Finite Group Databasebeta

← Group #13167399

Character table — Group #13167399

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
χ1922-2-2200-22-20000222-22-2-2-22222-2-2-2-2000000000000002-200002i2i−2i−2i000022-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2022-2-2200-22-20000222-22-2-2-22222-2-2-2-2000000000000002-20000−2i−2i2i2i000022-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2122-2-2200-22-20000222-22-2-2-22222-2-2-2-200000000000000-222i2i−2i−2i00000000-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2222-2-2200-22-20000222-22-2-2-22222-2-2-2-200000000000000-22−2i−2i2i2i00000000-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322-2-2-1001-1133−3−3222-22-2-2-2-1-1-1-1111100003333−3−3−3−3002-200002i2i−2i−2i33−3−3-1-111−i3−i3i3i3i3i3−i3−i3−i−iii−i−iii000000000000
χ2422-2-2-1001-1133−3−3222-22-2-2-2-1-1-1-1111100003333−3−3−3−3002-20000−2i−2i2i2i33−3−3-1-111i3i3−i3−i3−i3−i3i3i3ii−i−iii−i−i000000000000
χ2522-2-2-1001-1133−3−3222-22-2-2-2-1-1-1-1111100003333−3−3−3−300-222i2i−2i−2i0000−3−33311-1-1−i−iii−i−iiii3i3−i3−i3−i3−i3i3i3000000000000
χ2622-2-2-1001-1133−3−3222-22-2-2-2-1-1-1-1111100003333−3−3−3−300-22−2i−2i2i2i0000−3−33311-1-1ii−i−iii−i−i−i3−i3i3i3i3i3−i3−i3000000000000
χ2722-2-2-1001-11−3−333222-22-2-2-2-1-1-1-111110000−3−3−3−33333002-200002i2i−2i−2i−3−333-1-111i3i3−i3−i3−i3−i3i3i3−i−iii−i−iii000000000000
χ2822-2-2-1001-11−3−333222-22-2-2-2-1-1-1-111110000−3−3−3−33333002-20000−2i−2i2i2i−3−333-1-111−i3−i3i3i3i3i3−i3−i3ii−i−iii−i−i000000000000
χ2922-2-2-1001-11−3−333222-22-2-2-2-1-1-1-111110000−3−3−3−3333300-222i2i−2i−2i000033−3−311-1-1−i−iii−i−iii−i3−i3i3i3i3i3−i3−i3000000000000
χ3022-2-2-1001-11−3−333222-22-2-2-2-1-1-1-111110000−3−3−3−3333300-22−2i−2i2i2i000033−3−311-1-1ii−i−iii−i−ii3i3−i3−i3−i3−i3i3i3000000000000
χ312-22-2200-2-22000022-22-22-2-222-2-222-2-20000000000002-200−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ322-22-2200-2-22000022-22-22-2-222-2-222-2-20000000000002-200i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ332-22-2200-2-22000022-22-22-2-222-2-222-2-2000000000000-2200−i2i2−i2i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ342-22-2200-2-22000022-22-22-2-222-2-222-2-2000000000000-2200i2−i2i2−i2−i2i2−i2i2-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ352-22-2-10011-13−33−322-22-22-2-2-1-111-1-111000033−3−333−3−32-200−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
χ362-22-2-10011-13−33−322-22-22-2-2-1-111-1-111000033−3−333−3−32-200i2−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
χ372-22-2-10011-13−33−322-22-22-2-2-1-111-1-111000033−3−333−3−3-2200−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
χ382-22-2-10011-13−33−322-22-22-2-2-1-111-1-111000033−3−333−3−3-2200i2−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
χ392-22-2-10011-1−33−3322-22-22-2-2-1-111-1-1110000−3−333−3−3332-200−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
χ402-22-2-10011-1−33−3322-22-22-2-2-1-111-1-1110000−3−333−3−3332-200i2−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
