Finite Group Databasebeta

← Group #13155750

Character table — Group #13155750

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order12442333466612121212121233366666666121212121212121212121288882424242424242424366666121212121212246688121224242424242424242424242424242424666121212242424242424244466881212121212122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111
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
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1ii−i−iii−i−iii−i−i1-1-1-1-111111-1-11-111i−i-1-1i−iii−i−ii−iiiii−i−i−i−i111-1-1-1i−iii−i−i1-1i−i11i−i-1-1ii−i−iii−i−i1-1
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1ii−i−iii−i−iii−i−i1-1-1-1-111111-1-11-111−ii-1-1i−i−i−iiii−iiiii−i−i−i−i111-1-1-1−ii−i−iii-11−ii-1-1i−i11−i−iiiii−i−i-11
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1ii−i−iii−i−iii−i−i1-1-1-1-111111-1-1-11-1-1i−i11i−iii−i−ii−iiiii−i−i−i−i-1-1-1111i−iii−i−i1-1−ii11−ii-1-1−i−iii−i−iii-11
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1ii−i−iii−i−iii−i−i1-1-1-1-111111-1-1-11-1-1−ii11i−i−i−iiii−iiiii−i−i−i−i-1-1-1111−ii−i−iii-11i−i-1-1−ii11ii−i−i−i−iii1-1
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1−i−iii−i−iii−i−iii1-1-1-1-111111-1-11-111i−i-1-1−iiii−i−i−ii−i−i−i−iiiii111-1-1-1i−iii−i−i-11i−i-1-1−ii11ii−i−i−i−iii-11
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1−i−iii−i−iii−i−iii1-1-1-1-111111-1-11-111−ii-1-1−ii−i−iii−ii−i−i−i−iiiii111-1-1-1−ii−i−iii1-1−ii11−ii-1-1−i−iii−i−iii1-1
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1−i−iii−i−iii−i−iii1-1-1-1-111111-1-1-11-1-1i−i11−iiii−i−i−ii−i−i−i−iiiii-1-1-1111i−iii−i−i-11−ii-1-1i−i11−i−iiiii−i−i1-1
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-111111-1-1-1-1-1-1−i−iii−i−iii−i−iii1-1-1-1-111111-1-1-11-1-1−ii11−ii−i−iii−ii−i−i−i−iiiii-1-1-1111−ii−i−iii1-1i−i11i−i-1-1ii−i−iii−i−i-11
χ172222222-1222-122-1-122-1-122-1-1-1-1-12222-1-1-122-1-1-1-12222-1-1-1-12222-1-12-1-1-1-12-1-1-1-100002200-1-1-1-1-1-122-1-1-1-1-1-1-1-100000022-1-1-1-12200-1-100-1-10000000000
χ182222222-1222-122-1-122-1-122-1-1-1-1-12222-1-1-122-1-1-1-12222-1-1-1-12222-1-12-1-1-1-12-1-1-1-10000-2-200-1-1111122-1-1-1-1-1-1-1-1000000-2-21111-2-2001100110000000000
χ192222222-1222-122-1-122-1-122-1-1-1-1-12222-1-1-122-1-1-1-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-12-1-1-1-10000220011-1-1-1-1-2-21111111100000022-1-1-1-1-2-2001100110000000000
χ202222222-1222-122-1-122-1-122-1-1-1-1-12222-1-1-122-1-1-1-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-12-1-1-1-10000-2-200111111-2-211111111000000-2-211112200-1-100-1-10000000000
χ21222222-1222-122222-1-12-1-1-12-1-12-1-122-12-1-1-1-122-1-122222222-1-1-1-1-12-1-1-1-12-1-1-1-1-122-1-100-1-1220000-1-1-1-1-1-1-1-1-1-12-1-12-1-100000000000022000000-1-1-1-100
