Finite Group Databasebeta

← Group #13138970

Character table — Group #13138970

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222224444446666666666666666666612121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order12223446668888121224242424336666661212121224242424242424243666121212121212242424242424242424242424224466668888121212122424242424242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111
χ51111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ61111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-111-1-1-1-111
χ81111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-11-1-11111-1-1
χ9222222222222222222222-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ10222222222222222222222-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000
χ1122222222222222222222-1222-12-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000002200000-1-1-1-1
χ1222222222222222222222-1222-12-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-2-2000001111
χ132222222222-2-2-2-222-2-2-2-22-1-1-12-122-1-1-1-111111111-1-1-1-12-1-12-1-1-2-2-2-2111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ142222222222-2-2-2-222-2-2-2-22-1-1-12-122-1-1-1-111111111-1-1-1-12-1-12-1-1-2-2-2-211111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ152222222222-2-2-2-222-2-2-2-2-1222-12-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000002-200000-1-111
χ162222222222-2-2-2-222-2-2-2-2-1222-12-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000-220000011-1-1
χ1722222-2-22220000-2-2000022222222-2-2-2-2000000002222-2-2-2-2-2-200000000000022-2-222220000-2-2-2-200000000000000000000
χ1822222-2-22220000-2-2000022222222-2-2-2-2000000002222-2-2-2-2-2-2000000000000-2-222-2-2-2-20000222200000000000000000000
χ1922222-2-22220000-2-200002-1-1-12-12211113333−3−3−3−3-1-1-1-1-211-21100003333−3−3−3−322-2-2-1-1-1-1000011113333−3−3−3−3000000000000
χ2022222-2-22220000-2-200002-1-1-12-12211113333−3−3−3−3-1-1-1-1-211-21100003333−3−3−3−3-2-22211110000-1-1-1-1−3−3−3−33333000000000000
χ2122222-2-22220000-2-200002-1-1-12-1221111−3−3−3−33333-1-1-1-1-211-2110000−3−3−3−3333322-2-2-1-1-1-100001111−3−3−3−33333000000000000
χ2222222-2-22220000-2-200002-1-1-12-1221111−3−3−3−33333-1-1-1-1-211-2110000−3−3−3−33333-2-22211110000-1-1-1-13333−3−3−3−3000000000000
χ2322-2-22002-2-2−i2−i2i2i200−i2−i2i2i2222-2-2-22-20000−i2−i2i2i2−i2−i2i2i222-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i000022−2−22i2i−2i−2i22−2−222−2−2000000000000
χ2422-2-22002-2-2−i2−i2i2i200−i2−i2i2i2222-2-2-22-20000−i2−i2i2i2−i2−i2i2i222-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i0000−2−222−2i−2i2i2i−2−222−2−222000000000000
χ2522-2-22002-2-2−i2−i2i2i200−i2−i2i2i22-1-11-212-23−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23-1-11103−303−3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23002i−2i−i3−i3i3i322−2−2−i−iiiζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ2622-2-22002-2-2−i2−i2i2i200−i2−i2i2i22-1-11-212-23−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23-1-11103−303−3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−2i2ii3i3−i3−i3−2−222ii−i−i−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ2722-2-22002-2-2−i2−i2i2i200−i2−i2i2i22-1-11-212-2−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7-1-1110−330−33−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7002i−2ii3i3−i3−i322−2−2−i−iiiζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ2822-2-22002-2-2−i2−i2i2i200−i2−i2i2i22-1-11-212-2−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7-1-1110−330−33−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−2i2i−i3−i3i3i3−2−222ii−i−i−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ2922-2-22002-2-2i2i2−i2−i200i2i2−i2−i2222-2-2-22-20000i2i2−i2−i2i2i2−i2−i222-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i0000−2−2222i2i−2i−2i−2−222−2−222000000000000
χ3022-2-22002-2-2i2i2−i2−i200i2i2−i2−i2222-2-2-22-20000i2i2−i2−i2i2i2−i2−i222-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i000022−2−2−2i−2i2i2i22−2−222−2−2000000000000
χ3122-2-22002-2-2i2i2−i2−i200i2i2−i2−i22-1-11-212-23−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23-1-11103−303−3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23002i−2i−i3−i3i3i3−2−222−i−iii−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ3222-2-22002-2-2i2i2−i2−i200i2i2−i2−i22-1-11-212-23−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23-1-11103−303−3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−2i2ii3i3−i3−i322−2−2ii−i−iζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3322-2-22002-2-2i2i2−i2−i200i2i2−i2−i22-1-11-212-2−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7-1-1110−330−33i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7002i−2ii3i3−i3−i3−2−222−i−iii−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ3422-2-22002-2-2i2i2−i2−i200i2i2−i2−i22-1-11-212-2−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7-1-1110−330−33i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−2i2i−i3−i3i3i322−2−2ii−i−iζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ352-22-2200-22-2−i2i2−i2i200−i2i2−i2i222-22-2-2-220000−i2i2−i2i2−i2i2−i2i22-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-2002-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000000000
