Finite Group Databasebeta

← Group #13155503

Character table — Group #13155503

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order124423334666121212121212333666666661212121212121212121212888836666612121212121222448888242424242424242424242424242424242424242424242424246612122424242424242424242424246888812888824242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-11111-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1111111-1-1
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-111-1-11-1-1-1-111111-1-111-1-1i−ii−iii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1111-1-1i−ii−iii−i−iii−i−i-1i−ii−i111-1-1i−ii−i
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-111-1-11-1-1-1-111111-1-111-1-1−ii−ii−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1111-1-1−ii−ii−i−iii−i−iii-1−ii−ii111-1-1−ii−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-111-1-11-1-1-1-111111-1-1-1-111i−i−iiii−i−i−i−iii11111111-1-1-1-1-1-1-1-11-1-1-111i−i−iiii−i−i−i−iii1i−i−ii-1-1-111i−i−ii
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-111-1-11-1-1-1-111111-1-1-1-111−iii−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-11-1-1-111−iii−i−i−iiiii−i−i1−iii−i-1-1-111−iii−i
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-111111-1-111-1-1i−ii−iii−i−iii−i−i-1-1-1-1-1-1-1-111111111-1111-1-1i−ii−iii−i−iii−i−i-1−ii−ii1-1-111−ii−ii
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-111111-1-111-1-1−ii−ii−i−iii−i−iii-1-1-1-1-1-1-1-111111111-1111-1-1−ii−ii−i−iii−i−iii-1i−ii−i1-1-111i−ii−i
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111i−i−iiii−i−i−i−iii-1-1-1-1-1-1-1-1111111111-1-1-111i−i−iiii−i−i−i−iii1−iii−i-111-1-1−iii−i
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111−iii−i−i−iiiii−i−i-1-1-1-1-1-1-1-1111111111-1-1-111−iii−i−i−iiiii−i−i1i−i−ii-111-1-1i−i−ii
χ172222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-1-10000-100000000
χ182222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111000000000000000022-1-1-1-1-2-2-2-211111111-10000-100000000
χ192222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-111110000000000000000-2-2111122-2-2-1-1-1-1111110000100000000
χ202222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2221111-1-1-1-10000000000000000-2-21111-2-2221111-1-1-1-110000100000000
χ21222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-12222-12-1-1-1-12-1-1-1-1-1000000220000222222-1-1-1-1-1-122-1-1-1-1-1-100000000-1-10000-1-1-1-1000220000000-1-1
χ22222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-12222-12-1-1-1-12-1-1-1-1-1000000-2-20000-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-1000000001100001111000-2-2000000011
χ23222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-1-2-2-2-2-12-1-1-1-12-1-1-1-1-10000002200002222-2-2111111-2-211111100000000-1-10000-1-1-1-1000-2-2000000011
χ24222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-1-2-2-2-2-12-1-1-1-12-1-1-1-1-1000000-2-20000-2-2-2-2-2-2111111-2-2111111000000001100001111000220000000-1-1
χ2522222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-1222222-1-12-1-1-1-12-1-1-1-10000220022220000-1-122-1-1-1-1-1-122-1-1-1-1000000-1-100-1-1-1-100000220000000-1-100
χ2622222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-1222222-1-12-1-1-1-12-1-1-1-10000-2-200-2-2-2-20000-1-122-1-1-1-1-1-122-1-1-1-10000001100111100000-2-200000001100
χ2722222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-122-2-2-2-2-1-12-1-1-1-12-1-1-1-1000022002222000011-2-2111111-2-21111000000-1-100-1-1-1-100000-2-200000001100
χ2822222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-122-2-2-2-2-1-12-1-1-1-12-1-1-1-10000-2-200-2-2-2-2000011-2-2111111-2-211110000001100111100000220000000-1-100