χ22222222-1222-122222-1-12-1-1-12-1-12-1-122-12-1-1-1-122-1-122222222-1-1-1-1-12-1-1-1-12-1-1-1-1-1-2-2110011220000-1-1-1-1-1-1-1-1-1-1-211-211000000000000-2-2000000111100
χ23222222-1222-122222-1-12-1-1-12-1-12-1-122-12-1-1-1-122-1-1-2-2-2-2-2-2-2-21111-12-1-1-1-12-1-1-1-1-122-1-100-1-1-2-2000011111111112-1-12-1-1000000000000-2-2000000111100
χ24222222-1222-122222-1-12-1-1-12-1-12-1-122-12-1-1-1-122-1-1-2-2-2-2-2-2-2-21111-12-1-1-1-12-1-1-1-1-1-2-2110011-2-200001111111111-211-21100000000000022000000-1-1-1-100
χ2522222-1222-122-1-12222-12-12222-12-1-1-12222-1-1-1-122000000000000-1-1-1-1-1-1-1-1-1-1-1-1222222220022220000000000-1-1-1-1-1-1-1-1-1-1-1-10022000000-1-1-1-1000000
χ2622222-1222-122-1-12222-12-12222-12-1-1-12222-1-1-1-122000000000000-1-1-1-1-1-1-1-1-1-1-1-12222-2-22200-2-2-2-20000000000-1-1-1-1-1-111111100-2-20000001111000000
χ2722222-1222-122-1-12222-12-12222-12-1-1-12222-1-1-1-122000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-20022220000000000111111-1-1-1-1-1-100-2-20000001111000000
χ2822222-1222-122-1-12222-12-12222-12-1-1-12222-1-1-1-122000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-200-2-2-2-200000000001111111111110022000000-1-1-1-1000000
χ292222-2222-2222222222222-2-2-2-2222-2-2-2-2-2-22222222-22-22222-2-2-2-22-2-2-2-22-2-2-2-22200000000-2-200002222-2-222-2-200000000000000000000000000000000
χ302222-2222-2222222222222-2-2-2-2222-2-2-2-2-2-2222222-22-22-2-2-2-222222-2-2-2-22-2-2-2-22200000000220000-2-2-2-222-2-22200000000000000000000000000000000
χ312222-222-1-222-122-1-122-1-12-2111-1-12-2-2-211122-1-1-1-12-22-2-1-1-1-1-2-2-2-2-11-211-11-211-1-10000000011−i3i3−i3i322-1-111-1-11100000000−i3i3−i3i30000−i3i300−i3i30000000000
χ322222-222-1-222-122-1-122-1-12-2111-1-12-2-2-211122-1-1-1-12-22-2-1-1-1-1-2-2-2-2-11-211-11-211-1-10000000011i3−i3i3−i322-1-111-1-11100000000i3−i3i3−i30000i3−i300i3−i30000000000
χ332222-222-1-222-122-1-122-1-12-2111-1-12-2-2-211122-1-1-1-1-22-2211112222-11-211-11-211-1-100000000-1-1−i3i3−i3i3-2-211-1-111-1-100000000−i3i3−i3i30000i3−i300i3−i30000000000
χ342222-222-1-222-122-1-122-1-12-2111-1-12-2-2-211122-1-1-1-1-22-2211112222-11-211-11-211-1-100000000-1-1i3−i3i3−i3-2-211-1-111-1-100000000i3−i3i3−i30000−i3i300−i3i30000000000
χ352222-22-12-22-122222-1-12-1-11-2112-1-1-2-21-211-1-122-1-12-22-222221111-1-2111-1-2111-1-100−i3i300−i3i3-2-20000-1-1-1-111-1-1110−i3i30−i3i300000000000000000000−i3i3−i3i300
χ362222-22-12-22-122222-1-12-1-11-2112-1-1-2-21-211-1-122-1-12-22-222221111-1-2111-1-2111-1-100i3−i300i3−i3-2-20000-1-1-1-111-1-1110i3−i30i3−i300000000000000000000i3−i3i3−i300
