Finite Group Databasebeta

← Group #13155741

Character table — Group #13155741

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11112222222222222222224444444444444444444444446666666666666666666666668888888888999912121212121212121212121212121212121212121212121212121818181818181818181824242424242424243636363672727272108108
order124423334666661212121212121212333666666666121212121212121212121212444488881212121212121212242424242424242436666121212121288888812121212121212121212121224242424242424242424242488242424242424242424242424242424242488612242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1
χ911-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1-1-11111-1-1ii−i−ii−iiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1i−iiiii−i−i−i−ii−ii−iii−i−i1-1i−i1-1i−i1-1
χ1011-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1ii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11-1-1-11111-1-1ii−i−i−iiiiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1i−iiiii−i−i−i−i−ii−ii−i−iii-11−ii-11−ii-11
χ1111-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1ii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1-1-11111-1-1−i−iiii−iiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−ii−i−i−i−iiiiii−ii−iii−i−i1-1−ii1-1−ii-11
χ1211-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1ii−i−i-1-111iiii−i−i−i−i-1-1-1-111111-1-1-11111-1-1−i−iii−iiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−ii−i−i−i−iiiii−ii−ii−i−iii-11i−i-11i−i1-1
χ1311-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1-1-11111-1-1−i−iiii−i−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−ii−i−i−i−iiiiii−ii−iii−i−i-11i−i-11i−i-11
χ1411-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-11-1-1-11111-1-1−i−iii−ii−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−ii−i−i−i−iiiii−ii−ii−i−iii1-1−ii1-1−ii1-1
χ1511-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-1-11111-1-1ii−i−ii−i−i−i−i−i−i−iiiiiii-1-1-1-1-1-1111111i−iiiii−i−i−i−ii−ii−iii−i−i-11−ii-11−ii1-1
χ1611-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-1−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-1-11111-1-1ii−i−i−ii−i−i−i−i−i−iiiiiii-1-1-1-1-1-1111111i−iiiii−i−i−i−i−ii−ii−i−iii1-1i−i1-1i−i-11
χ172222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000-1-122-1-1-1-12200-1-10000
χ182222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-10000-2-2-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000011-2-21111-2-200110000
χ192222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-10000221111111111110000000000000000000000-1-122-1-1-1-1-2-200110000
χ202222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-10000-2-2111111111111000000000000000000000011-2-211112200-1-10000
χ21222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000022000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-1-1-1-1-1002200-1-100
χ22222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-10000-2-2000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-211111100-2-2001100
χ23222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000022000000000000111111111111000000000022-1-1-1-1-1-100-2-2001100
χ24222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-20000000000001111111111110000000000-2-2111111002200-1-100
χ2522222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1-122220022-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000
χ2622222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-1222222-2-2-2-2-1-1-1-1-1-1-1-111111111-12-1-1-12-1-1-1-1-2-2-2-20022-1-1-1-122-1-1-1-1-2-21111-2-21111-2-211111111000000000000000000
χ2722222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-122-2-2-2-2222211111111-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1-1-2-2-2-200-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-211111111000000000000000000
χ2822222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-122-2-2-2-2-2-2-2-21111111111111111-12-1-1-12-1-1-1-1222200-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-1-1-1-1000000000000000000
χ292222-2222-222-2-22-2-2222222222-2-2-2222-2-2-2-2-2-22222-2-2-2220000000000000000000000002-2-2-22-2-2-222222200000000000000000000000000-2-222-2-222-2-2000000000000000000
χ302222-2222-222-2-22-2-2222222222-2-2-2222-2-2-2-2-2-22222-2-2-2220000000000000000000000002-2-2-22-2-2-222-2-2-2-20000000000000000000000000022-2-222-2-222000000000000000000
χ312222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-211220000000033−3−333−3−333−3−333−3−3-1-211-1-211-1-12222000033−3−30033−3−30033−3−30033−3−3-2-2-1-111-1-111000000000000000000
χ322222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-211220000000033−3−333−3−3−3−333−3−333-1-211-1-211-1-1-2-2-2-2000033−3−30033−3−300−3−33300−3−3332211-1-111-1-1000000000000000000
χ332222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-2112200000000−3−333−3−33333−3−333−3−3-1-211-1-211-1-1-2-2-2-20000−3−33300−3−3330033−3−30033−3−32211-1-111-1-1000000000000000000
