Finite Group Databasebeta

← Group #13173341

Character table — Group #13173341

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order12223446662333333466666666666666666666121212126666666666661212121212121212121212121212121212121212121212124444441212121244121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111111111-1111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−iii
χ81111111111-1111111-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiii−i−i
χ911111-1-11111111111-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-11111-1-111-1-11-11-1
χ1011111-1-11111111111-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-111-1-111-1-111-11-11
χ1111111-1-11111111111-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1ii−i−i−i−iiii−i−ii
χ1211111-1-11111111111-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1−i−iiiii−i−i−iii−i
χ1311111-1-1111-11111111-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111111-1-1-111-1-111-1-111-1-1-11-11
χ1411111-1-1111-11111111-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111111-1-1-111-1-1-1-111-1-1111-11-1
χ1511111-1-1111-11111111-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iii−iii−i
χ1611111-1-1111-11111111-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−ii−i−ii
χ172222-122-1-1-1222-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1000000000000
χ182222-122-1-1-1222-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2111111000000000000
χ192222-122-1-1-1-222-1-1-1-1-21122-1-1-1-12222-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111222222-1-1-1-1-2-2-1-11111000000000000
χ202222-122-1-1-1-222-1-1-1-1-21122-1-1-1-12222-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2-2-211112211-1-1-1-1000000000000
χ212222-1-2-2-1-1-1222-1-1-1-1-2-1-122-1-1-1-12222-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-2-2-1-1-1-1-221111-1-1000000000000
χ222222-1-2-2-1-1-1222-1-1-1-1-2-1-122-1-1-1-12222-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-22211112-2-1-1-1-111000000000000
χ232222-1-2-2-1-1-1-222-1-1-1-121122-1-1-1-12222-1-1-1-1-1-1-1-111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-2-2-1-1-1-12-211-1-111000000000000
χ242222-1-2-2-1-1-1-222-1-1-1-121122-1-1-1-12222-1-1-1-1-1-1-1-111-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2221111-22-1-111-1-1000000000000
χ2522-2-22002-2-20222222000-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002i2i−2i−2i002i2i−2i−2i00000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000
χ2622-2-22002-2-20222222000-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002i2i−2i−2i002i2i−2i−2i0000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000
χ2722-2-22002-2-20222222000-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000−2i−2i2i2i00−2i−2i2i2i0000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000
χ2822-2-22002-2-20222222000-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000−2i−2i2i2i00−2i−2i2i2i00000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000
χ292-22-2200-22-20222222000-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000000000002i−2i2i−2i002i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000
χ302-22-2200-22-20222222000-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000000000002i−2i2i−2i002i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000
χ312-22-2200-22-20222222000-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000−2i2i−2i2i00−2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000
χ322-22-2200-22-20222222000-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000−2i2i−2i2i00−2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000
χ332-2-2222i−2i-2-220222222000222222-2-2-2-2-2-2-2-2-2-2-2-22i−2i000000000000002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000002-2-222i−2i2-2-22002i−2i0000000000000000
χ342-2-2222i−2i-2-220222222000222222-2-2-2-2-2-2-2-2-2-2-2-22i−2i000000000000002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000-222-2−2i2i-222-200−2i2i0000000000000000
χ352-2-222−2i2i-2-220222222000222222-2-2-2-2-2-2-2-2-2-2-2-2−2i2i00000000000000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000002-2-22−2i2i2-2-2200−2i2i0000000000000000
χ362-2-222−2i2i-2-220222222000222222-2-2-2-2-2-2-2-2-2-2-2-2−2i2i00000000000000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000-222-22i−2i-222-2002i−2i0000000000000000
χ372-2-22-12i−2i11-1022-1-1-1-10−i3i322-1-1-1-1-2-2-2-211111111−ii3−30000−i3−i3−i3−i3i3i3i3i32i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−32-2-222i−2i-111-100−ii3−3−i3i3000000000000
χ382-2-22-12i−2i11-1022-1-1-1-10−i3i322-1-1-1-1-2-2-2-211111111−ii3−30000−i3−i3−i3−i3i3i3i3i32i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−3-222-2−2i2i1-1-1100i−i−33i3−i3000000000000
χ392-2-22-12i−2i11-1022-1-1-1-10i3−i322-1-1-1-1-2-2-2-211111111−ii−330000i3i3i3i3−i3−i3−i3−i32i2i−2i−2i−i−i−i−iiiii0000−3−3−3−333332-2-222i−2i-111-100−ii−33i3−i3000000000000
