Finite Group Databasebeta

← Group #13138998

Character table — Group #13138998

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222224444446666666666666666666612121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order1222344666888812122424242433666666121212122424242424242424366612121212121224242424242424242424242422446666888812121212242424242424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ51111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ61111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1
χ71111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-1
χ81111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111
χ9222222222222222222222-12-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ10222222222222222222222-12-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000
χ1122222222222222222222-12-1222-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000002020000-1-1-1-1
χ1222222222222222222222-12-1222-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-200001111
χ132222222222-2-2-2-222-2-2-2-22-12-1-1-122-1-1-1-111111111-1-1-1-12-1-12-1-1-2-2-2-2111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ142222222222-2-2-2-222-2-2-2-22-12-1-1-122-1-1-1-111111111-1-1-1-12-1-12-1-1-2-2-2-211111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ152222222222-2-2-2-222-2-2-2-2-12-1222-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000020-20000-1-111
χ162222222222-2-2-2-222-2-2-2-2-12-1222-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000-202000011-1-1
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
χ1922222-2-22220000-2-200002-12-1-1-12211113333−3−3−3−3-1-1-1-1-211-21100003333−3−3−3−322-2-2-1-1-1-1000011113333−3−3−3−3000000000000
χ2022222-2-22220000-2-200002-12-1-1-12211113333−3−3−3−3-1-1-1-1-211-21100003333−3−3−3−3-2-22211110000-1-1-1-1−3−3−3−33333000000000000
χ2122222-2-22220000-2-200002-12-1-1-1221111−3−3−3−33333-1-1-1-1-211-2110000−3−3−3−3333322-2-2-1-1-1-100001111−3−3−3−33333000000000000
χ2222222-2-22220000-2-200002-12-1-1-1221111−3−3−3−33333-1-1-1-1-211-2110000−3−3−3−33333-2-22211110000-1-1-1-13333−3−3−3−3000000000000
χ2322-2-22002-2-222−2−20022−2−22222-2-2-2-2000022−2−222−2−222-2-200000022−2−222−2−222−2−22-20022-2-222−2−2000022−2−222−2−2000000000000
χ2422-2-22002-2-222−2−20022−2−22222-2-2-2-2000022−2−222−2−222-2-200000022−2−222−2−222−2−2-2200-2-222−2−2220000−2−222−2−222000000000000
χ2522-2-22002-2-222−2−20022−2−22-12-111-2-23−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-1-11103−303−322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232-200-1-11122−2−233−3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ2622-2-22002-2-222−2−20022−2−22-12-111-2-23−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-1-11103−303−322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-220011-1-1−2−222−3−333−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ2722-2-22002-2-222−2−20022−2−22-12-111-2-2−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-1-1110−330−3322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72-200-1-11122−2−2−3−333ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ2822-2-22002-2-222−2−20022−2−22-12-111-2-2−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-1-1110−330−3322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-220011-1-1−2−22233−3−3−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ2922-2-22002-2-2−2−22200−2−2222222-2-2-2-20000−2−222−2−22222-2-2000000−2−222−2−222−2−2222-20022-2-2−2−2220000−2−222−2−222000000000000
χ3022-2-22002-2-2−2−22200−2−2222222-2-2-2-20000−2−222−2−22222-2-2000000−2−222−2−222−2−222-2200-2-22222−2−2000022−2−222−2−2000000000000
χ3122-2-22002-2-2−2−22200−2−2222-12-111-2-23−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-1-11103−303−3−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ232-200-1-111−2−22233−3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ3222-2-22002-2-2−2−22200−2−2222-12-111-2-23−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-1-11103−303−3−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-220011-1-122−2−2−3−333ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3322-2-22002-2-2−2−22200−2−2222-12-111-2-2−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-1-1110−330−33−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ72-200-1-111−2−222−3−333−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ3422-2-22002-2-2−2−22200−2−2222-12-111-2-2−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-1-1110−330−33−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-220011-1-122−2−233−3−3ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ352-22-2200-22-2−i2i2−i2i200−i2i2−i2i222-2-22-22-20000−i2i2−i2i2−i2i2−i2i22-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002i−2i00002−22−22i−2i2i−2i2−22−22−22−2000000000000
