Finite Group Databasebeta

← Group #13155509

Character table — Group #13155509

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order124423334666121212121212333666666661212121212121212121212366666121212121212888888242424242424242424242424242424242424242424242424224466121224242424242424242424242468888122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-11-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1i−ii−i1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-11-11-111-1-1i−ii−iii−i−iii−i−i-1i−ii−i1i−ii−i1-1
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1i−ii−i-11ii−i−iii−i−i-1-1-1-1-1-1-1-1111111111-11-111-1-1i−ii−iii−i−iii−i−i-1−ii−ii1−ii−ii-11
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1i−i−ii1-1ii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-11-11-1-111i−i−iiii−i−i−i−iii1i−i−ii-1i−i−ii-11
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1i−i−ii-11ii−i−i−i−iii-1-1-1-1-1-1-1-111111111-11-11-1-111i−i−iiii−i−i−i−iii1−iii−i-1−iii−i1-1
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1−iii−i1-1−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-11-11-1-111−iii−i−i−iiiii−i−i1−iii−i-1−iii−i-11
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1−iii−i-11−i−iiiii−i−i-1-1-1-1-1-1-1-111111111-11-11-1-111−iii−i−i−iiiii−i−i1i−i−ii-1i−i−ii1-1
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1−ii−ii1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-11-11-111-1-1−ii−ii−i−iii−i−iii-1−ii−ii1−ii−ii1-1
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-111111-1-1−ii−ii-11−i−iii−i−iii-1-1-1-1-1-1-1-1111111111-11-111-1-1−ii−ii−i−iii−i−iii-1i−ii−i1i−ii−i-11
χ172222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-100000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-1-10000-1000000
χ182222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111110000000000000000-2-2-2-2111122-2-2-1-1-1-11111100001000000
χ192222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-1-1-10000000000000000-2-2-2-21111-2-2221111-1-1-1-1100001000000
χ202222222-1222-1-1-122222-1-122-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2001111111100000000000000002222-1-1-1-1-2-2-2-211111111-10000-1000000
χ21222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-1-12-1-1-1-12-1-1-1-1-10022220000222222-1-1-1-1-1-122-1-1-1-1-1-10000000000-1-10000-1-1-1-100022000-1-100
χ22222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-1-12-1-1-1-12-1-1-1-1-10022-2-200002222-2-2111111-2-21111110000000000-1-10000-1-1-1-1000-2-20001100
χ23222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-1-12-1-1-1-12-1-1-1-1-100-2-2220000-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-100000000001100001111000-2-20001100
χ24222222-1222-122222-1-1-12-12-12-1-1-12-12-1-12-1-1-122-1-1-12-1-1-1-12-1-1-1-1-100-2-2-2-20000-2-2-2-2-2-2111111-2-21111110000000000110000111100022000-1-100
χ2522222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-122-1-12-1-1-1-12-1-1-1-122002222220000-1-122-1-1-1-1-1-122-1-1-1-100000000-1-100-1-1-1-10000022000-1-10000
χ2622222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-122-1-12-1-1-1-12-1-1-1-12200-2-22222000011-2-2111111-2-2111100000000-1-100-1-1-1-100000-2-2000110000
χ2722222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-122-1-12-1-1-1-12-1-1-1-1-2-20022-2-2-2-20000-1-122-1-1-1-1-1-122-1-1-1-1000000001100111100000-2-2000110000
χ2822222-1222-12222-1-122-1-12-122-1-1-1-122-1-1-12-1-1-1-122-1-12-1-1-1-12-1-1-1-1-2-200-2-2-2-2-2-2000011-2-2111111-2-2111100000000110011110000022000-1-10000
χ292222-2222-2222222222222-2-2-2-2-2222-222-2-2-2-222222-2-2-2-22-2-2-2-2220000000000000000000000000000002-2-222222000000000000-20000-2000000
χ302222-2222-2222222222222-2-2-2-2-2222-222-2-2-2-222222-2-2-2-22-2-2-2-222000000000000000000000000000000-222-2-2-2-2-2000000000000200002000000