χ402-2-22-12i−2i11-1022-1-1-1-10i3−i322-1-1-1-1-2-2-2-211111111−ii−330000i3i3i3i3−i3−i3−i3−i32i2i−2i−2i−i−i−i−iiiii0000−3−3−3−33333-222-2−2i2i1-1-1100i−i3−3−i3i3000000000000
χ412-2-22-1−2i2i11-1022-1-1-1-10−i3i322-1-1-1-1-2-2-2-211111111i−i−330000−i3−i3−i3−i3i3i3i3i3−2i−2i2i2iiiii−i−i−i−i0000−3−3−3−333332-2-22−2i2i-111-100i−i−33−i3i3000000000000
χ422-2-22-1−2i2i11-1022-1-1-1-10−i3i322-1-1-1-1-2-2-2-211111111i−i−330000−i3−i3−i3−i3i3i3i3i3−2i−2i2i2iiiii−i−i−i−i0000−3−3−3−33333-222-22i−2i1-1-1100−ii3−3i3−i3000000000000
χ432-2-22-1−2i2i11-1022-1-1-1-10i3−i322-1-1-1-1-2-2-2-211111111i−i3−30000i3i3i3i3−i3−i3−i3−i3−2i−2i2i2iiiii−i−i−i−i00003333−3−3−3−32-2-22−2i2i-111-100i−i3−3i3−i3000000000000
χ442-2-22-1−2i2i11-1022-1-1-1-10i3−i322-1-1-1-1-2-2-2-211111111i−i3−30000i3i3i3i3−i3−i3−i3−i3−2i−2i2i2iiiii−i−i−i−i00003333−3−3−3−3-222-22i−2i1-1-1100−ii−33−i3i3000000000000
χ45444444444441-211-2-24441-211-2-21-21-211-2-211-2-2444411-2-211-2-211-2-21-21-211-2-211-2-211-2-211-2-211-2-2000000000000000000000000000000
χ4644444444444-21-2-211444-21-2-211-21-21-2-211-2-2114444-2-211-2-211-2-211-21-21-2-211-2-211-2-211-2-211-2-211000000000000000000000000000000
χ474444444444-41-211-2-2-4-4-41-211-2-21-21-211-2-211-2-244-4-4-1-122-1-122-1-1221-21-211-2-211-2-2-1-122-1-122-1-122000000000000000000000000000000
χ484444444444-4-21-2-211-4-4-4-21-2-211-21-21-2-211-2-21144-4-422-1-122-1-122-1-1-21-21-2-211-2-21122-1-122-1-122-1-1000000000000000000000000000000
χ4944444-4-444441-211-2-2-4441-211-2-21-21-211-2-211-2-2-4-4-4-411-2-211-2-211-2-2-12-12-1-122-1-122-1-122-1-122-1-122000000000000000000000000000000
χ5044444-4-44444-21-2-211-444-21-2-211-21-21-2-211-2-211-4-4-4-4-2-211-2-211-2-2112-12-122-1-122-1-122-1-122-1-122-1-1000000000000000000000000000000
χ5144444-4-4444-41-211-2-24-4-41-211-2-21-21-211-2-211-2-2-4-444-1-122-1-122-1-122-12-12-1-122-1-12211-2-211-2-211-2-2000000000000000000000000000000
χ5244444-4-4444-4-21-2-2114-4-4-21-2-211-21-21-2-211-2-211-4-44422-1-122-1-122-1-12-12-122-1-122-1-1-2-211-2-211-2-211000000000000000000000000000000
χ534444-244-2-2-241-2−1−3i32−1+3i32114-2-21-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-2-2-2-211-2-2−1−3i32−1+3i3211−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000000000000
χ544444-244-2-2-241-2−1+3i32−1−3i32114-2-21-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-2-2-2-211-2-2−1+3i32−1−3i3211−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000000000000
χ554444-244-2-2-24-2111−1−3i32−1+3i324-2-2-2111−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-2-2-2-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000000000000000000
χ564444-244-2-2-24-2111−1+3i32−1−3i324-2-2-2111−1+3i32−1−3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2-2-2-2-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i32000000000000000000000000000000
χ574444-244-2-2-2-41-2−1−3i32−1+3i3211-4221-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-2-222-1-1221+3i321−3i32-1-11+3i321−3i32-1-11-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
χ584444-244-2-2-2-41-2−1+3i32−1−3i3211-4221-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-2-222-1-1221−3i321+3i32-1-11−3i321+3i32-1-11-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-1000000000000000000000000000000
χ594444-244-2-2-2-4-2111−1−3i32−1+3i32-422-2111−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-22222-1-1-1-11+3i321−3i32-1-11+3i321−3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i32000000000000000000000000000000
χ604444-244-2-2-2-4-2111−1+3i32−1−3i32-422-2111−1+3i32−1−3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2-22222-1-1-1-11−3i321+3i32-1-11−3i321+3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i32000000000000000000000000000000
χ614444-2-4-4-2-2-241-2−1−3i32−1+3i3211-4-2-21-2−1−3i32−1+3i32111-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211222211-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211-12-121+3i321−3i32-1-11+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
χ624444-2-4-4-2-2-241-2−1+3i32−1−3i3211-4-2-21-2−1+3i32−1−3i32111-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211222211-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211-12-121−3i321+3i32-1-11−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-1000000000000000000000000000000
χ634444-2-4-4-2-2-24-2111−1−3i32−1+3i32-4-2-2-2111−1−3i32−1+3i32-21-2111−1−3i32−1+3i3211−1−3i32−1+3i322222-2-21111−1−3i32−1+3i3211−1−3i32−1+3i322-12-1-1-11+3i321−3i32-1-11+3i321−3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i32000000000000000000000000000000
χ644444-2-4-4-2-2-24-2111−1+3i32−1−3i32-4-2-2-2111−1+3i32−1−3i32-21-2111−1+3i32−1−3i3211−1+3i32−1−3i322222-2-21111−1+3i32−1−3i3211−1+3i32−1−3i322-12-1-1-11−3i321+3i32-1-11−3i321+3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i32000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.