Finite Group Databasebeta

← Group #72230156

Character table — Group #72230156

Order 2880.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size112222222222244444444444444445588888888888888888888888888888888881010101010101010101010202020202020202020202020363660606060606060606060606060606060606060606060606072727272180180
order122223366666635666666666661010102210101515151530303030303030303030303030303030303030303030303030303030222666666666666666666662444444444121212121212121212121212121212121010202024
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ511111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1
χ611111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1
χ711111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111
χ811111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111
χ9111-1-11111-1-1-1-11111-1-1111-1-1-1-111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1-1-11-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-11-1
χ10111-1-11111-1-1-1-11111-1-1111-1-1-1-111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1-1-11-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-11-1
χ11111-1-11111-1-1-1-11111-1-1111-1-1-1-111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1-1-1-11i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-11
χ12111-1-11111-1-1-1-11111-1-1111-1-1-1-111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1-1-1-11−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-11
χ13111-1-11111-1-1-1-11111-1-1111-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-11-1-111-1-1111-1-1-1-11111-1-1-1-11111-1-1-11
χ14111-1-11111-1-1-1-11111-1-1111-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-1-111-1-111-1-1-11111-1-1-1-11111-1-111-1-1-11
χ15111-1-11111-1-1-1-11111-1-1111-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-111-1-11-111-111-1-1-1-111-1-11111-1-1-1-1111-1
χ16111-1-11111-1-1-1-11111-1-1111-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-11-111-11-1-11-1-11111-1-111-1-1-1-111-1-1111-1
χ17222222-12-122-1-1-122-12-1-1-1-1-1-1-1-122222222-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222-1-122-1-12-12-1-1-1-1-1-1-1-1-1000000222200000000-1-1-1-1-1-1-1-1000000
χ18222222-12-122-1-1-122-12-1-1-1-1-1-1-1-122222222-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222-1-122-1-12-12-1-1-1-1-1-1-1-1-1000000-2-2-2-20000000011111111000000
χ19222222-12-122-1-1-122-12-1-1-1-1-1-1-1-1222-2-2222-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-211-2-211-21-21111111110000002i2i−2i−2i00000000−i−i−i−iiiii000000
χ20222222-12-122-1-1-122-12-1-1-1-1-1-1-1-1222-2-2222-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-211-2-211-21-2111111111000000−2i−2i2i2i00000000iiii−i−i−i−i000000
χ2122222-12-12-1-122-12-12-12-1-1-1-1-1-1-12222222-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-122-1-122-12-12-1-1-1-1-1-1-1-10022220000-1-1-1-1-1-1-1-100000000000000
χ2222222-12-12-1-122-12-12-12-1-1-1-1-1-1-12222222-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-122-1-122-12-12-1-1-1-1-1-1-1-100-2-2-2-200001111111100000000000000
χ2322222-12-12-1-122-12-12-12-1-1-1-1-1-1-1222-2-222-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-211-2-211-2-21-21-211111111002i2i−2i−2i0000−i−i−i−iiiii00000000000000
χ2422222-12-12-1-122-12-12-12-1-1-1-1-1-1-1222-2-222-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-211-2-211-2-21-21-21111111100−2i−2i2i2i0000iiii−i−i−i−i00000000000000
