Finite Group Databasebeta

← Group #13155007

Character table — Group #13155007

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218181818363636363636363672727272108108108108
order1244234666121212123333666666666612121212121212121212121212123666612121212128888242424242424242424242424242424242424242424242424242424242424242422446688881212242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ51111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1ii−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1-11-11-111-1-11-111-1-1ii−i−i
χ61111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1ii−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i1-11-11-1-1-1111-1-1-111−i−iii
χ71111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1−i−iii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1-11-11-111-1-11-111-1-1−i−iii
χ81111-11-1-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-111-1-1−i−iii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii1-11-11-1-1-1111-1-1-111ii−i−i
χ911-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-111i−ii−i-1-1i−ii−i1-11-1
χ1011-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-111−ii−ii-1-1−ii−ii-11-11
χ1111-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii11-1-111i−ii−i-1-1i−ii−i-11-11
χ1211-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii11-1-111−ii−ii-1-1−ii−ii1-11-1
χ1311-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1i−i−ii-11i−i−ii−iii−i
χ1411-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1−iii−i-11−iii−ii−i−ii
χ1511-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-111-111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-111-1i−i−ii-11i−i−iii−i−ii
χ1611-1-1-111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-111-1-111-111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-111-1−iii−i-11−iii−i−iii−i
χ172222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-2-2-20000-2-200000000
χ1822222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-10000−i3i3−i3i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-2-2-21100001100000000
χ1922222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-10000i3−i3i3−i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-2-2-21100001100000000
χ2022222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-10000-1-100000000
χ2122222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-21111-2-211112222-1-10000-1-100000000
χ222222-22-2-2-2222-2-22222-2-2-2-2-2-22222222222-2-2-2-2-2-2222-2-2-22-222-2-2000000000000000000000000000000000000-22-22-220000-2200000000
χ232222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-11100003−33−3−33−330033−3−30033−3−300−3−33300−3−333-22-221-100001-100000000
χ242222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-1110000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-22-221-100001-100000000
χ252222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-1112i2i−2i−2i−i−i−i−iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2-22-2-110000-1100000000
χ262222-2-1-211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-2111122-1-211-1-2-1-111−2i−2i2i2iiiii−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i2-22-2-110000-1100000000
χ2722-2-222-2222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2000000000000000000000000000000000000-2-222-2-200002200000000
χ2822-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-2111100003−3−333−3−330033−3−300−3−3330033−3−300−3−333-2-222110000-1-100000000
χ2922-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-211110000−333−3−333−300−3−3330033−3−300−3−3330033−3−3-2-222110000-1-100000000
χ3022-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-211112i−2i2i−2i−i−iii−i−iii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii22-2-2-1-100001100000000
χ3122-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2-12-1-1-1-21111−2i2i−2i2iii−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i22-2-2-1-100001100000000
χ3222-2-2-222-2-22-2-2222222-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-22-2-2-222-2-222000000000000000000000000000000000000-222-2-2200002-200000000
χ3322-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-10000−i3i3i3−i3i3−i3−i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i3-222-21-10000-1100000000
χ3422-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-10000i3−i3−i3i3−i3i3i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i3-222-21-10000-1100000000
χ3522-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-12-2-22-1-11111-1-122-1-1-1-1-2-21111-2-2111122-1-1-1-12-2-22-1100001-100000000
χ3622-2-2-2-1211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1-2-2-1-211-1211-1-1-222-211-1-1-1-111-2-2111122-1-1-1-122-1-1-1-1-2-211112-2-22-1100001-100000000
χ37444444444444441-2111111111-211111111111111-2-2-2-2-2-2-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ38444444444444441-2111111111-211111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000000
χ3944444444444444-21-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000222200-1-1-1-10000
χ4044444444444444-21-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000-2-2-2-20011110000
χ4144444-24-2-2-2-2-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-2111-211112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ4244444-24-2-2-2-2-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-21-2111-21111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ4344444-24-2-2-2-2-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-2111-211112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ4444444-24-2-2-2-2-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-21-2111-21111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ454444-44-4-4-4444-4-41-211-1-1-1-1-1-11-211111111-1-1-1-1-1-1-2-2-2222-22-2-2222i2i−2i−2i2i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii00000000000000000000