χ312222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-1-11111-11111-1-1000000−i3i3−i3i3−i3i3−i3i300000000000000002-2-22-1-1-1-10000−i3i3−i3i3−i3i3−i3i3100001000000
χ322222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-1-11111-11111-1-1000000−i3i3−i3i3i3−i3i3−i30000000000000000-222-211110000−i3i3−i3i3i3−i3i3−i3-10000-1000000
χ332222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-1-11111-11111-1-1000000i3−i3i3−i3−i3i3−i3i30000000000000000-222-211110000i3−i3i3−i3−i3i3−i3i3-10000-1000000
χ342222-222-1-222-1-1-122222-1-1-2-21-2-22-1-1122-2-2-2-2-1-1-1-1-11111-11111-1-1000000i3−i3i3−i3i3−i3i3−i300000000000000002-2-22-1-1-1-10000i3−i3i3−i3i3−i3i3−i3100001000000
χ3522-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000022-2-222-2-200000000000020000-2000000
χ3622-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000-2-222-2-222000000000000-200002000000
χ3722-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-21111-1-1-1-1-1-11111110000003−3−333−3−33000000000000000022-2-2-1-11100003−3−333−3−33-100001000000
χ3822-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-21111-1-1-1-1-1-11111110000003−3−33−333−30000000000000000-2-22211-1-100003−3−33−333−310000-1000000
χ3922-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-21111-1-1-1-1-1-1111111000000−333−33−3−330000000000000000-2-22211-1-10000−333−33−3−3310000-1000000
χ4022-2-2222-1-222-111-2-2-2-22-1-122-1222-1-11-2-2-2-2-2-21111-1-1-1-1-1-1111111000000−333−3−333−3000000000000000022-2-2-1-1110000−333−3−333−3-100001000000
χ4122-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-222221111-11111-1-1-1-1-1112i−2i2i−2i00−i−iii−i−iii00000000000000002-22-2-1-1112i−2i2i−2i−i−iii−i−iii10000-1000000
χ4222-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-222221111-11111-1-1-1-1-1112i−2i−2i2i00−i−iiiii−i−i0000000000000000-22-2211-1-12i−2i−2i2i−i−iiiii−i−i-100001000000
χ4322-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-222221111-11111-1-1-1-1-111−2i2i2i−2i00ii−i−i−i−iii0000000000000000-22-2211-1-1−2i2i2i−2iii−i−i−i−iii-100001000000
χ4422-2-2-222-1222-111-2-2-2-22-1-1-2-21-2-22-1-1-1-2-222221111-11111-1-1-1-1-111−2i2i−2i2i00ii−i−iii−i−i00000000000000002-22-2-1-111−2i2i−2i2iii−i−iii−i−i10000-1000000
χ4522-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-211-1-2111-12-1-1-111002i−2i2-200002i2i−2i−2i22-1-1-1-1-1-1-2-21111110000000000−ii0000−i−iii0002i−2i000−ii00
χ4622-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-211-1-2111-12-1-1-111002i−2i-2200002i2i−2i−2i-2-211111122-1-1-1-1-1-10000000000−ii0000−i−iii000−2i2i000i−i00
χ4722-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-211-1-2111-12-1-1-11100−2i2i2-20000−2i−2i2i2i22-1-1-1-1-1-1-2-21111110000000000i−i0000ii−i−i000−2i2i000i−i00
χ4822-2-2-22-1222-12-2-2-2-211-12-1-21-211-12-12112-1-1-1-2-211-1-2111-12-1-1-11100−2i2i-220000−2i−2i2i2i-2-211111122-1-1-1-1-1-10000000000i−i0000ii−i−i0002i−2i000−ii00
χ4922-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-2-11-211-1-12-1-1112i−2i002-22i2i−2i−2i0000-1-122-1-1-1-111-2-2111100000000−ii00−i−iii000002i−2i000−ii0000
χ5022-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-2-11-211-1-12-1-1112i−2i00-222i2i−2i−2i000011-2-21111-1-122-1-1-1-100000000−ii00−i−iii00000−2i2i000i−i0000
χ5122-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-2-11-211-1-12-1-111−2i2i002-2−2i−2i2i2i0000-1-122-1-1-1-111-2-2111100000000i−i00ii−i−i00000−2i2i000i−i0000
χ5222-2-2-2-1222-122-2-211-2-2-1-121-2-211-1-12211-12-1-111-2-2-11-211-1-12-1-111−2i2i00-22−2i−2i2i2i000011-2-21111-1-122-1-1-1-100000000i−i00ii−i−i000002i−2i000−ii0000
χ53444444-2-244-2-2-2-244-2-2-2-214-2-2-2-2-2-21-2-2-24-2-2-2-2-2111-21111-2111110044000000-2-2-2-200000000000000000000000000-2-200001111000000000000
χ54444444-2-244-2-2-2-244-2-2-2-214-2-2-2-2-2-21-2-2-24-2-2-2-2-2111-21111-21111100-4-4000000222200000000000000000000000000220000-1-1-1-1000000000000