χ25222-2-22-12-1-2-211-122-1-21-1-1-1111122222-2-22-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-21111111111112-2-222-1-1-2-2112-1-21-1-1-1-111110000002i−2i2i−2i00000000−i−iii−i−iii000000
χ26222-2-22-12-1-2-211-122-1-21-1-1-1111122222-2-22-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-21111111111112-2-222-1-1-2-2112-1-21-1-1-1-11111000000−2i2i−2i2i00000000ii−i−iii−i−i000000
χ27222-2-22-12-1-2-211-122-1-21-1-1-11111222-2-2-2-22-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-222-2-21122-1-1-212-11111-1-1-1-10000002-2-2200000000-1-11111-1-1000000
χ28222-2-22-12-1-2-211-122-1-21-1-1-11111222-2-2-2-22-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-222-2-21122-1-1-212-11111-1-1-1-1000000-222-20000000011-1-1-1-111000000
χ29222-2-2-12-1211-2-2-12-121-2-1-1-1111122222-2-2-12-1-1-1-1-1222-1-1-1-1-1-11111-2-2-2-2111111112-2-2-1-12211-2-2-121-2-1-1-1-11111002i−2i2i−2i0000−i−iii−i−iii00000000000000
χ30222-2-2-12-1211-2-2-12-121-2-1-1-1111122222-2-2-12-1-1-1-1-1222-1-1-1-1-1-11111-2-2-2-2111111112-2-2-1-12211-2-2-121-2-1-1-1-1111100−2i2i−2i2i0000ii−i−iii−i−i00000000000000
χ31222-2-2-12-1211-2-2-12-121-2-1-1-11111222-2-2-2-2-12-1-1-1-1-1222-1-1-1-1-1-11111-2-2-2-211111111-22211-2-2-1-1221-2-121111-1-1-1-1002-2-220000-1-11111-1-100000000000000
χ32222-2-2-12-1211-2-2-12-121-2-1-1-11111222-2-2-2-2-12-1-1-1-1-1222-1-1-1-1-1-11111-2-2-2-211111111-22211-2-2-1-1221-2-121111-1-1-1-100-222-2000011-1-1-1-11100000000000000
χ3322-22-2222222-2-222-2-2-222-2-222-2-2-2-22222-222222-2-22-2-222-2-2-2-222-2-222-2-22222-2-2-2-2-22-2222222-2-2-2-2-2222-2-222-2-200000000000000000000000000000000
χ3422-22-2222222-2-222-2-2-222-2-222-2-2-2-22-2-22-222222-2-22-2-222-2-2-2-222-2-222-2-22222-2-2-2-22-22-2-2-2-2-2-222222-2-2-222-2-22200000000000000000000000000000000
χ3522-22-22-12-12211-12-21-2-1-111-1-111-2-22222-22-1-1-12-2-2-111-1-1111122-2-2-1-111-1-1-1-11111-22-222-1-12211-21-2-1-1-111-1-1110000000000000000003−33−33−33−3000000
χ3622-22-22-12-12211-12-21-2-1-111-1-111-2-22222-22-1-1-12-2-2-111-1-1111122-2-2-1-111-1-1-1-11111-22-222-1-12211-21-2-1-1-111-1-111000000000000000000−33−33−33−33000000
χ3722-22-22-12-12211-12-21-2-1-111-1-111-2-22-2-22-22-1-1-12-2-2-111-1-1111122-2-2-1-111-1-1-1-111112-22-2-211-2-2-1-12-12111-1-111-1-1000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ3822-22-22-12-12211-12-21-2-1-111-1-111-2-22-2-22-22-1-1-12-2-2-111-1-1111122-2-2-1-111-1-1-1-111112-22-2-211-2-2-1-12-12111-1-111-1-1000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ3922-22-2-12-12-1-1-2-2-121-212-111-1-111-2-22222-2-12-1-1-1112-2-2-1-11111-1-11122-2-2-1-1-1-11111-22-2-1-122-1-1-2-21-212-1-111-1-1110000000000−i3i3−i3i3−i3i3−i3i300000000000000
χ4022-22-2-12-12-1-1-2-2-121-212-111-1-111-2-22222-2-12-1-1-1112-2-2-1-11111-1-11122-2-2-1-1-1-11111-22-2-1-122-1-1-2-21-212-1-111-1-1110000000000i3−i3i3−i3i3−i3i3−i300000000000000
χ4122-22-2-12-12-1-1-2-2-121-212-111-1-111-2-22-2-22-2-12-1-1-1112-2-2-1-11111-1-11122-2-2-1-1-1-111112-2211-2-21122-12-1-211-1-111-1-100000000003−33−3−33−3300000000000000
χ4222-22-2-12-12-1-1-2-2-121-212-111-1-111-2-22-2-22-2-12-1-1-1112-2-2-1-11111-1-11122-2-2-1-1-1-111112-2211-2-21122-12-1-211-1-111-1-10000000000−33−333−33−300000000000000
χ4322-2-222222-2-22222-2-22-22-2-2-2-222-2-2222-2222222-2-22-2-222-2-2-2-2-2-222-2-222-2-2-2-22222-2-222222-2-222-2-22-222-2-2-2-22200000000000000000000000000000000
χ4422-2-222222-2-22222-2-22-22-2-2-2-222-2-22-2-2-2222222-2-22-2-222-2-2-2-2-2-222-2-222-2-2-2-2222222-2-2-2-2-222-2-222-22-2-22222-2-200000000000000000000000000000000