χ464444-44-4-4-4444-4-41-211-1-1-1-1-1-11-211111111-1-1-1-1-1-1-2-2-2222-22-2-222−2i−2i2i2i−2i−2i−2i−2i2i2i2i2iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i00000000000000000000
χ474444-44-4-4-4444-4-4-21-2-2222222-21-2-2-2-2-2-2-2-2222222111-1-1-11-111-1-100000000000000000000000000000000000000000022-2-200-1-1110000
χ484444-44-4-4-4444-4-4-21-2-2222222-21-2-2-2-2-2-2-2-2222222111-1-1-11-111-1-1000000000000000000000000000000000000000000-2-2220011-1-10000
χ494444-4-2-422-2-2-2221-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i321-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-2-212-1-11211-1-12i2i−2i−2i2ζ222ζ142ζ222ζ14−2ζ22−2ζ14−2ζ22−2ζ14−i−i−ζ22−ζ22−ζ14−ζ14−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ14iiζ22ζ22ζ14ζ1400000000000000000000
χ504444-4-2-422-2-2-2221-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i321-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-2-212-1-11211-1-1−2i−2i2i2i−2ζ22−2ζ14−2ζ22−2ζ142ζ222ζ142ζ222ζ14iiζ22ζ22ζ14ζ14iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ14−i−i−ζ22−ζ22−ζ14−ζ1400000000000000000000
χ514444-4-2-422-2-2-2221-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i321-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-2-212-1-11211-1-12i2i−2i−2i2ζ142ζ222ζ142ζ22−2ζ14−2ζ22−2ζ14−2ζ22−i−i−ζ14−ζ14−ζ22−ζ22−i−i−ζ14−ζ14−ζ22−ζ22iiζ14ζ14ζ22ζ22iiζ14ζ14ζ22ζ2200000000000000000000
χ524444-4-2-422-2-2-2221-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i321-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-2-212-1-11211-1-1−2i−2i2i2i−2ζ14−2ζ22−2ζ14−2ζ222ζ142ζ222ζ142ζ22iiζ14ζ14ζ22ζ22iiζ14ζ14ζ22ζ22−i−i−ζ14−ζ14−ζ22−ζ22−i−i−ζ14−ζ14−ζ22−ζ2200000000000000000000
χ5344-4-444-4444-4-4-4-41-2111111111-211-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2222222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii00000000000000000000
χ5444-4-444-4444-4-4-4-41-2111111111-211-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-222222−2i2i−2i2i−2i−2i2i2i−2i−2i2i2iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i00000000000000000000
χ5544-4-444-4444-4-4-4-4-21-2-2-2-2-2-2-2-2-21-2-2222222222222-1-111111-1-1-1-1-10000000000000000000000000000000000000000002i−2i2i−2i00−ii−ii0000
χ5644-4-444-4444-4-4-4-4-21-2-2-2-2-2-2-2-2-21-2-2222222222222-1-111111-1-1-1-1-1000000000000000000000000000000000000000000−2i2i−2i2i00i−ii−i0000
χ5744-4-44-2-4-2-2-222221-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32221-21112-1-1-1-12i−2i2i−2i2ζ222ζ14−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ14−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ1400000000000000000000
χ5844-4-44-2-4-2-2-222221-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32221-21112-1-1-1-1−2i2i−2i2i−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ142ζ222ζ14iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ1400000000000000000000
χ5944-4-44-2-4-2-2-222221-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i32221-21112-1-1-1-12i−2i2i−2i2ζ142ζ22−2ζ14−2ζ222ζ142ζ22−2ζ14−2ζ22−i−i−ζ14−ζ14−ζ22−ζ22iiζ14ζ14ζ22ζ22−i−i−ζ14−ζ14−ζ22−ζ22iiζ14ζ14ζ22ζ2200000000000000000000
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χ974-4−4i4i0-202i3−2i322i−2i23−231-2−1+3i32−1−3i323-3−3+i323−i32−3−i323+i32-121−3i321+3i32−ii−2ζ14+ζ222ζ14−ζ22ζ14−2ζ22−ζ14+2ζ22−3i3i−2ζ14−ζ222ζ14+ζ22−ζ14−2ζ22ζ14+2ζ22−2i2i10i3−i3-10i−i3−3000000000000ζ7−ζ23−ζ7+ζ23−2ζ7−ζ232ζ7+ζ23ζ7+2ζ23−ζ7−2ζ23−ζ5+ζ13ζ5−ζ13−ζ5−2ζ13ζ5+2ζ132ζ5+ζ13−2ζ5−ζ13ζ7−ζ23−ζ7+ζ23−2ζ7−ζ232ζ7+ζ23ζ7+2ζ23−ζ7−2ζ23−ζ5+ζ13ζ5−ζ13−ζ5−2ζ13ζ5+2ζ132ζ5+ζ13−2ζ5−ζ1300000000000000000000
χ984-4−4i4i0-202i3−2i322i−2i23−2344-2-2002i3−2i3−2i32i3-4-422−4i4i2i−2i2i−2i0023−23−23234i−4i-20−2i32i320−2i2i−232300000000000000000000000000000000000000000000000000000000
χ9988888-48-4-4-4-4-4-4-4-4222-4-42222-4222-4-42222-4-4222222-12-1-1-12-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1008888-8-4-844-4-4-444-422244-2-2-2-2-4222-4-4222244-2-2-2-222-1-211-1-2-1-11100000000000000000000000000000000000000000000000000000000
χ10188-8-88-4-8-4-4-44444-4222-4-42222-422244-2-2-2-244-2-2-2-2-2-2-12-1-1-1-2111100000000000000000000000000000000000000000000000000000000
χ10288-8-8-8-4844-444-4-4-422244-2-2-2-2-422244-2-2-2-2-4-42222-2-2-1-211-1211-1-100000000000000000000000000000000000000000000000000000000
χ1038-88i−8i08000-88i−8i00-42-4-40000004-244−4i4i−4i4i−4i4i000000−2i2i2000-20−2i2i0000000000000000000000000000000000000000000000000000000000
χ1048-88i−8i0-40−4i34i34−4i4i43−43-4222002i3−2i3−2i32i34-2-2-2−4i4i2i−2i2i−2i00−232323−23−2i2i-10i3−i310i−i−3300000000000000000000000000000000000000000000000000000000
χ1058-88i−8i0-404i3−4i34−4i4i−4343-422200−2i32i32i3−2i34-2-2-2−4i4i2i−2i2i−2i0023−23−2323−2i2i-10−i3i310i−i3−300000000000000000000000000000000000000000000000000000000
χ1068-8−8i8i08000-8−8i8i00-42-4-40000004-2444i−4i4i−4i4i−4i0000002i−2i2000-202i−2i0000000000000000000000000000000000000000000000000000000000
χ1078-8−8i8i0-40−4i34i344i−4i−4343-4222002i3−2i3−2i32i34-2-2-24i−4i−2i2i−2i2i0023−23−23232i−2i-10i3−i310−ii3−300000000000000000000000000000000000000000000000000000000
χ1088-8−8i8i0-404i3−4i344i−4i43−43-422200−2i32i32i3−2i34-2-2-24i−4i−2i2i−2i2i00−232323−232i−2i-10−i3i310−ii−3300000000000000000000000000000000000000000000000000000000

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