χ292222-2222-2222222222222-2-2-2-2-2222-222-2-2-2-2222200002-2-2-2-22-2-2-2-22222220000000000000000000000000000-2-22222000000000000-20000-200000000
χ302222-2222-2222222222222-2-2-2-2-2222-222-2-2-2-2222200002-2-2-2-22-2-2-2-222-2-2-2-2000000000000000000000000000022-2-2-2-200000000000020000200000000
χ312222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-10000-11111-11111-1-122220000−i3i3−i3i3−i3i3−i3i30000000000000000-2-2-1-1-1-10000−i3i3−i3i3−i3i3−i3i310000100000000
χ322222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-10000-11111-11111-1-122220000i3−i3i3−i3i3−i3i3−i30000000000000000-2-2-1-1-1-10000i3−i3i3−i3i3−i3i3−i310000100000000
χ332222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-10000-11111-11111-1-1-2-2-2-20000−i3i3−i3i3i3−i3i3−i300000000000000002211110000−i3i3−i3i3i3−i3i3−i3-10000-100000000
χ342222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-10000-11111-11111-1-1-2-2-2-20000i3−i3i3−i3−i3i3−i3i300000000000000002211110000i3−i3i3−i3−i3i3−i3i3-10000-100000000
χ3522-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-222-2-200000000000000000000000000002-222-2-200000000000020000-200000000
χ3622-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2-2-2220000000000000000000000000000-22-2-222000000000000-20000200000000
χ3722-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-211110000-1-1-1-1-1-111111122-2-200003−3−333−3−3300000000000000002-2-1-11100003−3−333−3−33-10000100000000
χ3822-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-211110000-1-1-1-1-1-111111122-2-20000−333−3−333−300000000000000002-2-1-1110000−333−3−333−3-10000100000000
χ3922-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-211110000-1-1-1-1-1-1111111-2-22200003−3−33−333−30000000000000000-2211-1-100003−3−33−333−310000-100000000
χ4022-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-211110000-1-1-1-1-1-1111111-2-2220000−333−33−3−330000000000000000-2211-1-10000−333−33−3−3310000-100000000
χ4122-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-2222211110000-11111-1-1-1-1-11122-2-22i−2i2i−2i−i−iii−i−iii0000000000000000-22-1-1112i−2i2i−2i−i−iii−i−iii10000-100000000
χ4222-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-2222211110000-11111-1-1-1-1-11122-2-2−2i2i−2i2iii−i−iii−i−i0000000000000000-22-1-111−2i2i−2i2iii−i−iii−i−i10000-100000000
χ4322-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-2222211110000-11111-1-1-1-1-111-2-2222i−2i−2i2i−i−iiiii−i−i00000000000000002-211-1-12i−2i−2i2i−i−iiiii−i−i-10000100000000
χ4422-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-2222211110000-11111-1-1-1-1-111-2-222−2i2i2i−2iii−i−i−i−iii00000000000000002-211-1-1−2i2i2i−2iii−i−i−i−iii-10000100000000
χ4522-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-21122-2-2-1-2111-12-1-1-1110000002i−2i00002i2i−2i−2i22-1-1-1-1-1-1-2-211111100000000−ii0000−i−iii0002i−2i0000000−ii
χ4622-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-21122-2-2-1-2111-12-1-1-111000000−2i2i0000−2i−2i2i2i22-1-1-1-1-1-1-2-211111100000000i−i0000ii−i−i000−2i2i0000000i−i
χ4722-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-211-2-222-1-2111-12-1-1-1110000002i−2i00002i2i−2i−2i-2-211111122-1-1-1-1-1-100000000−ii0000−i−iii000−2i2i0000000i−i
χ4822-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-211-2-222-1-2111-12-1-1-111000000−2i2i0000−2i−2i2i2i-2-211111122-1-1-1-1-1-100000000i−i0000ii−i−i0002i−2i0000000−ii
χ4922-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-222-2-2-11-211-1-12-1-11100002i−2i002i2i−2i−2i0000-1-122-1-1-1-111-2-21111000000−ii00−i−iii000002i−2i0000000−ii00
χ5022-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-222-2-2-11-211-1-12-1-1110000−2i2i00−2i−2i2i2i0000-1-122-1-1-1-111-2-21111000000i−i00ii−i−i00000−2i2i0000000i−i00
