Finite Group Databasebeta

← Group #13167516

Character table — Group #13167516

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444488888888888888888888181818181818181818181818181818181818181818181818181818181818181818181818727272727272727272727272
order12223446661212121233666666336666661212121212121212121212124444888888881212121212121212242424242424242424242424242424242244666612121212
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
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ1022222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000002222-2-2-2-20000000000000000000000000000
χ112222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ122222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ132222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000111111113333−3−3−3−33333−3−3−3−3000000000000
χ142222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000000011111111−3−3−3−33333−3−3−3−33333000000000000
χ152222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-200000000-1-1-1-111113333−3−3−3−3−3−3−3−33333000000000000
χ162222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-200000000-1-1-1-11111−3−3−3−333333333−3−3−3−3000000000000
χ172222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2222222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000
χ182222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-222-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ1922-2-222-22-2-222-2-222-2-2-222-222-2-2-2-22222-2-22222-2-2-2-20000−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2022-2-222-22-2-222-2-222-2-2-222-222-2-2-2-22222-2-22222-2-2-2-20000i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2122-2-22-222-2-2-2-22222-2-2-222-222-2-2-2-222-2-222-2-2-2-222220000−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2222-2-22-222-2-2-2-22222-2-2-222-222-2-2-2-222-2-222-2-2-2-222220000i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2322-2-2-12-2-111-1-11122-2-2-222-2-1-11111-1-122-2-2-1-1-1-111110000−i2−i2i2i2−i2−i2i2i233−3−333−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ2422-2-2-12-2-111-1-11122-2-2-222-2-1-11111-1-122-2-2-1-1-1-111110000−i2−i2i2i2−i2−i2i2i2−3−333−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ2522-2-2-12-2-111-1-11122-2-2-222-2-1-11111-1-122-2-2-1-1-1-111110000i2i2−i2−i2i2i2−i2−i233−3−333−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ2622-2-2-12-2-111-1-11122-2-2-222-2-1-11111-1-122-2-2-1-1-1-111110000i2i2−i2−i2i2i2−i2−i2−3−333−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2722-2-2-1-22-11111-1-122-2-2-222-2-1-11111-1-1-2-2221111-1-1-1-10000−i2−i2i2i2i2i2−i2−i233−3−3−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2822-2-2-1-22-11111-1-122-2-2-222-2-1-11111-1-1-2-2221111-1-1-1-10000−i2−i2i2i2i2i2−i2−i2−3−33333−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ2922-2-2-1-22-11111-1-122-2-2-222-2-1-11111-1-1-2-2221111-1-1-1-10000i2i2−i2−i2−i2−i2i2i233−3−3−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ3022-2-2-1-22-11111-1-122-2-2-222-2-1-11111-1-1-2-2221111-1-1-1-10000i2i2−i2−i2−i2−i2i2i2−3−33333−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ312-22-2200-22-200002222-2-2-2-22222-2-2-2-20000000000002-200−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ322-22-2200-22-200002222-2-2-2-22222-2-2-2-20000000000002-200i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ332-22-2200-22-200002222-2-2-2-22222-2-2-2-2000000000000-2200−i2i2−i2i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ342-22-2200-22-200002222-2-2-2-22222-2-2-2-2000