χ412-22-2-10011-1−33−3322-22-22-2-2-1-111-1-1110000−3−333−3−333-2200−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
χ422-22-2-10011-1−33−3322-22-22-2-2-1-111-1-1110000−3−333−3−333-2200i2−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
χ432-2-2222-22-2-22-2-2222-2-2-2-22222-2-2-2-2222-22-222-2-2-2-22200002−2−222−2−22000000002−2−222−2−222−2−222−2−22000000000000
χ442-2-2222-22-2-22-2-2222-2-2-2-22222-2-2-2-2222-22-222-2-2-2-2220000−222−2−222−200000000−222−2−222−2−222−2−222−2000000000000
χ452-2-222-222-2-2-222-222-2-2-2-22222-2-2-2-222-22-22-2-22222-2-200002−2−22−222−2000000002−2−222−2−22−222−2−222−2000000000000
χ462-2-222-222-2-2-222-222-2-2-2-22222-2-2-2-222-22-22-2-22222-2-20000−222−22−2−2200000000−222−2−222−22−2−222−2−22000000000000
χ472-2-22-12-2-111-111-122-2-2-2-222-1-11111-1-12-22-2-1-11111-1-100002−2−222−2−223−3−33−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ482-2-22-12-2-111-111-122-2-2-2-222-1-11111-1-12-22-2-1-11111-1-100002−2−222−2−22−333−33−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ492-2-22-12-2-111-111-122-2-2-2-222-1-11111-1-12-22-2-1-11111-1-10000−222−2−222−23−3−33−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ502-2-22-12-2-111-111-122-2-2-2-222-1-11111-1-12-22-2-1-11111-1-10000−222−2−222−2−333−33−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ512-2-22-1-22-1111-1-1122-2-2-2-222-1-11111-1-1-22-2211-1-1-1-11100002−2−22−222−23−3−333−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ522-2-22-1-22-1111-1-1122-2-2-2-222-1-11111-1-1-22-2211-1-1-1-11100002−2−22−222−2−333−3−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ532-2-22-1-22-1111-1-1122-2-2-2-222-1-11111-1-1-22-2211-1-1-1-1110000−222−22−2−223−3−333−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ542-2-22-1-22-1111-1-1122-2-2-2-222-1-11111-1-1-22-2211-1-1-1-1110000−222−22−2−22−333−3−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ55444444444444441-211-2-2-211-21-21-21-2-2-2111-21-21-21-200000000000000000000000000000000000000220000-1-1-1-1
χ56444444444444441-211-2-2-211-21-21-21-2-2-2111-21-21-21-200000000000000000000000000000000000000-2-200001111
χ5744444444444444-21-2-2111-2-21-21-21-2111-2-2-21-21-21-210000000000000000000000000000000000002200-1-1-1-10000
χ5844444444444444-21-2-2111-2-21-21-21-2111-2-2-21-21-21-21000000000000000000000000000000000000-2-20011110000
χ5944444-4-4444-4-4-4-41-211-2-2-211-21-21-21-222-1-1-12-12-12-12000000000000000000000000000000000000002-20000-1-111
χ6044444-4-4444-4-4-4-41-211-2-2-211-21-21-21-222-1-1-12-12-12-1200000000000000000000000000000000000000-22000011-1-1
χ6144444-4-4444-4-4-4-4-21-2-2111-2-21-21-21-21-1-1222-12-12-12-10000000000000000000000000000000000002-200-1-1110000
χ6244444-4-4444-4-4-4-4-21-2-2111-2-21-21-21-21-1-1222-12-12-12-1000000000000000000000000000000000000-220011-1-10000
χ634-4-4444-44-4-44-4-441-2-1-122-211-2-12-121-2-221-11-2-12-121-200000000000000000000000000000000000000000000−i3i3−i3i3
χ644-4-4444-44-4-44-4-441-2-1-122-211-2-12-121-2-221-11-2-12-121-200000000000000000000000000000000000000000000i3−i3i3−i3