χ362-22-2200-22-2−i2i2−i2i200−i2i2−i2i222-2-22-22-20000−i2i2−i2i2−i2i2−i2i22-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−2i2i0000−22−22−2i2i−2i2i−22−22−22−22000000000000
χ372-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-1-21-112-23−3−33ζ13+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−ζ7002i−2i−i3i3−i3i32−22−2−ii−iiζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ382-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-1-21-112-23−3−33ζ13+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−ζ700−2i2ii3−i3i3−i3−22−22i−ii−i−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ392-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-1-21-112-2−333−3ζ5+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−ζ23002i−2ii3−i3i3−i32−22−2−ii−iiζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ402-22-2200-22-2−i2i2−i2i200−i2i2−i2i22-1-21-112-2−333−3ζ5+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−ζ2300−2i2i−i3i3−i3i3−22−22i−ii−i−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ412-22-2200-22-2i2−i2i2−i200i2−i2i2−i222-2-22-22-20000i2−i2i2−i2i2−i2i2−i22-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2002i−2i0000−22−222i−2i2i−2i−22−22−22−22000000000000
χ422-22-2200-22-2i2−i2i2−i200i2−i2i2−i222-2-22-22-20000i2−i2i2−i2i2−i2i2−i22-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200−2i2i00002−22−2−2i2i−2i2i2−22−22−22−2000000000000
χ432-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-1-21-112-23−3−33−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+ζ7002i−2i−i3i3−i3i3−22−22−ii−ii−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ442-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-1-21-112-23−3−33−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+ζ700−2i2ii3−i3i3−i32−22−2i−ii−iζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ452-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-1-21-112-2−333−3−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+ζ23002i−2ii3−i3i3−i3−22−22−ii−ii−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ462-22-2200-22-2i2−i2i2−i200i2−i2i2−i22-1-21-112-2−333−3−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+ζ2300−2i2i−i3i3−i3i32−22−2i−ii−iζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ472-2-2222-2-2-222i−2i−2i2i2-22i−2i−2i2i22-2-2-22-2222-2-22i−2i−2i2i2i−2i−2i2i2-2-22222-2-2-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ482-2-2222-2-2-222i−2i−2i2i2-22i−2i−2i2i2-1-211-1-22-1-111−iii−i−iii−i-111-12-1-1-2112i−2i−2i2i−iii−i−iii−i0000−i3i3i3−i30000−i3i3i3−i33−3−33−333−3000000000000
χ492-2-2222-2-2-222i−2i−2i2i2-22i−2i−2i2i2-1-211-1-22-1-111−iii−i−iii−i-111-12-1-1-2112i−2i−2i2i−iii−i−iii−i0000i3−i3−i3i30000i3−i3−i3i3−333−33−3−33000000000000
χ502-2-2222-2-2-222i−2i−2i2i2-22i−2i−2i2i-121-2-221-122-2-22i−2i−2i2i2i−2i−2i2i-111-1-1-1-1111−iii−i−iii−i−iii−i000000000000000000000000000000003−3−i3i3
χ512-2-2222-2-2-222i−2i−2i2i2-22i−2i−2i2i-121-2-221-122-2-22i−2i−2i2i2i−2i−2i2i-111-1-1-1-1111−iii−i−iii−i−iii−i00000000000000000000000000000000−33i3−i3
χ522-2-2222-2-2-22−2i2i2i−2i2-2−2i2i2i−2i22-2-2-22-2222-2-2−2i2i2i−2i−2i2i2i−2i2-2-22222-2-2-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ532-2-2222-2-2-22−2i2i2i−2i2-2−2i2i2i−2i2-1-211-1-22-1-111i−i−iii−i−ii-111-12-1-1-211−2i2i2i−2ii−i−iii−i−ii0000−i3i3i3−i30000−i3i3i3−i3−333−33−3−33000000000000
χ542-2-2222-2-2-22−2i2i2i−2i2-2−2i2i2i−2i2-1-211-1-22-1-111i−i−iii−i−ii-111-12-1-1-211−2i2i2i−2ii−i−iii−i−ii0000i3−i3−i3i30000i3−i3−i3i33−3−33−333−3000000000000
χ552-2-2222-2-2-22−2i2i2i−2i2-2−2i2i2i−2i-121-2-221-122-2-2−2i2i2i−2i−2i2i2i−2i-111-1-1-1-1111i−i−iii−i−iii−i−ii000000000000000000000000000000003−3i3−i3
χ562-2-2222-2-2-22−2i2i2i−2i2-2−2i2i2i−2i-121-2-221-122-2-2−2i2i2i−2i−2i2i2i−2i-111-1-1-1-1111i−i−iii−i−iii−i−ii00000000000000000000000000000000−33−i3i3
χ572-2-222-22-2-220000-22000022-2-2-22-22-2-222000000002-2-22-2-2-2222000000000000000000002-2-2200002-2-222-2-22000000000000
χ582-2-222-22-2-220000-22000022-2-2-22-22-2-222000000002-2-22-2-2-222200000000000000000000-222-20000-222-2-222-2000000000000
χ592-2-222-22-2-220000-2200002-1-211-1-2211-1-1−i3i3i3−i3i3−i3−i3i3-111-1-2112-1-10000−i3i3i3−i3i3−i3−i3i30000−i3i3i3−i32-2-22i3−i3−i3i3-111-1-111-1000000000000
χ602-2-222-22-2-220000-2200002-1-211-1-2211-1-1−i3i3i3−i3i3−i3−i3i3-111-1-2112-1-10000−i3i3i3−i3i3−i3−i3i30000i3−i3−i3i3-222-2−i3i3i3−i31-1-111-1-11000000000000
χ612-2-222-22-2-220000-2200002-1-211-1-2211-1-1i3−i3−i3i3−i3i3i3−i3-111-1-2112-1-10000i3−i3−i3i3−i3i3i3−i30000−i3i3i3−i3-222-2i3−i3−i3i31-1-111-1-11000000000000
χ622-2-222-22-2-220000-2200002-1-211-1-2211-1-1i3−i3−i3i3−i3i3i3−i3-111-1-2112-1-10000i3−i3−i3i3−i3i3i3−i30000i3−i3−i3i32-2-22−i3i3i3−i3-111-1-111-1000000000000
χ6344444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-211-211-2-2-2-211111111000000000000000000000000000000000000
χ644444444444-4-4-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2222222221111-211-2112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.