372-22-2-222-22-22-22-2222-2-2-2-2222-22-22-2-222-2-2-2-222-2-2220000−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-22-2-222-22-22-22-2222-2-2-2-2222-22-22-2-222-2-2-2-222-2-2220000i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-22-2-22-11-11-11-11222-2-2-2-22-1-1-22-2211-1-11111-1-111-1-10000−i2i2−i2i2i2−i2i2−i23−3−33−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ402-22-2-22-11-11-11-11222-2-2-2-22-1-1-22-2211-1-11111-1-111-1-10000−i2i2−i2i2i2−i2i2−i2−333−33−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ412-22-2-22-11-11-11-11222-2-2-2-22-1-1-22-2211-1-11111-1-111-1-10000i2−i2i2−i2−i2i2−i2i23−3−33−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ422-22-2-22-11-11-11-11222-2-2-2-22-1-1-22-2211-1-11111-1-111-1-10000i2−i2i2−i2−i2i2−i2i2−333−33−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ432-2-22002-2-20000222-2-22-22-2220000-2-2-2-22200000000200-22i−2i−2i2i0000220000-2-22i−2i−2i2i2i−2i−2i2i00000000000000000000
χ442-2-22002-2-20000222-2-22-22-2220000-2-2-2-22200000000200-2−2i2i2i−2i0000220000-2-2−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ452-2-22002-2-20000222-2-22-22-2220000-2-2-2-22200000000-200200002-2-22-2-2000022000000002-2-222-2-22000000000000
χ462-2-22002-2-20000222-2-22-22-2220000-2-2-2-22200000000-20020000-222-2-2-200002200000000-222-2-222-2000000000000
χ472-2-2200-111−i3i3i3−i3-122-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3200-22i−2i−2i2i0000-1-1−i3i3i3−i311−iii−i−iii−i−333−33−3−33000000000000
χ482-2-2200-111−i3i3i3−i3-122-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3200-2−2i2i2i−2i0000-1-1−i3i3i3−i311i−i−iii−i−ii3−3−33−333−3000000000000
χ492-2-2200-111−i3i3i3−i3-122-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3-200200002-2-2211i3−i3−i3i3-1-1i3−i3−i3i3−i3i3i3−i3-111-1-111-1000000000000
χ502-2-2200-111−i3i3i3−i3-122-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3-20020000-222-211i3−i3−i3i3-1-1−i3i3i3−i3i3−i3−i3i31-1-111-1-11000000000000
χ512-2-2200-111i3−i3−i3i3-122-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3200-22i−2i−2i2i0000-1-1i3−i3−i3i311−iii−i−iii−i3−3−33−333−3000000000000
χ522-2-2200-111i3−i3−i3i3-122-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3200-2−2i2i2i−2i0000-1-1i3−i3−i3i311i−i−iii−i−ii−333−33−3−33000000000000
χ532-2-2200-111i3−i3−i3i3-122-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3-200200002-2-2211−i3i3i3−i3-1-1−i3i3i3−i3i3−i3−i3i3-111-1-111-1000000000000
χ542-2-2200-111i3−i3−i3i3-122-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3-20020000-222-211−i3i3i3−i3-1-1i3−i3−i3i3−i3i3i3−i31-1-111-1-11000000000000
χ55444444444444441-21-2-211-21-211-2-21-21-21-21-21-21-21-200000000000000000000000000000000000000220000-1-1-1-1
χ56444444444444441-21-2-211-21-211-2-21-21-21-21-21-21-21-200000000000000000000000000000000000000-2-200001111
χ5744444444444444-21-211-2-21-21-2-211-21-21-21-21-21-21-210000000000000000000000000000000000002200-1-1-1-10000
χ5844444444444444-21-211-2-21-21-2-211-21-21-21-21-21-21-21000000000000000000000000000000000000-2-20011110000
χ594444-4-4444-4-4-4-441-21-2-211-21-2-1-1221-21-21-2-12-12-12-12000000000000000000000000000000000000002-20000-1-111
χ604444-4-4444-4-4-4-441-21-2-211-21-2-1-1221-21-21-2-12-12-12-1200000000000000000000000000000000000000-22000011-1-1
χ614444-4-4444-4-4-4-44-21-211-2-21-2122-1-1-21-21-212-12-12-12-10000000000000000000000000000000000002-200-1-1110000
χ624444-4-4444-4-4-4-44-21-211-2-21-2122-1-1-21-21-212-12-12-12-1000000000000000000000000000000000000-220011-1-10000