000000000-2200i2−i2i2−i2−i2i2−i2i2-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ352-22-2-1001-113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−32-200−i2i2−i2i2−i2i2−i2i2-11-113−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ362-22-2-1001-113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−32-200i2−i2i2−i2i2−i2i2−i2-11-113−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ372-22-2-1001-113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−3-2200−i2i2−i2i2i2−i2i2−i21-11-1−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ382-22-2-1001-113−33−32222-2-2-2-2-1-1-1-11111000033−3−333−3−3-2200i2−i2i2−i2−i2i2−i2i21-11-1−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ392-22-2-1001-11−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−3332-200−i2i2−i2i2−i2i2−i2i2-11-11−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ402-22-2-1001-11−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−3332-200i2−i2i2−i2i2−i2i2−i2-11-11−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ412-22-2-1001-11−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−333-2200−i2i2−i2i2i2−i2i2−i21-11-13−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ422-22-2-1001-11−33−332222-2-2-2-2-1-1-1-111110000−3−333−3−333-2200i2−i2i2−i2−i2i2−i2i21-11-13−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ432-2-22200-2-22000022-2-22-2-2222-2-222-2-2000000000000002-200002-2-220000-222-2000000002-2-222-2-22000000000000
χ442-2-22200-2-22000022-2-22-2-2222-2-222-2-2000000000000002-20000-222-20000-222-200000000-222-2-222-2000000000000
χ452-2-22200-2-22000022-2-22-2-2222-2-222-2-200000000000000-222-2-22000000002-2-222-2-222-2-2200000000000000000000
χ462-2-22200-2-22000022-2-22-2-2222-2-222-2-200000000000000-22-222-2000000002-2-22-222-2-222-200000000000000000000
χ472-2-22-10011-13−3−3322-2-22-2-22-1-111-1-111000033−3−3−3−333002-200002-2-223−3−331-1-11−333−33−3−33-111-1-111-1000000000000
χ482-2-22-10011-13−3−3322-2-22-2-22-1-111-1-111000033−3−3−3−333002-20000-222-23−3−331-1-113−3−33−333−31-1-111-1-11000000000000
χ492-2-22-10011-13−3−3322-2-22-2-22-1-111-1-111000033−3−3−3−33300-222-2-220000−333−3-111-1-111-1-111-13−3−33−333−3000000000000
χ502-2-22-10011-13−3−3322-2-22-2-22-1-111-1-111000033−3−3−3−33300-22-222-20000−333−3-111-11-1-111-1-11−333−33−3−33000000000000
χ512-2-22-10011-1−333−322-2-22-2-22-1-111-1-1110000−3−33333−3−3002-200002-2-22−333−31-1-113−3−33−333−3-111-1-111-1000000000000
χ522-2-22-10011-1−333−322-2-22-2-22-1-111-1-1110000−3−33333−3−3002-20000-222-2−333−31-1-11−333−33−3−331-1-111-1-11000000000000
χ532-2-22-10011-1−333−322-2-22-2-22-1-111-1-1110000−3−33333−3−300-222-2-2200003−3−33-111-1-111-1-111-1−333−33−3−33000000000000
χ542-2-22-10011-1−333−322-2-22-2-22-1-111-1-1110000−3−33333−3−300-22-222-200003−3−33-111-11-1-111-1-113−3−33−333−3000000000000
χ55444444444444441-21-2-21-211-21-21-21-21-21-21-21-21-21-200000000000000000000000000000000000000220000-1-1-1-1
χ56444444444444441-21-2-21-211-21-21-21-21-21-21-21-21-21-200000000000000000000000000000000000000-2-200001111
χ5744444444444444-21-211-21-2-21-21-21-21-21-21-21-21-21-210000000000000000000000000000000000002200-1-1-1-10000
χ5844444444444444-21-211-21-2-21-21-21-21-21-21-21-21-21-21000000000000000000000000000000000000-2-20011110000
χ5944444-4-4444-4-4-4-41-21-2-21-211-21-21-21-2-12-12-12-12-12-12000000000000000000000000000000000000002-20000-1-111
χ6044444-4-4444-4-4-4-41-21-2-21-211-21-21-21-2-12-12-12-12-12-1200000000000000000000000000000000000000-22000011-1-1
