Finite Group Databasebeta

← Group #13155740

Character table — Group #13155740

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order124423334666121212121212333666666661212121212121212121212444436666612121212121288882466881212121212121212121212121212121212122424242488242424246661212122424242424242488242488886122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-111
χ911-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1ii−i−i1-1-1-1-111111-1-1ii−i−i1-111i−i-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−ii−iii−i−i111-1-1-1i−iii−i−i1-1i−ii−i11-1-11-1i−i
χ1011-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1ii−i−i1-1-1-1-111111-1-1ii−i−i-11-1-1−ii11iiiiiiii−i−i−i−i−i−i−i−i−i−iiii−iii−i−i-1-1-1111−ii−i−iii-11−iii−i11-1-1-11−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1ii−i−i1-1-1-1-111111-1-1−i−iii1-111−ii-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−ii−i−iii111-1-1-1−ii−i−iii-11i−i−ii-1-111-11i−i
χ1211-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1ii−i−i1-1-1-1-111111-1-1−i−iii-11-1-1i−i11iiiiiiii−i−i−i−i−i−i−i−iii−i−i−ii−i−iii-1-1-1111i−iii−i−i1-1−ii−ii-1-1111-1−ii
χ1311-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1−i−iii1-1-1-1-111111-1-1ii−i−i1-111i−i-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−ii−iii−i−i111-1-1-1i−iii−i−i-11−iii−i-1-111-11−ii
χ1411-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1−i−iii1-1-1-1-111111-1-1ii−i−i-11-1-1−ii11−i−i−i−i−i−i−i−iiiiiiiii−i−iiii−iii−i−i-1-1-1111−ii−i−iii1-1i−ii−i-1-1111-1i−i
χ1511-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1−i−iii1-1-1-1-111111-1-1−i−iii1-111−ii-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−ii−i−iii111-1-1-1−ii−i−iii1-1−ii−ii11-1-11-1−ii
χ1611-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1111111-1-1-1-1-1-1−i−iii1-1-1-1-111111-1-1−i−iii-11-1-1i−i11−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−ii−i−iii-1-1-1111i−iii−i−i-11i−i−ii11-1-1-11i−i
χ172222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-12222-1-12-1-1-1-12-1-1-1-100000000220022-1-1-1-1-1-122-1-1-1-1-1-12222000000000000-1-1-1-1-1-12200000000-1-100
χ182222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-12222-1-12-1-1-1-12-1-1-1-100000000-2-20022-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2000000000000111111-2-2000000001100
χ192222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-2-2-2-2-1-12-1-1-1-12-1-1-1-1000000002200-2-2111111-2-21111112222000000000000-1-1-1-1-1-1-2-2000000001100
χ202222222-1222-1-1-12222-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-2-2-2-2-1-12-1-1-1-12-1-1-1-100000000-2-200-2-2111111-2-2111111-2-2-2-20000000000001111112200000000-1-100
χ21222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1222222-1-122-1-10000000000000000-1-1-1-122-1-1-1-12-1-12-1-122-1-1-1-10000-1-100000000
χ22222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-12222-2-211-2-2110000000000000000111122-1-1-1-1-211-211-2-211110000-1-100000000
χ23222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-1-2-2-1-100000000000000001111-2-211112-1-12-1-1-2-2111100001100000000
χ24222222-1222-122222-1-12-1-1-12-12222-12-122222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21122110000000000000000-1-1-1-1-2-21111-211-21122-1-1-1-100001100000000
χ2522222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-1222222-12-1-1-1-12-1-1-1-1-1000022220022-1-122-1-1-1-1-1-122-1-1-1-10000000000-1-1-1-1-1-1000000002200000000-1-1
χ2622222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-1222222-12-1-1-1-12-1-1-1-1-10000-2-2-2-200-2-2-1-122-1-1-1-1-1-122-1-1-1-1000000000011111100000000-2-20000000011
χ2722222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-122-2-2-2-2-12-1-1-1-12-1-1-1-1-100002222002211-2-2111111-2-211110000000000-1-1-1-1-1-100000000-2-20000000011
χ2822222-1222-12222-1-122-12-12-12-12-1-1-1-122-1-1-1-1-1-122-2-2-2-2-12-1-1-1-12-1-1-1-1-10000-2-2-2-200-2-211-2-2111111-2-211110000000000111111000000002200000000-1-1
χ292222-2222-2222222222222-222-2-2-2-22-2-2-2-2-222222200002-2-2-2-22-2-2-2-22222220000000000000000000000000000-2-222220000000000000000-2-200000000
χ302222-2222-2222222222222-222-2-2-2-22-2-2-2-2-222222200002-2-2-2-22-2-2-2-222-2-2-2-2000000000000000000000000000022-2-2-2-200000000000000002200000000
χ312222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-10000-11111-11111-1-1222200−i3i300−i3i30000000000000000−i3i3−i3i3-2-2-1-1-1-10−i3i30−i3i300−i3i3−i3i300001100000000
χ322222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-10000-11111-11111-1-1222200i3−i300i3−i30000000000000000i3−i3i3−i3-2-2-1-1-1-10i3−i30i3−i300i3−i3i3−i300001100000000
χ332222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-10000-11111-11111-1-1-2-2-2-200−i3i300−i3i30000000000000000i3−i3i3−i32211110−i3i30−i3i300i3−i3i3−i30000-1-100000000
χ342222-22-12-22-122222-1-12-1-112-1-2-2-2-2-1-21-2-2-222-1-1-1-10000-11111-11111-1-1-2-2-2-200i3−i300i3−i30000000000000000−i3i3−i3i32211110i3−i30i3−i300−i3i3−i3i30000-1-100000000
χ3522-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-22i2i−2i−2i0000000000000000000000000000−2i2i2i2i−2i−2i0000000000000000−2i2i00000000
χ3622-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2−2i−2i2i2i00000000000000000000000000002i−2i−2i−2i2i2i00000000000000002i−2i00000000
