Finite Group Databasebeta

← Group #13155743

Character table — Group #13155743

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order12442333466612121212121233366666666121212121212121212121288882424242424242424366666121212121212224466661212121224242424242424242424242466666612121212121288888824242424242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-11-111-1-111-1-11111111111111-111-1-11-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-111111111111111-11-1-111-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i111111-1-1-1-1-1-1i−ii−i1-1ii−i−iii−i−i11-1-1i−i
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-11-1-1111-1-1-1-111ii−i−iiiii−i−i−i−i1-111-1-1-11-1-111i−i−ii-11ii−i−i−i−iii-1-111−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-1-111-1-1-11111-1-1ii−i−iiiii−i−i−i−i-11-1-1111-111-1-1−iii−i-11−i−iiiii−i−i-1-111−ii
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-1-1-111-1-1-1-11111ii−i−iiiii−i−i−i−i-1-1-1-1-1-1111111−ii−ii1-1−i−iii−i−iii11-1-1i−i
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii111111-1-1-1-1-1-1−ii−ii1-1−i−iii−i−iii11-1-1−ii
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-11-1-1111-1-1-1-111−i−iii−i−i−i−iiiii1-111-1-1-11-1-111−iii−i-11−i−iiiii−i−i-1-111i−i
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-1-111-1-1-11111-1-1−i−iii−i−i−i−iiiii-11-1-1111-111-1-1i−i−ii-11ii−i−i−i−iii-1-111i−i
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-1-1-111-1-1-1-11111−i−iii−i−i−i−iiiii-1-1-1-1-1-1111111i−ii−i1-1ii−i−iii−i−i11-1-1−ii
χ172222222-1222-1-1-122222-1-122-1222-1-12222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-100002200000000-1-1-1-100
χ182222222-1222-1-1-122222-1-122-1222-1-12222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-12-22-222-2-222-2-2000000000000-11-1-111-11-1-1110000-2-200000000111100
χ192222222-1222-1-1-122222-1-122-1222-1-12222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-22-22-2-222-2-2220000000000001-111-1-11-111-1-10000-2-200000000111100
χ202222222-1222-1-1-122222-1-122-1222-1-12222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-200000000000011111111111100002200000000-1-1-1-100
χ21222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-122-1-1-1-12222222-1-122-1-1-12-1-1-1-12-1-1-1-1-1020200-1-100-1-12-12-1-1-1-1-1-1-1-1-10200-1-10200-1-10022000000-1-1-1-1000000
χ22222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-122-1-1-1-12222222-1-122-1-1-12-1-1-1-12-1-1-1-1-10-20-2001100112-12-1-1-1-1-1-1-1-1-10-200110-2001100-2-20000001111000000
χ23222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-122-1-1-1-12-2-2-2-2-2-211-2-211-12-1-1-1-12-1-1-1-1-1020200-1-100-1-1-21-21111111110200-1-10200-1-100-2-20000001111000000
χ24222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-122-1-1-1-12-2-2-2-2-2-211-2-211-12-1-1-1-12-1-1-1-1-10-20-200110011-21-21111111110-200110-200110022000000-1-1-1-1000000
χ2522222-1222-12222-1-122-1-12-122-1-1-1-12-12-1-1-1-122-1-122222-1-122-1-122-1-12-1-1-1-12-1-1-1-12020-1-100-1-100-12-12-1-1-1-1-1-1-1-120-1-10020-1-100220000-1-1-1-10000000000
χ2622222-1222-12222-1-122-1-12-122-1-1-1-12-12-1-1-1-122-1-122222-1-122-1-122-1-12-1-1-1-12-1-1-1-1-20-2011001100-12-12-1-1-1-1-1-1-1-1-201100-201100-2-2000011110000000000
χ2722222-1222-12222-1-122-1-12-122-1-1-1-12-12-1-1-1-122-1-12-2-2-2-211-2-211-2-2-1-12-1-1-1-12-1-1-1-12020-1-100-1-1001-21-21111111120-1-10020-1-100-2-2000011110000000000
χ2822222-1222-12222-1-122-1-12-122-1-1-1-12-12-1-1-1-122-1-12-2-2-2-211-2-211-2-2-1-12-1-1-1-12-1-1-1-1-20-20110011001-21-211111111-201100-201100220000-1-1-1-10000000000