χ372222-22-12-22-122222-1-12-1-11-2112-1-1-2-21-211-1-122-1-1-22-22-2-2-2-2-1-1-1-1-1-2111-1-2111-1-100−i3i300−i3i32200001111-1-111-1-10−i3i30−i3i300000000000000000000i3−i3i3−i300
χ382222-22-12-22-122222-1-12-1-11-2112-1-1-2-21-211-1-122-1-1-22-22-2-2-2-2-1-1-1-1-1-2111-1-2111-1-100i3−i300i3−i32200001111-1-111-1-10i3−i30i3−i300000000000000000000−i3i3−i3i300
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−2i2i2i222222-2-2-2-2-2-200000000−2i2i00002i−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−2i222222-2-2-2-2-2-2000000002i−2i0000−2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4122-2-2222-1-222-1-2-211-2-2-1-122-1-1-1-1-122-2-2111-2-211112i−2i−2i2i−i−iii−2i−2i2i2i-1-12-1-1-11-2111100000000i−i3−3−332i−2i−i−iiiii−i−i000000003−3−330000−i3i300i3−i30000000000
χ4222-2-2222-1-222-1-2-211-2-2-1-122-1-1-1-1-122-2-2111-2-211112i−2i−2i2i−i−iii−2i−2i2i2i-1-12-1-1-11-2111100000000i−i−333−32i−2i−i−iiiii−i−i00000000−333−30000i3−i300−i3i30000000000
χ4322-2-2222-1-222-1-2-211-2-2-1-122-1-1-1-1-122-2-2111-2-21111−2i2i2i−2iii−i−i2i2i−2i−2i-1-12-1-1-11-2111100000000−ii3−3−33−2i2iii−i−i−i−iii000000003−3−330000i3−i300−i3i30000000000
χ4422-2-2222-1-222-1-2-211-2-2-1-122-1-1-1-1-122-2-2111-2-21111−2i2i2i−2iii−i−i2i2i−2i−2i-1-12-1-1-11-2111100000000−ii−333−3−2i2iii−i−i−i−iii00000000−333−30000−i3i300i3−i30000000000
χ4522-2-222-12-22-12-2-2-2-2112-1-1-12-1-12-1-12-21-21111-2-2112i−2i−2i2i2i2i−2i−2iii−i−i-12-1-1-1-1-21111100−i3i300i3−i3−2i2i0000−ii−i−iiiii−i−i0−i3i30i3−i3000000000000000000003−3−3300
χ4622-2-222-12-22-12-2-2-2-2112-1-1-12-1-12-1-12-21-21111-2-2112i−2i−2i2i2i2i−2i−2iii−i−i-12-1-1-1-1-21111100i3−i300−i3i3−2i2i0000−ii−i−iiiii−i−i0i3−i30−i3i300000000000000000000−333−300
χ4722-2-222-12-22-12-2-2-2-2112-1-1-12-1-12-1-12-21-21111-2-211−2i2i2i−2i−2i−2i2i2i−i−iii-12-1-1-1-1-21111100−i3i300i3−i32i−2i0000i−iii−i−i−i−iii0−i3i30i3−i300000000000000000000−333−300
χ4822-2-222-12-22-12-2-2-2-2112-1-1-12-1-12-1-12-21-21111-2-211−2i2i2i−2i−2i−2i2i2i−i−iii-12-1-1-1-1-21111100i3−i300−i3i32i−2i0000i−iii−i−i−i−iii0i3−i30−i3i3000000000000000000003−3−3300
χ4922-2-2-222-1222-1-2-211-2-2-1-12-2111-1-12-222-1-1-1-2-211112i2i−2i−2i−i−iii2i2i−2i−2i-11-211-1-12-1-11100002i−2i00−ii−i−iii2i−2i−i−i−i−iiiii0000002i−2i−i−iii2-200-1-100110000000000
χ5022-2-2-222-1222-1-2-211-2-2-1-12-2111-1-12-222-1-1-1-2-211112i2i−2i−2i−i−iii2i2i−2i−2i-11-211-1-12-1-1110000−2i2i00−iiii−i−i2i−2i−i−i−i−iiiii000000−2i2iii−i−i-22001100-1-10000000000
χ5122-2-2-222-1222-1-2-211-2-2-1-12-2111-1-12-222-1-1-1-2-21111−2i−2i2i2iii−i−i−2i−2i2i2i-11-211-1-12-1-11100002i−2i00i−i−i−iii−2i2iiiii−i−i−i−i0000002i−2i−i−iii-22001100-1-10000000000