χ362-22-2200-22-2−i2i2−i2i200−i2i2−i2i222-22-2-2-220000−i2i2−i2i2−i2i2−i2i22-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200-22-22i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000000000
χ372-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-11-1-21-223−3−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-11-1103−30−33−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72-200-11-11−i2i2−i2i23−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ382-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-11-1-21-223−3−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-11-1103−30−33−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-22001-11-1i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ392-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-11-1-21-22−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-11-110−3303−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232-200-11-11−i2i2−i2i2−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ402-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-11-1-21-22−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-11-110−3303−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-22001-11-1i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ412-22-2200-22-2i2−i2i2−i200i2−i2i2−i222-22-2-2-220000i2−i2i2−i2i2−i2i2−i22-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-2002-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000000000
χ422-22-2200-22-2i2−i2i2−i200i2−i2i2−i222-22-2-2-220000i2−i2i2−i2i2−i2i2−i22-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200-22-22−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000000000
χ432-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-11-1-21-223−3−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-11-1103−30−33i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ72-200-11-11i2−i2i2−i23−33−3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ442-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-11-1-21-223−3−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-11-1103−30−33i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-22001-11-1−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ452-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-11-1-21-22−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-11-110−3303−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232-200-11-11i2−i2i2−i2−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ462-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-11-1-21-22−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-11-110−3303−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-22001-11-1−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ472-2-2222-2-2-2200002-2000022-2-222-2-222-2-2000000002-2-22222-2-2-2000000000000000000002i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i000000000000
χ482-2-2222-2-2-2200002-2000022-2-222-2-222-2-2000000002-2-22222-2-2-200000000000000000000−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i000000000000
χ492-2-2222-2-2-2200002-200002-1112-1-2-2-1-1113−3−33−333−3-111-12-1-1-21100003−3−33−333−30000−i3i3i3−i3−2i2i2i−2i−i3i3i3−i3i−i−iii−i−ii000000000000
χ502-2-2222-2-2-2200002-200002-1112-1-2-2-1-1113−3−33−333−3-111-12-1-1-21100003−3−33−333−30000i3−i3−i3i32i−2i−2i2ii3−i3−i3i3−iii−i−iii−i000000000000
χ512-2-2222-2-2-2200002-200002-1112-1-2-2-1-111−333−33−3−33-111-12-1-1-2110000−333−33−3−330000−i3i3i3−i32i−2i−2i2i−i3i3i3−i3−iii−i−iii−i000000000000
χ522-2-2222-2-2-2200002-200002-1112-1-2-2-1-111−333−33−3−33-111-12-1-1-2110000−333−33−3−330000i3−i3−i3i3−2i2i2i−2ii3−i3−i3i3i−i−iii−i−ii000000000000
χ532-2-222-22-2-222-2-22-222-2-2222-2-222-2-2-2-2222-2-222-2-222-2-22-2-2-22222-2-222-2-222-2-22000000000000000000000000000000000000
χ542-2-222-22-2-222-2-22-222-2-222-1112-1-2-211-1-1-111-1-111-1-111-1-2112-1-12-2-22-111-1-111-10000−i3i3i3−i30000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000
χ552-2-222-22-2-222-2-22-222-2-222-1112-1-2-211-1-1-111-1-111-1-111-1-2112-1-12-2-22-111-1-111-10000i3−i3−i3i30000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000
χ562-2-222-22-2-222-2-22-222-2-22-12-2-2-1211-2-2222-2-222-2-22-111-1111-1-1-1-111-1-111-1-111-1000000000000000000000000000000003−33−3
χ572-2-222-22-2-222-2-22-222-2-22-12-2-2-1211-2-2222-2-222-2-22-111-1111-1-1-1-111-1-111-1-111-100000000000000000000000000000000−33−33
χ582-2-222-22-2-22-222-2-22-222-222-2-222-2-2-2-222-222-2-222-22-2-22-2-2-2222-222-2-222-2-222-2000000000000000000000000000000000000
χ592-2-222-22-2-22-222-2-22-222-22-1112-1-2-211-1-11-1-111-1-11-111-1-2112-1-1-222-21-1-111-1-110000−i3i3i3−i30000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000
χ602-2-222-22-2-22-222-2-22-222-22-1112-1-2-211-1-11-1-111-1-11-111-1-2112-1-1-222-21-1-111-1-110000i3−i3−i3i30000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000
χ612-2-222-22-2-22-222-2-22-222-2-12-2-2-1211-2-222-222-2-222-2-111-1111-1-1-11-1-111-1-111-1-11000000000000000000000000000000003−3−33
χ622-2-222-22-2-22-222-2-22-222-2-12-2-2-1211-2-222-222-2-222-2-111-1111-1-1-11-1-111-1-111-1-1100000000000000000000000000000000−333−3
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.