χ292222-2222-2222222222222-2-2-2-2-2222-2-2-2-2222222-22-22-222-2-222-2-22-2-2-2-22-2-2-2-222000000000000-22-2222-2-222-2-200000000000000000000000000000000
χ302222-2222-2222222222222-2-2-2-2-2222-2-2-2-2222222-2-22-22-2-222-2-2222-2-2-2-22-2-2-2-2220000000000002-22-2-2-222-2-22200000000000000000000000000000000
χ312222-22-12-22-122222-1-1-12-1-21-211-12-1-211122-1-1-1-1-22-22-222112211-1-2111-1-2111-1-1000000−i3i300−i3i3-2-1-2-1-1-111-1-1110000−i3i30000−i3i30000000000−i3i3−i3i3000000
χ322222-22-12-22-122222-1-1-12-1-21-211-12-1-211122-1-1-1-1-22-22-222112211-1-2111-1-2111-1-1000000i3−i300i3−i3-2-1-2-1-1-111-1-1110000i3−i30000i3−i30000000000i3−i3i3−i3000000
χ332222-22-12-22-122222-1-1-12-1-21-211-12-1-211122-1-1-1-1-2-22-22-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1000000−i3i300−i3i3212111-1-111-1-10000−i3i30000−i3i30000000000i3−i3i3−i3000000
χ342222-22-12-22-122222-1-1-12-1-21-211-12-1-211122-1-1-1-1-2-22-22-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1000000i3−i300i3−i3212111-1-111-1-10000i3−i30000i3−i30000000000−i3i3−i3i3000000
χ352222-2-122-2-12222-1-122-1-121-2-211-1-121-211-1-122-1-1-22-22-2-1-1-2-2-1-1-2-2-11-211-11-211-1-10000−i3i300−i3i3001212-1-111-1-11100−i3i30000−i3i300000000−i3i3−i3i30000000000
χ362222-2-122-2-12222-1-122-1-121-2-211-1-121-211-1-122-1-1-22-22-2-1-1-2-2-1-1-2-2-11-211-11-211-1-10000i3−i300i3−i3001212-1-111-1-11100i3−i30000i3−i300000000i3−i3i3−i30000000000
χ372222-2-122-2-12222-1-122-1-121-2-211-1-121-211-1-122-1-1-2-22-2211221122-11-211-11-211-1-10000−i3i300−i3i300-1-2-1-211-1-111-1-100−i3i30000−i3i300000000i3−i3i3−i30000000000
χ382222-2-122-2-12222-1-122-1-121-2-211-1-121-211-1-122-1-1-2-22-2211221122-11-211-11-211-1-10000i3−i300i3−i300-1-2-1-211-1-111-1-100i3−i30000i3−i300000000−i3i3−i3i30000000000
χ3922-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i222222-2-2-2-2-2-2000000000000−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4022-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i222222-2-2-2-2-2-20000000000002i−2i−2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4122-2-222-12-22-12-2-2-2-211-12-12-12-1-1-12-1-2111-2-21111-22i−2i−2i2i2i2iii−2i−2i−i−i-12-1-1-1-1-211111000000−i3i300i3−i3−2i−i2ii−i−iiiii−i−i0000−i3i30000i3−i300000000003−3−33000000
χ4222-2-222-12-22-12-2-2-2-211-12-12-12-1-1-12-1-2111-2-21111-22i−2i−2i2i2i2iii−2i−2i−i−i-12-1-1-1-1-211111000000i3−i300−i3i3−2i−i2ii−i−iiiii−i−i0000i3−i30000−i3i30000000000−333−3000000
χ4322-2-222-12-22-12-2-2-2-211-12-12-12-1-1-12-1-2111-2-21111-2−2i2i2i−2i−2i−2i−i−i2i2iii-12-1-1-1-1-211111000000−i3i300i3−i32ii−2i−iii−i−i−i−iii0000−i3i30000i3−i30000000000−333−3000000
χ4422-2-222-12-22-12-2-2-2-211-12-12-12-1-1-12-1-2111-2-21111-2−2i2i2i−2i−2i−2i−i−i2i2iii-12-1-1-1-1-211111000000i3−i300−i3i32ii−2i−iii−i−i−i−iii0000i3−i30000−i3i300000000003−3−33000000
χ4522-2-22-122-2-122-2-211-2-2-1-12-122-1-1-1-121-21111-2-211-22i−2i−2i2i−i−i−2i−2iii2i2i-1-12-1-1-11-211110000−i3i300i3−i300i2i−i−2i−i−iiiii−i−i00−i3i30000i3−i3000000003−3−330000000000
χ4622-2-22-122-2-122-2-211-2-2-1-12-122-1-1-1-121-21111-2-211-22i−2i−2i2i−i−i−2i−2iii2i2i-1-12-1-1-11-211110000i3−i300−i3i300i2i−i−2i−i−iiiii−i−i00i3−i30000−i3i300000000−333−30000000000
χ4722-2-22-122-2-122-2-211-2-2-1-12-122-1-1-1-121-21111-2-211-2−2i2i2i−2iii2i2i−i−i−2i−2i-1-12-1-1-11-211110000−i3i300i3−i300−i−2ii2iii−i−i−i−iii00−i3i30000i3−i300000000−333−30000000000
χ4822-2-22-122-2-122-2-211-2-2-1-12-122-1-1-1-121-21111-2-211-2−2i2i2i−2iii2i2i−i−i−2i−2i-1-12-1-1-11-211110000i3−i300−i3i300−i−2ii2iii−i−i−i−iii00i3−i30000−i3i3000000003−3−330000000000