χ5222-2-2-222-1222-1-2-211-2-2-1-12-2111-1-12-222-1-1-1-2-21111−2i−2i2i2iii−i−i−2i−2i2i2i-11-211-1-12-1-1110000−2i2i00i−iii−i−i−2i2iiiii−i−i−i−i000000−2i2iii−i−i2-200-1-100110000000000
χ5322-2-2-22-1222-12-2-2-2-2112-1-11-2112-1-1-22-12-1-111-2-2112i2i−2i−2i2i2i−2i−2i−i−iii-1-2111-12-1-1-1112-2-1-100112i−2i0000−ii−i−i−i−iiiii2-1-1-2110000000000002i−2i000000−i−iii00
χ5422-2-2-22-1222-12-2-2-2-2112-1-11-2112-1-1-22-12-1-111-2-2112i2i−2i−2i2i2i−2i−2i−i−iii-1-2111-12-1-1-111-221100-1-12i−2i0000−ii−i−i−i−iiiii-2112-1-1000000000000−2i2i000000ii−i−i00
χ5522-2-2-22-1222-12-2-2-2-2112-1-11-2112-1-1-22-12-1-111-2-211−2i−2i2i2i−2i−2i2i2iii−i−i-1-2111-12-1-1-1112-2-1-10011−2i2i0000i−iiiii−i−i−i−i2-1-1-211000000000000−2i2i000000ii−i−i00
χ5622-2-2-22-1222-12-2-2-2-2112-1-11-2112-1-1-22-12-1-111-2-211−2i−2i2i2i−2i−2i2i2iii−i−i-1-2111-12-1-1-111-221100-1-1−2i2i0000i−iiiii−i−i−i−i-2112-1-10000000000002i−2i000000−i−iii00
χ5722-2-2-2-1222-12211-2-2-2-2-12-1-2-2-2-2-12-11-122221111-2-2000000000000-11111-1-1-1-1-1112-2222i−2i-2-2002i2i−2i−2i0000000000-1-1-1111−ii−i−iii002i−2i000000−i−iii000000
χ5822-2-2-2-1222-12211-2-2-2-2-12-1-2-2-2-2-12-11-122221111-2-2000000000000-11111-1-1-1-1-1112-222−2i2i-2-200−2i−2i2i2i0000000000-1-1-1111i−iii−i−i00−2i2i000000ii−i−i000000
χ5922-2-2-2-1222-12211-2-2-2-2-12-1-2-2-2-2-12-11-122221111-2-2000000000000-11111-1-1-1-1-111-22-2-22i−2i22002i2i−2i−2i0000000000111-1-1-1−ii−i−iii00−2i2i000000ii−i−i000000
χ6022-2-2-2-1222-12211-2-2-2-2-12-1-2-2-2-2-12-11-122221111-2-2000000000000-11111-1-1-1-1-111-22-2-2−2i2i2200−2i−2i2i2i0000000000111-1-1-1i−iii−i−i002i−2i000000−i−iii000000
χ61444444-2-244-2-244-2-2-2-2-21-2-2-211-21-244-2-211-2-2-2-2114444-2-2-2-2-2-2-2-21-2-2111-2-2111100000000-2-20000-2-21111111100000000000000000000000000000000
χ62444444-2-244-2-244-2-2-2-2-21-2-2-211-21-244-2-211-2-2-2-211-4-4-4-4222222221-2-2111-2-211110000000022000022-1-1-1-1-1-1-1-100000000000000000000000000000000
χ6344444-24-24-24-2-2-2-2-2441-2-24-2-2-21-2-2-2-24-2-2-2-2-211-2-200000000000011-21111-211110000440000-2-2-2-20000000000000000-2-2111100000000000000000000
χ6444444-24-24-24-2-2-2-2-2441-2-24-2-2-21-2-2-2-24-2-2-2-2-211-2-200000000000011-21111-211110000-4-400002222000000000000000022-1-1-1-100000000000000000000
χ6544444-2-244-2-24-2-244-2-2-2-21-24-2-2-2-21-2-2-24-2-211-2-2-2-20000000000001-21111-21111144-2-200-2-20000000000000000-211-21100000000000000000000000000
χ6644444-2-244-2-24-2-244-2-2-2-21-24-2-2-2-21-2-2-24-2-211-2-2-2-20000000000001-21111-211111-4-422002200000000000000002-1-12-1-100000000000000000000000000
χ674444-44-2-2-44-2-244-2-2-2-2-21-222-1-1-21-2-4-422-1-1-2-2-2-2114-44-4-2-2-2-22222122-1-1122-1-11100000000220000-2-211-1-111-1-100000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.