χ342222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-2112200000000−3−333−3−333−3−333−3−333-1-211-1-211-1-122220000−3−33300−3−33300−3−33300−3−333-2-2-1-111-1-111000000000000000000
χ3522-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000022222-2-2-2-2-22i2i−2i−2i00000000000000000000000000−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000
χ3622-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000022222-2-2-2-2-2−2i−2i2i2i000000000000000000000000002i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000
χ3722-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-200000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333-12-1-1-1-21111−2i−2i2i2i0000−i3−i3i3i300i3i3−i3−i30033−3−300−3−3332i−2iii−i−i−i−iii000000000000000000
χ3822-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-200000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3-12-1-1-1-211112i2i−2i−2i0000−i3−i3i3i300i3i3−i3−i300−3−3330033−3−3−2i2i−i−iiiii−i−i000000000000000000
χ3922-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-200000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333-12-1-1-1-211112i2i−2i−2i0000i3i3−i3−i300−i3−i3i3i30033−3−300−3−333−2i2i−i−iiiii−i−i000000000000000000
χ4022-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-200000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3-12-1-1-1-21111−2i−2i2i2i0000i3i3−i3−i300−i3−i3i3i300−3−3330033−3−32i−2iii−i−i−i−iii000000000000000000
χ4122-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-211222112i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i00000000-1111-1-1-1-11100002i−2i−i−i−i−i−i−iiiiiii0000000000000000000000−ii2i−2i−i−iii2-200-110000
χ4222-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-211222112i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i00000000-1111-1-1-1-1110000−2i2i−i−i−i−i−i−iiiiiii0000000000000000000000i−i−2i2iii−i−i-22001-10000
χ4322-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-21122211−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i00000000-1111-1-1-1-11100002i−2iiiiiii−i−i−i−i−i−i0000000000000000000000−ii2i−2i−i−iii-22001-10000
χ4422-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-21122211−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i00000000-1111-1-1-1-1110000−2i2iiiiiii−i−i−i−i−i−i0000000000000000000000i−i−2i2iii−i−i2-200-110000
χ4522-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-111000022-2-2000000002222-2-2-2-2-1111-1-1-1-11100002i−2i000000000000-1-1-1-1-1-111111100000000002i−2i−ii−i−iii002i−2i00−ii00
χ4622-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-111000022-2-2000000002222-2-2-2-2-1111-1-1-1-1110000−2i2i000000000000-1-1-1-1-1-11111110000000000−2i2ii−iii−i−i00−2i2i00i−i00
χ4722-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-1110000-2-22200000000-2-2-2-22222-1111-1-1-1-11100002i−2i000000000000111111-1-1-1-1-1-100000000002i−2i−ii−i−iii00−2i2i00i−i00
χ4822-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-1110000-2-22200000000-2-2-2-22222-1111-1-1-1-1110000−2i2i000000000000111111-1-1-1-1-1-10000000000−2i2ii−iii−i−i002i−2i00−ii00
χ4922-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-22i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-11111-1-211-12-1-1112i2i−2i−2i002i2i−i−i−i−i−2i−2iiiii22-1-1-1-1-2-211112i−2i−i−i−i−iiiii000000000000000000
χ5022-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-22i2i−2i−2i-2-222−i−i−i−iiiii1111-1-1-1-1-1-211-12-1-111−2i−2i2i2i002i2i−i−i−i−i−2i−2iiiii-2-2111122-1-1-1-1−2i2iiiii−i−i−i−i000000000000000000
χ5122-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-2−2i−2i2i2i22-2-2iiii−i−i−i−i-1-1-1-11111-1-211-12-1-111−2i−2i2i2i00−2i−2iiiii2i2i−i−i−i−i22-1-1-1-1-2-21111−2i2iiiii−i−i−i−i000000000000000000
χ5222-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-2−2i−2i2i2i-2-222iiii−i−i−i−i1111-1-1-1-1-1-211-12-1-1112i2i−2i−2i00−2i−2iiiii2i2i−i−i−i−i-2-2111122-1-1-1-12i−2i−i−i−i−iiiii000000000000000000
χ532-22i−2i02220-2-200-2002i−2i2i−2i2i−2i222000-2-2-20000002i−2i2i−2i0002i−2i1+i−1−i1−i−1+i2−2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2−i2i2−i2i22000-20002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13001+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i2−22−22−2−i2i2−i2i2−i2i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ542-22i−2i02220-2-200-2002i−2i2i−2i2i−2i222000-2-2-20000002i−2i2i−2i0002i−2i1+i−1−i1−i−1+i−22i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−22i2−i2i2−i22000-20002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13001+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i−22−22−22i2−i2i2−i2i2−i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
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χ1388-8−8i8i0-4-4-40444i3−4i3443−434i−4i4i−4i4i−4i2220−2i32i3-2-2-20−2i32i30−2323−2i2i−2i2i0−2323−2i2i000000000000000000000000-10i3−i3103−3i−i0000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.