Finite Group Databasebeta

← Group #13138980

Character table — Group #13138980

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222224444446666666666666666666612121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order1222344666888812122424242433666666121212122424242424242424366612121212121224242424242424242424242444448888121212121212121224242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ51111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222-1-12-122-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-100-1-1
χ10222222222222222222222-1-12-122-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-200110011
χ1122222222222222222222-122-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1222222222222222222222-122-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ132222222222-2-2-2-222-2-2-2-22-1-12-122-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000020-200-1-10011
χ142222222222-2-2-2-222-2-2-2-22-1-12-122-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000000-202001100-1-1
χ152222222222-2-2-2-222-2-2-2-2-122-12-1-12-1-1-1-111111111-1-1-1-12-1-12-1-1-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ162222222222-2-2-2-222-2-2-2-2-122-12-1-12-1-1-1-111111111-1-1-1-12-1-12-1-1-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ1722222-2-22220000-2-2000022222222-2-2-2-2000000002222-2-2-2-2-2-200000000000022-2-200002222-2-2-2-200000000000000000000
χ1822222-2-22220000-2-2000022222222-2-2-2-2000000002222-2-2-2-2-2-2000000000000-2-2220000-2-2-2-2222200000000000000000000
χ1922222-2-22220000-2-20000-122-12-1-1211113333−3−3−3−3-1-1-1-1-211-21100003333−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−3000000000000
χ2022222-2-22220000-2-20000-122-12-1-1211113333−3−3−3−3-1-1-1-1-211-21100003333−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−33333000000000000
χ2122222-2-22220000-2-20000-122-12-1-121111−3−3−3−33333-1-1-1-1-211-2110000−3−3−3−3333322-2-20000-1-1-1-11111−3−3−3−33333000000000000
χ2222222-2-22220000-2-20000-122-12-1-121111−3−3−3−33333-1-1-1-1-211-2110000−3−3−3−33333-2-22200001111-1-1-1-13333−3−3−3−3000000000000
χ2322-2-222-2-22-20000-22000022-222-2-2-222-2-2000000002-2-22-2-2-222200000000000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2422-2-222-2-22-20000-22000022-222-2-2-222-2-2000000002-2-22-2-2-22220000000000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2522-2-222-2-22-20000-220000-12-2-1211-2-1-111−i3−i3i3i3−i3−i3i3i3-111-1-2112-1-10000−i3−i3i3i3−i3−i3i3i300002i2i−2i−2i33−3−333−3−3−i−iii−i−iii000000000000
χ2622-2-222-2-22-20000-220000-12-2-1211-2-1-111−i3−i3i3i3−i3−i3i3i3-111-1-2112-1-10000−i3−i3i3i3−i3−i3i3i30000−2i−2i2i2i−3−333−3−333ii−i−iii−i−i000000000000
χ2722-2-222-2-22-20000-220000-12-2-1211-2-1-111i3i3−i3−i3i3i3−i3−i3-111-1-2112-1-10000i3i3−i3−i3i3i3−i3−i300002i2i−2i−2i−3−333−3−333−i−iii−i−iii000000000000
χ2822-2-222-2-22-20000-220000-12-2-1211-2-1-111i3i3−i3−i3i3i3−i3−i3-111-1-2112-1-10000i3i3−i3−i3i3i3−i3−i30000−2i−2i2i2i33−3−333−3−3ii−i−iii−i−i000000000000
χ2922-2-22-22-22-22i2i−2i−2i2-22i2i−2i−2i22-222-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-2-22222-2-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3022-2-22-22-22-22i2i−2i−2i2-22i2i−2i−2i2-112-1-2-21-2-2222i2i−2i−2i−2i−2i2i2i-111-1-1-1-1111−i−iii−i−iiiii−i−i000000000000000000000000000000−i3i3003−3
χ3122-2-22-22-22-22i2i−2i−2i2-22i2i−2i−2i2-112-1-2-21-2-2222i2i−2i−2i−2i−2i2i2i-111-1-1-1-1111−i−iii−i−iiiii−i−i000000000000000000000000000000i3−i300−33
χ3222-2-22-22-22-22i2i−2i−2i2-22i2i−2i−2i-12-2-1211-211-1-1−i−iiiii−i−i-111-12-1-1-2112i2i−2i−2i−i−iiiii−i−i0000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ3322-2-22-22-22-22i2i−2i−2i2-22i2i−2i−2i-12-2-1211-211-1-1−i−iiiii−i−i-111-12-1-1-2112i2i−2i−2i−i−iiiii−i−i00000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ3422-2-22-22-22-2−2i−2i2i2i2-2−2i−2i2i2i22-222-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-2-22222-2-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ3522-2-22-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-112-1-2-21-2-222−2i−2i2i2i2i2i−2i−2i-111-1-1-1-1111ii−i−iii−i−i−i−iii000000000000000000000000000000−i3i300−33
χ3622-2-22-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-112-1-2-21-2-222−2i−2i2i2i2i2i−2i−2i-111-1-1-1-1111ii−i−iii−i−i−i−iii000000000000000000000000000000i3−i3003−3
χ3722-2-22-22-22-2−2i−2i2i2i2-2−2i−2i2i2i-12-2-1211-211-1-1ii−i−i−i−iii-111-12-1-1-211−2i−2i2i2iii−i−i−i−iii0000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ3822-2-22-22-22-2−2i−2i2i2i2-2−2i−2i2i2i-12-2-1211-211-1-1ii−i−i−i−iii-111-12-1-1-211−2i−2i2i2iii−i−i−i−iii00000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ392-22-22002-2-2−i2i2−i2i200−i2i2−i2i2222-2-22-2-20000−i2i2−i2i2−i2i2−i2i222-2-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-200−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2000000000000
χ402-22-22002-2-2−i2i2−i2i200−i2i2−i2i2222-2-22-2-20000−i2i2−i2i2−i2i2−i2i222-2-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200i2−i2i2−i2-22-220000i2−i2i2−i2i2−i2i2−i2000000000000