χ4922-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-122221111-2-2-1000000000000-11111-1-1-1-1-11122-2-22222-2-2-2-2000000000000-1-1-1-1-1-111111100002-200000000-1-11100
χ5022-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-122221111-2-2-1000000000000-11111-1-1-1-1-1112-2-2222-2-2-2-222000000000000-11-1-1111-111-1-10000-220000000011-1-100
χ5122-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-122221111-2-2-1000000000000-11111-1-1-1-1-111-222-2-2-22222-2-20000000000001-111-1-1-11-1-1110000-220000000011-1-100
χ5222-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-122221111-2-2-1000000000000-11111-1-1-1-1-111-2-222-2-2-2-22222000000000000111111-1-1-1-1-1-100002-200000000-1-11100
χ5322-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12-1-1-1-2-2111122i2i−2i−2i2i2i−i−i−2i−2iii-1-2111-12-1-1-111020-200-1-100112i−i−2ii−i−i−i−iiiii0200-1-10-20011002i−2i000000−i−iii000000
χ5422-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12-1-1-1-2-2111122i2i−2i−2i2i2i−i−i−2i−2iii-1-2111-12-1-1-1110-202001100-1-12i−i−2ii−i−i−i−iiiii0-200110200-1-100−2i2i000000ii−i−i000000
χ5522-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12-1-1-1-2-211112−2i−2i2i2i−2i−2iii2i2i−i−i-1-2111-12-1-1-111020-200-1-10011−2ii2i−iiiii−i−i−i−i0200-1-10-2001100−2i2i000000ii−i−i000000
χ5622-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12-1-1-1-2-211112−2i−2i2i2i−2i−2iii2i2i−i−i-1-2111-12-1-1-1110-202001100-1-1−2ii2i−iiiii−i−i−i−i0-200110200-1-1002i−2i000000−i−iii000000
χ5722-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12-12-1-111-2-21122i2i−2i−2i−i−i2i2iii−2i−2i-11-211-1-12-1-11120-20-1-1001100−i2ii−2i−i−i−i−iiiii20-1-100-2011002i−2i0000−i−iii0000000000
χ5822-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12-12-1-111-2-21122i2i−2i−2i−i−i2i2iii−2i−2i-11-211-1-12-1-111-20201100-1-100−i2ii−2i−i−i−i−iiiii-20110020-1-100−2i2i0000ii−i−i0000000000
χ5922-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12-12-1-111-2-2112−2i−2i2i2iii−2i−2i−i−i2i2i-11-211-1-12-1-11120-20-1-1001100i−2i−i2iiiii−i−i−i−i20-1-100-201100−2i2i0000ii−i−i0000000000
χ6022-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12-12-1-111-2-2112−2i−2i2i2iii−2i−2i−i−i2i2i-11-211-1-12-1-111-20201100-1-100i−2i−i2iiiii−i−i−i−i-20110020-1-1002i−2i0000−i−iii0000000000
χ61444444-2-244-2-2-2-244-2-2-2-214-2-2-2-2-2-214-2-2-2-2-211-2-2-20000000000001-21111-211111040400-2-200-2-20000000000000-200110-2001100000000000000000000
χ62444444-2-244-2-2-2-244-2-2-2-214-2-2-2-2-2-214-2-2-2-2-211-2-2-20000000000001-21111-2111110-40-4002200220000000000000200-1-10200-1-100000000000000000000
χ6344444-24-24-24-2-2-2-2-244-21-2-24-2-2-2-21-2-24-2-211-2-2-2-2-200000000000011-21111-211114040-2-200-2-200000000000000-201100-20110000000000000000000000
χ6444444-24-24-24-2-2-2-2-244-21-2-24-2-2-2-21-2-24-2-211-2-2-2-2-200000000000011-21111-21111-40-402200220000000000000020-1-10020-1-10000000000000000000000
χ6544444-2-244-2-2444-2-2-2-21-2-2-2-24111-2-2-2-211-2-2-2-21144444-2-2-2-2-2-2-2-21-2-2111-2-21111000000000000-2-2-2-21111111100000000000000000000000000000000
χ6644444-2-244-2-2444-2-2-2-21-2-2-2-24111-2-2-2-211-2-2-2-2114-4-4-4-4222222221-2-2111-2-211110000000000002222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ674444-444-2-444-2-2-244444-2-2-4-42-4-44-2-2-4-4-4-4-2-2-2-2442000000000000-22222-22222-2-200000000000000000000000000000000000000000000000000000000
χ684444-44-2-2-44-2-2-2-244-2-2-2-21-42222-2-21-4222-2-211-2-2200000000000012-1-1-112-1-1-111000000−2i32i300−2i32i30000000000000000i3−i30000i3−i300000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.