χ3722-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-211110000-1-1-1-1-1-11111112i2i−2i−2i00−i3i300i3−i300000000000000003−3−33−2i2i−i−iii0−i3i30i3−i3003−3−330000i−i00000000
χ3822-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-211110000-1-1-1-1-1-11111112i2i−2i−2i00i3−i300−i3i30000000000000000−333−3−2i2i−i−iii0i3−i30−i3i300−333−30000i−i00000000
χ3922-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-211110000-1-1-1-1-1-1111111−2i−2i2i2i00−i3i300i3−i30000000000000000−333−32i−2iii−i−i0−i3i30i3−i300−333−30000−ii00000000
χ4022-2-222-12-22-12-2-2-2-2112-1-1-12-12222-1-21-2-2-2-2-211110000-1-1-1-1-1-1111111−2i−2i2i2i00i3−i300−i3i300000000000000003−3−332i−2iii−i−i0i3−i30−i3i3003−3−330000−ii00000000
χ4122-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-2112i2i−2i−2i-11-211-1-12-1-111000000002i−2i002i2i−i−i−i−i−i−i−2i−2iiiiiii2i2i−2i−2i000000000000−ii−i−iii2-200000000-1100
χ4222-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-2112i2i−2i−2i-11-211-1-12-1-11100000000−2i2i002i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2i2i2i000000000000i−iii−i−i-22000000001-100
χ4322-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-211−2i−2i2i2i-11-211-1-12-1-111000000002i−2i00−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−2i−2i000000000000−ii−i−iii-22000000001-100
χ4422-2-2-222-1222-111-2-2-2-2-1-12-2-1-1-2111222-1-1-111-2-211−2i−2i2i2i-11-211-1-12-1-11100000000−2i2i00−2i−2iiiiiii2i2i−i−i−i−i−i−i−2i−2i2i2i000000000000i−iii−i−i2-200000000-1100
χ4522-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-211110000-11111-1-1-1-1-1112i2i−2i−2i2-2-1-12i−2i110000000000000000−i−iii2i−2i−i−iii2-1-1-2112i−2i−i−iii0000−ii00000000
χ4622-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-211110000-11111-1-1-1-1-1112i2i−2i−2i-2211−2i2i-1-10000000000000000ii−i−i2i−2i−i−iii-2112-1-1−2i2iii−i−i0000−ii00000000
χ4722-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-211110000-11111-1-1-1-1-111−2i−2i2i2i2-2-1-1−2i2i110000000000000000ii−i−i−2i2iii−i−i2-1-1-211−2i2iii−i−i0000i−i00000000
χ4822-2-2-22-1222-12-2-2-2-2112-1-112-1-2-2-2-2-12-1222-2-211110000-11111-1-1-1-1-111−2i−2i2i2i-22112i−2i-1-10000000000000000−i−iii−2i2iii−i−i-2112-1-12i−2i−i−iii0000i−i00000000
χ4922-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-22i2i−2i−2i-1-2111-12-1-1-11100002-22200-2-2−i−i2i2i−i−i−i−iii−2i−2iiiii0000000000-1-1-1111000000002i−2i00000000−ii
χ5022-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-22i2i−2i−2i-1-2111-12-1-1-1110000-22-2-20022−i−i2i2i−i−i−i−iii−2i−2iiiii0000000000111-1-1-100000000−2i2i00000000i−i
χ5122-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-2−2i−2i2i2i-1-2111-12-1-1-11100002-22200-2-2ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000-1-1-111100000000−2i2i00000000i−i
χ5222-2-2-2-1222-122-2-211-2-2-12-1-2-121-211-1-122-1-11111-2-2−2i−2i2i2i-1-2111-12-1-1-1110000-22-2-20022ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000111-1-1-1000000002i−2i00000000−ii
χ532-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-20000-2000002i−2i2i−2i2i−2i1+i−1−i1−i−1+i20000-200002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000001+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000002−2−i2i20000
χ542-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-20000-2000002i−2i2i−2i2i−2i1+i−1−i1−i−1+i20000-200002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000001+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000−22i2−i20000
χ552-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-20000-2000002i−2i2i−2i2i−2i−1−i1+i−1+i1−i20000-200002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000−22i2−i20000
χ562-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-20000-2000002i−2i2i−2i2i−2i−1−i1+i−1+i1−i20000-200002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000002−2−i2i20000
χ572-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-20000-200000−2i2i−2i2i−2i2i1−i−1+i1+i−1−i20000-20000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000001−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000002−2i2−i20000
χ582-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-20000-200000−2i2i−2i2i−2i2i1−i−1+i1+i−1−i20000-20000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000001−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000−22−i2i20000
χ592-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-20000-200000−2i2i−2i2i−2i2i−1+i1−i−1−i1+i20000-20000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−1+i1−i−1+i1−i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1−i−1−i1+i1+i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000−22−i2i20000
χ602-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-20000-200000−2i2i−2i2i−2i2i−1+i1−i−1−i1+i20000-20000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−1+i1−i−1+i1−i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1−i−1−i1+i1+i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000002−2i2−i20000
χ61444444-2-244-2-2-2-244-2-2-21-2-2-214-2-2-2-24-2-2-2-2-2-2-2-211000011-21111-211110000000044000000000000000000-2-2-2-2000000000000-2-2111100000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.