χ412-22-22002-2-2−i2i2−i2i200−i2i2−i2i2-1221-2-11-23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-11103−303−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232-200−i2i2−i2i2-11-113−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ422-22-22002-2-2−i2i2−i2i200−i2i2−i2i2-1221-2-11-23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-11103−303−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-2200i2−i2i2−i21-11-1−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ432-22-22002-2-2−i2i2−i2i200−i2i2−i2i2-1221-2-11-2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-1-1110−330−33−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72-200−i2i2−i2i2-11-11−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ442-22-22002-2-2−i2i2−i2i200−i2i2−i2i2-1221-2-11-2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-1-1110−330−33−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-2200i2−i2i2−i21-11-13−33−3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ452-22-22002-2-2i2−i2i2−i200i2−i2i2−i2222-2-22-2-20000i2−i2i2−i2i2−i2i2−i222-2-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-200i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2000000000000
χ462-22-22002-2-2i2−i2i2−i200i2−i2i2−i2222-2-22-2-20000i2−i2i2−i2i2−i2i2−i222-2-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200−i2i2−i2i2-22-220000−i2i2−i2i2−i2i2−i2i2000000000000
χ472-22-22002-2-2i2−i2i2−i200i2−i2i2−i2-1221-2-11-23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-1-11103−303−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232-200i2−i2i2−i2-11-113−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ482-22-22002-2-2i2−i2i2−i200i2−i2i2−i2-1221-2-11-23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-1-11103−303−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-2200−i2i2−i2i21-11-1−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ492-22-22002-2-2i2−i2i2−i200i2−i2i2−i2-1221-2-11-2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-1-1110−330−33i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ72-200i2−i2i2−i2-11-11−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ502-22-22002-2-2i2−i2i2−i200i2−i2i2−i2-1221-2-11-2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-1-1110−330−33i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-2200−i2i2−i2i21-11-13−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ512-2-22200-2-222−2−22002−2−2222-2-2-2-22200002−2−22−222−22-22-20000002−2−222−2−22−222−2002-22−2−2200002-2-222−2−222−2−22000000000000
χ522-2-22200-2-222−2−22002−2−2222-2-2-2-22200002−2−22−222−22-22-20000002−2−222−2−22−222−200-22−222−20000-222-2−222−2−222−2000000000000
χ532-2-22200-2-222−2−22002−2−22-12-21-21-123−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23-11-110−3303−32−2−22ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23002-22−2−22−333−3-111-1ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ542-2-22200-2-222−2−22002−2−22-12-21-21-123−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23-11-110−3303−32−2−22ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300-22−222−23−3−331-1-11−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ552-2-22200-2-222−2−22002−2−22-12-21-21-12−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7-11-1103−30−332−2−22ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7002-22−2−223−3−33-111-1ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ562-2-22200-2-222−2−22002−2−22-12-21-21-12−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7-11-1103−30−332−2−22ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700-22−222−2−333−31-1-11−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ572-2-22200-2-22−222−200−222−222-2-2-2-2220000−222−22−2−222-22-2000000−222−2−222−22−2−22002-2−222−200002-2-22−222−2−222−2000000000000
χ582-2-22200-2-22−222−200−222−222-2-2-2-2220000−222−22−2−222-22-2000000−222−2−222−22−2−2200-222−2−220000-222-22−2−222−2−22000000000000
χ592-2-22200-2-22−222−200−222−2-12-21-21-123−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23-11-110−3303−3−222−2−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23002-2−222−2−333−3-111-1−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ602-2-22200-2-22−222−200−222−2-12-21-21-123−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23-11-110−3303−3−222−2−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300-222−2−223−3−331-1-11ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ612-2-22200-2-22−222−200−222−2-12-21-21-12−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7-11-1103−30−33−222−2−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7002-2−222−23−3−33-111-1−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ622-2-22200-2-22−222−200−222−2-12-21-21-12−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7-11-1103−30−33−222−2−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700-222−2−22−333−31-1-11ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.