χ6144444-4-4444-4-4-4-4-21-211-21-2-21-21-21-212-12-12-12-12-12-10000000000000000000000000000000000002-200-1-1110000
χ6244444-4-4444-4-4-4-4-21-211-21-2-21-21-21-212-12-12-12-12-12-1000000000000000000000000000000000000-220011-1-10000
χ6344-4-444-44-4-444-4-41-2-1221-2-11-2-12-121-21-2-121-21-2-12-12000000000000000000000000000000000000000000003−33−3
χ6444-4-444-44-4-444-4-41-2-1221-2-11-2-12-121-21-2-121-21-2-12-1200000000000000000000000000000000000000000000−33−33
χ6544-4-444-44-4-444-4-4-212-1-1-212-212-12-1-21-212-1-21-212-12-10000000000000000000000000000000000000000−i3i3−i3i30000
χ6644-4-444-44-4-444-4-4-212-1-1-212-212-12-1-21-212-1-21-212-12-10000000000000000000000000000000000000000i3−i3i3−i30000
χ6744-4-44-444-4-4-4-4441-2-1221-2-11-2-12-121-2-121-2-12-121-21-2000000000000000000000000000000000000000000003−3−33
χ6844-4-44-444-4-4-4-4441-2-1221-2-11-2-12-121-2-121-2-12-121-21-200000000000000000000000000000000000000000000−333−3
χ6944-4-44-444-4-4-4-444-212-1-1-212-212-12-1-212-1-212-12-1-21-210000000000000000000000000000000000000000−i3i3i3−i30000
χ7044-4-44-444-4-4-4-444-212-1-1-212-212-12-1-212-1-212-12-1-21-210000000000000000000000000000000000000000i3−i3−i3i30000
χ718888-488-4-4-4-4-4-4-42-42-4-42-42-12-12-12-122-42-4-12-12-12-12000000000000000000000000000000000000000000000000
χ728888-488-4-4-4-4-4-4-4-42-422-42-42-12-12-12-1-42-422-12-12-12-1000000000000000000000000000000000000000000000000
χ738888-4-8-8-4-4-444442-42-4-42-42-12-12-12-12-24-241-21-21-21-2000000000000000000000000000000000000000000000000
χ748888-4-8-8-4-4-44444-42-422-42-42-12-12-12-14-24-2-21-21-21-21000000000000000000000000000000000000000000000000
χ7588-8-8-48-8-444-4-4442-4-2442-4-2-121-21-2-122-4-24-12-121-21-2000000000000000000000000000000000000000000000000
χ7688-8-8-48-8-444-4-444-424-2-2-4242-1-21-212-1-424-22-12-1-21-21000000000000000000000000000000000000000000000000
χ7788-8-8-4-88-44444-4-42-4-2442-4-2-121-21-2-12-242-41-21-2-12-12000000000000000000000000000000000000000000000000
χ7888-8-8-4-88-44444-4-4-424-2-2-4242-1-21-212-14-2-42-21-212-12-1000000000000000000000000000000000000000000000000
χ798-88-8800-88-800002-42-44-24-22-42-4-24-24000000000000000000000000000000000000000000000000000000000000
χ808-88-8800-88-80000-42-42-24-24-42-424-24-2000000000000000000000000000000000000000000000000000000000000
χ818-88-8-4004-4443−4343−432-42-44-24-2-12-121-21-200003−23−3233−23−323000000000000000000000000000000000000000000000000
χ828-88-8-4004-4443−4343−43-42-42-24-242-12-1-21-210000−23323−3−23323−3000000000000000000000000000000000000000000000000
χ838-88-8-4004-44−4343−43432-42-44-24-2-12-121-21-20000−3233−23−3233−23000000000000000000000000000000000000000000000000
χ848-88-8-4004-44−4343−4343-42-42-24-242-12-1-21-21000023−3−23323−3−233000000000000000000000000000000000000000000000000
χ858-8-88800-8-8800002-4-24-4-2422-4-242-4-24000000000000000000000000000000000000000000000000000000000000
χ868-8-88800-8-880000-424-224-2-4-424-2-424-2000000000000000000000000000000000000000000000000000000000000
χ878-8-88-40044-443−43−43432-4-24-4-242-121-2-121-200003−23−323−3233−23000000000000000000000000000000000000000000000000
χ888-8-88-40044-443−43−4343-424-224-2-42-1-212-1-210000−23323−323−3−233000000000000000000000000000000000000000000000000
χ898-8-88-40044-4−434343−432-4-24-4-242-121-2-121-20000−3233−233−23−323000000000000000000000000000000000000000000000000
χ908-8-88-40044-4−434343−43-424-224-2-42-1-212-1-21000023−3−233−23323−3000000000000000000000000000000000000000000000000

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