χ634-44-44-44-444-44-4-41-2122-1-1-21-21-1-22-121-2-121-2-121-2-12000000000000000000000000000000000000000000003−33−3
χ644-44-44-44-444-44-4-41-2122-1-1-21-21-1-22-121-2-121-2-121-2-1200000000000000000000000000000000000000000000−33−33
χ654-44-44-44-444-44-4-4-21-2-1-1221-21-221-12-1-212-1-212-1-212-10000000000000000000000000000000000000000−i3i3−i3i30000
χ664-44-44-44-444-44-4-4-21-2-1-1221-21-221-12-1-212-1-212-1-212-10000000000000000000000000000000000000000i3−i3i3−i30000
χ674-44-4-444-44-44-44-41-2122-1-1-21-2-112-2-121-2-12-121-2-121-2000000000000000000000000000000000000000000003−3−33
χ684-44-4-444-44-44-44-41-2122-1-1-21-2-112-2-121-2-12-121-2-121-200000000000000000000000000000000000000000000−333−3
χ694-44-4-444-44-44-44-4-21-2-1-1221-212-2-112-1-212-12-1-212-1-210000000000000000000000000000000000000000−i3i3i3−i30000
χ704-44-4-444-44-44-44-4-21-2-1-1221-212-2-112-1-212-12-1-212-1-210000000000000000000000000000000000000000i3−i3−i3i30000
χ71888888-4-4-4-4-4-4-4-42-42-4-422-4-1222-4-4-12-12-12-12-12-12-12000000000000000000000000000000000000000000000000
χ72888888-4-4-4-4-4-4-4-4-42-422-4-422-1-4-4222-12-12-12-12-12-12-1000000000000000000000000000000000000000000000000
χ738888-8-8-4-4-44444-42-42-4-422-4-12-2-244-12-12-121-21-21-21-2000000000000000000000000000000000000000000000000
χ748888-8-8-4-4-44444-4-42-422-4-422-144-2-22-12-12-1-21-21-21-21000000000000000000000000000000000000000000000000
χ7588-8-80088-80000-82-4-2-442-242-400002-4-24-2400000000000000000000000000000000000000000000000000000000
χ7688-8-80088-80000-8-4242-2-44-2-420000-424-24-200000000000000000000000000000000000000000000000000000000
χ7788-8-800-4-44−4i3−4i34i34i342-4-2-442-24-120000-121-21-2−i32i3−i32i3i3−2i3i3−2i3000000000000000000000000000000000000000000000000
χ7888-8-800-4-44−4i3−4i34i34i34-4242-2-44-22-100002-1-21-212i3−i32i3−i3−2i3i3−2i3i3000000000000000000000000000000000000000000000000
χ7988-8-800-4-444i34i3−4i3−4i342-4-2-442-24-120000-121-21-2i3−2i3i3−2i3−i32i3−i32i3000000000000000000000000000000000000000000000000
χ8088-8-800-4-444i34i3−4i3−4i34-4242-2-44-22-100002-1-21-21−2i3i3−2i3i32i3−i32i3−i3000000000000000000000000000000000000000000000000
χ818-88-88-8-44-4-44-4442-4244-2-2-4-122-2-441-2-121-2-121-2-121-2000000000000000000000000000000000000000000000000
χ828-88-88-8-44-4-44-444-42-4-2-24422-1-442-2-212-1-212-1-212-1-21000000000000000000000000000000000000000000000000
χ838-88-8-88-44-44-44-442-4244-2-2-4-12-224-41-2-121-21-2-121-2-12000000000000000000000000000000000000000000000000
χ848-88-8-88-44-44-44-44-42-4-2-24422-14-4-22-212-1-21-212-1-212-1000000000000000000000000000000000000000000000000
χ858-8-88008-8-8000082-4-24-4-2242-40000-24-242-400000000000000000000000000000000000000000000000000000000
χ868-8-88008-8-800008-424-224-4-2-4200004-24-2-4200000000000000000000000000000000000000000000000000000000
χ878-8-8800-444−4i34i34i3−4i3-42-4-24-4-224-1200001-21-2-12−i32i3i3−2i3i3−2i3−i32i3000000000000000000000000000000000000000000000000
χ888-8-8800-444−4i34i34i3−4i3-4-424-224-4-22-10000-21-212-12i3−i3−2i3i3−2i3i32i3−i3000000000000000000000000000000000000000000000000
χ898-8-8800-4444i3−4i3−4i34i3-42-4-24-4-224-1200001-21-2-12i3−2i3−i32i3−i32i3i3−2i3000000000000000000000000000000000000000000000000
χ908-8-8800-4444i3−4i3−4i34i3-4-424-224-4-22-10000-21-212-1−2i3i32i3−i32i3−i3−2i3i3000000000000000000000000000000000000000000000000

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