χ5544444-24-24-24-2-2-2-2-244-21-2-24-2-2-2-21-2-2-2-2-24-2-211-2-211-21111-21111440000-2-2-2-20000000000000000000000000000-2-20011110000000000000000
χ5644444-24-24-24-2-2-2-2-244-21-2-24-2-2-2-21-2-2-2-2-24-2-211-2-211-21111-21111-4-40000222200000000000000000000000000002200-1-1-1-10000000000000000
χ5744444-2-244-2-2444-2-2-2-21-2-2-2-24111-2-2411-2-211-2-2-2-21-2-2111-2-2111100004400000000-2-2-2-21111-2-2-2-2111100000000000000000000000000000000
χ5844444-2-244-2-2444-2-2-2-21-2-2-2-24111-2-2411-2-211-2-2-2-21-2-2111-2-211110000-4-4000000002222-1-1-1-12222-1-1-1-100000000000000000000000000000000
χ594444-44-24-44-244444-2-2-24-2-42-422-24-2-4-2-2-422244-2-2-2-4222-2-4222-2-200000000000000000000000000000000000000000000000000000000000000
χ604444-44-2-2-44-2-2-2-244-2-2-2-21-42222-2-212-2-2-4222-2-21112-1-1-112-1-1-1110000000000−2i32i3−2i32i300000000000000000000000000000000i3−i3i3−i3000000000000
χ614444-44-2-2-44-2-2-2-244-2-2-2-21-42222-2-212-2-2-4222-2-21112-1-1-112-1-1-11100000000002i3−2i32i3−2i300000000000000000000000000000000−i3i3−i3i3000000000000
χ624444-4-244-4-24444-2-244-2-242-4-422-2-24-4-2-22-422-2-244-22-422-22-422-2-200000000000000000000000000000000000000000000000000000000000000
χ634444-4-24-2-4-24-2-2-2-2-244-21-22-4222-21-22-2-22-42211-2-21-12-1-11-12-1-111000000−2i32i3−2i32i300000000000000000000000000000000i3−i3i3−i30000000000000000
χ644444-4-24-2-4-24-2-2-2-2-244-21-22-4222-21-22-2-22-42211-2-21-12-1-11-12-1-1110000002i3−2i32i3−2i300000000000000000000000000000000−i3i3−i3i30000000000000000
χ654444-4-2-24-4-2-2444-2-2-2-21-2-222-4-1-11-2-2-41122-1-1-2-2-2-2122-1-1122-1-1110000000000000000003i3i−3i−3i00003i3i−3i−3i00000000000000000000000000000000
χ664444-4-2-24-4-2-2444-2-2-2-21-2-222-4-1-11-2-2-41122-1-1-2-2-2-2122-1-1122-1-111000000000000000000−3i−3i3i3i0000−3i−3i3i3i00000000000000000000000000000000
χ6744-4-444-24-44-24-4-4-4-422-24-24-24-2-2-24-2-422-4222-4-422-24-2-2-2-2-42222200000000000000000000000000000000000000000000000000000000000000
χ6844-4-444-2-2-44-2-222-4-422-2-214-2-2-2-2-2-21222-422222-1-11-211112-1-1-1-1-1000000000023−23−232300000000000000000000000000000000−333−3000000000000
χ6944-4-444-2-2-44-2-222-4-422-2-214-2-2-2-2-2-21222-422222-1-11-211112-1-1-1-1-10000000000−232323−23000000000000000000000000000000003−3−33000000000000
χ7044-4-44-244-4-244-4-422-4-4-2-24-244-2-2-2-24-4222-42222-4-4-2-24-2-2-22-4222200000000000000000000000000000000000000000000000000000000000000
χ7144-4-44-24-2-4-24-22222-4-4-21-2-24-2-2-2-21-22222-422-1-12211-2111-12-1-1-1-100000023−23−232300000000000000000000000000000000−333−30000000000000000
χ7244-4-44-24-2-4-24-22222-4-4-21-2-24-2-2-2-21-22222-422-1-12211-2111-12-1-1-1-1000000−232323−23000000000000000000000000000000003−3−330000000000000000
χ7344-4-44-2-24-4-2-24-4-422221-2-2-2-24111-2-2-4-1-122-1-122221-2-211122-1-1-1-10000000000000000003i3i−3i−3i0000−3i−3i3i3i00000000000000000000000000000000
χ7444-4-44-2-24-4-2-24-4-422221-2-2-2-24111-2-2-4-1-122-1-122221-2-211122-1-1-1-1000000000000000000−3i−3i3i3i00003i3i−3i−3i00000000000000000000000000000000
χ7544-4-4-44-2-244-2-222-4-422-2-21-42222-2-21-2224-2-2-222-1-112-1-1-11-2111-1-1004i−4i000000−2i−2i2i2i00000000000000000000000000−2i2i0000ii−i−i000000000000
χ7644-4-4-44-2-244-2-222-4-422-2-21-42222-2-21-2224-2-2-222-1-112-1-1-11-2111-1-100−4i4i0000002i2i−2i−2i000000000000000000000000002i−2i0000−i−iii000000000000
χ7744-4-4-4-24-24-24-22222-4-4-21-22-4222-21-2-222-24-2-2-1-1221-12-1-111-211-1-14i−4i0000−2i−2i2i2i0000000000000000000000000000−2i2i00ii−i−i0000000000000000
χ7844-4-4-4-24-24-24-22222-4-4-21-22-4222-21-2-222-24-2-2-1-1221-12-1-111-211-1-1−4i4i00002i2i−2i−2i00000000000000000000000000002i−2i00−i−iii0000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.