χ5122-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-2-2-222-11-211-1-12-1-11100002i−2i002i2i−2i−2i000011-2-21111-1-122-1-1-1-1000000−ii00−i−iii00000−2i2i0000000i−i00
χ5222-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-2-2-222-11-211-1-12-1-1110000−2i2i00−2i−2i2i2i000011-2-21111-1-122-1-1-1-1000000i−i00ii−i−i000002i−2i0000000−ii00
χ532-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i00002i−2i2i−2i2−2−i2i220000-200002i−2i2-22i−2i0000000000002−22−222−2−2−i2i2−i2i2−i2−i2i2i2002-22i−2i0000000000000000002−2−i2i20000
χ542-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i00002i−2i2i−2i2−2−i2i220000-200002i−2i-22−2i2i0000000000002−22−222−2−2−i2i2−i2i2−i2−i2i2i200-22−2i2i000000000000000000−22i2−i20000
χ552-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i00002i−2i2i−2i−22i2−i220000-200002i−2i2-22i−2i000000000000−22−22−2−222i2−i2i2−i2i2i2−i2−i2002-22i−2i000000000000000000−22i2−i20000
χ562-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i00002i−2i2i−2i−22i2−i220000-200002i−2i-22−2i2i000000000000−22−22−2−222i2−i2i2−i2i2i2−i2−i200-22−2i2i0000000000000000002−2−i2i20000
χ572-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-20−2i2i0000−2i2i−2i2i2−2i2−i220000-20000−2i2i2-2−2i2i0000000000002−22−222−2−2i2−i2i2−i2i2i2−i2−i2002-2−2i2i0000000000000000002−2i2−i20000
χ582-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-20−2i2i0000−2i2i−2i2i2−2i2−i220000-20000−2i2i-222i−2i0000000000002−22−222−2−2i2−i2i2−i2i2i2−i2−i200-222i−2i000000000000000000−22−i2i20000
χ592-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-20−2i2i0000−2i2i−2i2i−22−i2i220000-20000−2i2i2-2−2i2i000000000000−22−22−2−222−i2i2−i2i2−i2−i2i2i2002-2−2i2i000000000000000000−22−i2i20000
χ602-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-20−2i2i0000−2i2i−2i2i−22−i2i220000-20000−2i2i-222i−2i000000000000−22−22−2−222−i2i2−i2i2−i2−i2i2i200-222i−2i0000000000000000002−2i2−i20000
χ61444444-2-244-2-2-2-244-2-2-2-214-2-2-2-2-2-21-2-2-24-2-2-2-2-21100001-21111-211111000000440000-2-2-2-2000000000000000000000000-2-20000111100000000000000
χ62444444-2-244-2-2-2-244-2-2-2-214-2-2-2-2-2-21-2-2-24-2-2-2-2-21100001-21111-211111000000-4-400002222000000000000000000000000220000-1-1-1-100000000000000
χ6344444-24-24-24-2-2-2-2-244-21-2-24-2-2-2-21-2-2-2-2-24-2-211-2-2000011-21111-2111100004400-2-2-2-200000000000000000000000000-2-2001111000000000000000000
χ6444444-24-24-24-2-2-2-2-244-21-2-24-2-2-2-21-2-2-2-2-24-2-211-2-2000011-21111-211110000-4-4002222000000000000000000000000002200-1-1-1-1000000000000000000
χ6544444-2-244-2-2444-2-2-2-21-2-2-2-24111-2-2411-2-211-2-2-2-244441-2-2111-2-211110000000000000000-2-2-2-21111-2-2-2-2111100000000000000000000000000000000
χ6644444-2-244-2-2444-2-2-2-21-2-2-2-24111-2-2411-2-211-2-2-2-2-4-4-4-41-2-2111-2-2111100000000000000002222-1-1-1-12222-1-1-1-100000000000000000000000000000000
χ674444-44-24-44-244444-2-2-24-2-42-422-24-2-4-2-2-422244-2-20000-2-4222-2-4222-2-20000000000000000000000000000000000000000000000000000000000000000
χ684444-44-2-2-44-2-2-2-244-2-2-2-21-42222-2-212-2-2-4222-2-211000012-1-1-112-1-1-111000000000000−2i32i3−2i32i3000000000000000000000000000000i3−i3i3−i300000000000000
χ694444-44-2-2-44-2-2-2-244-2-2-2-21-42222-2-212-2-2-4222-2-211000012-1-1-112-1-1-1110000000000002i3−2i32i3−2i3000000000000000000000000000000−i3i3−i3i300000000000000
χ704444-4-244-4-24444-2-244-2-242-4-422-2-24-4-2-22-422-2-2440000-22-422-22-422-2-20000000000000000000000000000000000000000000000000000000000000000
χ714444-4-24-2-4-24-2-2-2-2-244-21-22-4222-21-22-2-22-42211-2-200001-12-1-11-12-1-11100000000−2i32i3−2i32i3000000000000000000000000000000i3−i3i3−i3000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.