χ654-4-4444-44-4-44-4-44-2122-1-11-2-212-12-1-211-1-22-212-12-1-210000000000000000000000000000000000000000−i3i3−i3i30000
χ664-4-4444-44-4-44-4-44-2122-1-11-2-212-12-1-211-1-22-212-12-1-210000000000000000000000000000000000000000i3−i3i3−i30000
χ674-4-444-444-4-4-444-41-2-1-122-211-2-12-121-22-2-11-121-21-2-1200000000000000000000000000000000000000000000−i3i3i3−i3
χ684-4-444-444-4-4-444-41-2-1-122-211-2-12-121-22-2-11-121-21-2-1200000000000000000000000000000000000000000000i3−i3−i3i3
χ694-4-444-444-4-4-444-4-2122-1-11-2-212-12-1-21-112-22-1-21-212-10000000000000000000000000000000000000000−i3i3i3−i30000
χ704-4-444-444-4-4-444-4-2122-1-11-2-212-12-1-21-112-22-1-21-212-10000000000000000000000000000000000000000i3−i3−i3i30000
χ718888-488-4-4-4-4-4-4-42-422-4-4-42-12-12-12-12-4-422-12-12-12-12000000000000000000000000000000000000000000000000
χ728888-488-4-4-4-4-4-4-4-42-4-4222-42-12-12-12-122-4-42-12-12-12-1000000000000000000000000000000000000000000000000
χ738888-4-8-8-4-4-444442-422-4-4-42-12-12-12-1244-2-21-21-21-21-2000000000000000000000000000000000000000000000000
χ748888-4-8-8-4-4-44444-42-4-4222-42-12-12-12-1-2-244-21-21-21-21000000000000000000000000000000000000000000000000
χ7588-8-8800-88-800002-42-2-444-22-42-4-24-24000000000000000000000000000000000000000000000000000000000000
χ7688-8-8800-88-80000-42-442-2-24-42-424-24-2000000000000000000000000000000000000000000000000000000000000
χ7788-8-8-4004-444343−43−432-42-2-444-2-12-121-21-200003−233−23−323−323000000000000000000000000000000000000000000000000
χ7888-8-8-4004-444343−43−43-42-442-2-242-12-1-21-210000−233−23323−323−3000000000000000000000000000000000000000000000000
χ7988-8-8-4004-44−43−4343432-42-2-444-2-12-121-21-20000−323−3233−233−23000000000000000000000000000000000000000000000000
χ8088-8-8-4004-44−43−434343-42-442-2-242-12-1-21-21000023−323−3−233−233000000000000000000000000000000000000000000000000
χ818-88-8800-8-8800002-4-224-44-22-4-242-4-24000000000000000000000000000000000000000000000000000000000000
χ828-88-8800-8-880000-424-4-22-24-424-2-424-2000000000000000000000000000000000000000000000000000000000000
χ838-88-8-40044-443−4343−432-4-224-44-2-121-2-121-200003−23−3233−23−323000000000000000000000000000000000000000000000000
χ848-88-8-40044-443−4343−43-424-4-22-242-1-212-1-210000−23323−3−23323−3000000000000000000000000000000000000000000000000
χ858-88-8-40044-4−4343−43432-4-224-44-2-121-2-121-20000−3233−23−3233−23000000000000000000000000000000000000000000000000
χ868-88-8-40044-4−4343−4343-424-4-22-242-1-212-1-21000023−3−23323−3−233000000000000000000000000000000000000000000000000
χ878-8-88-48-8-444-444-42-4-2-244-42-121-21-2-12-442-2-121-21-2-12000000000000000000000000000000000000000000000000
χ888-8-88-48-8-444-444-4-4244-2-22-42-1-21-212-12-2-442-1-21-212-1000000000000000000000000000000000000000000000000
χ898-8-88-4-88-4444-4-442-4-2-244-42-121-21-2-124-4-221-2-12-121-2000000000000000000000000000000000000000000000000
χ908-8-88-4-88-4444-4-44-4244-2-22-42-1-21-212-1-224-4-212-12-1-21000000000000000000000000000000000000000000000000

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