χ4522-2-222-12-1-2-2-1-1-12-2121-11111-1-1-2-2222-222-1-1-12-2-2-111-1-11111-2-22211-1-11111-1-1-1-1-2-2222-1-1-2-2-1-1-2121-1-11111-1-1000000000000000000−i3i3i3−i3−i3i3i3−i3000000
χ4622-2-222-12-1-2-2-1-1-12-2121-11111-1-1-2-2222-222-1-1-12-2-2-111-1-11111-2-22211-1-11111-1-1-1-1-2-2222-1-1-2-2-1-1-2121-1-11111-1-1000000000000000000i3−i3−i3i3i3−i3−i3i3000000
χ4722-2-222-12-1-2-2-1-1-12-2121-11111-1-1-2-22-2-2-222-1-1-12-2-2-111-1-11111-2-22211-1-11111-1-1-1-122-2-2-21122112-1-2-111-1-1-1-1110000000000000000003−3−33−333−3000000
χ4822-2-222-12-1-2-2-1-1-12-2121-11111-1-1-2-22-2-2-222-1-1-12-2-2-111-1-11111-2-22211-1-11111-1-1-1-122-2-2-21122112-1-2-111-1-1-1-111000000000000000000−333−33−3−33000000
χ4922-2-22-12-121122-121-2-1-2-11111-1-1-2-2222-22-12-1-1-1112-2-2-1-1111111-1-1-2-2221111-1-1-1-1-2-22-1-12211221-2-1-2-1-11111-1-100000000003−3−333−3−3300000000000000
χ5022-2-22-12-121122-121-2-1-2-11111-1-1-2-2222-22-12-1-1-1112-2-2-1-1111111-1-1-2-2221111-1-1-1-1-2-22-1-12211221-2-1-2-1-11111-1-10000000000−333−3−333−300000000000000
χ5122-2-22-12-121122-121-2-1-2-11111-1-1-2-22-2-2-22-12-1-1-1112-2-2-1-1111111-1-1-2-2221111-1-1-1-122-211-2-2-1-1-2-2-121211-1-1-1-1110000000000−i3i3i3−i3i3−i3−i3i300000000000000
χ5222-2-22-12-121122-121-2-1-2-11111-1-1-2-22-2-2-22-12-1-1-1112-2-2-1-1111111-1-1-2-2221111-1-1-1-122-211-2-2-1-1-2-2-121211-1-1-1-1110000000000i3−i3−i3i3−i3i3i3−i300000000000000
χ5344444444444444-144444444444-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000044000000000000000000000000-1-1-1-100
χ5444444444444444-144444444444-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000-4-4000000000000000000000000111100
χ5544444-2-2-2-2-2-2-2-214-2-2-2-211111114444444-2-211-2-2-2-2-2-2111111-2-2-2-2-2-2-2-211111111444-2-2-2-2-2-2-2-2-2-2-2-21111111100000000000000000000000000000000
χ5644444-2-2-2-2-2-2-2-214-2-2-2-21111111444-4-444-2-211-2-2-2-2-2-2111111-2-2-2-2-2-2-2-211111111-4-4-4222222222222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ57444-4-44444-4-4-4-44-144-4-4444-4-4-4-4-1-1-10011-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000000000004-4000000000000000000000000-1-11100
χ58444-4-44444-4-4-4-44-144-4-4444-4-4-4-4-1-1-10011-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000000-4400000000000000000000000011-1-100
χ59444-4-4-2-2-2-2222214-2-222111-1-1-1-144444-4-4-2-211-2-2-2-2-2-211111122222222-1-1-1-1-1-1-1-14-4-4-2-2-2-22222-2-2221111-1-1-1-100000000000000000000000000000000
χ60444-4-4-2-2-2-2222214-2-222111-1-1-1-1444-4-4-4-4-2-211-2-2-2-2-2-211111122222222-1-1-1-1-1-1-1-1-4442222-2-2-2-222-2-2-1-1-1-1111100000000000000000000000000000000
χ6144-44-4444444-4-44-1-4-4-444-4-444-4-411-100-11-1-1-1-1-111-111-1-11111-1-111-1-111-1-1-1-111110000000000000000000000000000000000000000000000000−55−5500
χ6244-44-4444444-4-44-1-4-4-444-4-444-4-411-100-11-1-1-1-1-111-111-1-11111-1-111-1-111-1-1-1-1111100000000000000000000000000000000000000000000000005−55−500
χ6344-44-4-2-2-2-2-2-22214222-21-1-111-1-1-4-44444-4-2-211-222-22211-1-1-1-1-2-222-2-2221111-1-1-1-1-44-4-2-2-2-2-2-222222-211-1-111-1-100000000000000000000000000000000
χ6444-44-4-2-2-2-2-2-22214222-21-1-111-1-1-4-44-4-44-4-2-211-222-22211-1-1-1-1-2-222-2-2221111-1-1-1-14-44222222-2-2-2-2-22-1-111-1-11100000000000000000000000000000000
χ6544-4-444444-4-4444-1-4-44-44-4-4-4-44411-1001-1-1-1-1-1-111-111-1-1111111-1-111-1-11111-1-1-1-10000000000000000000000000000000000000000000000000−555−500
χ6644-4-444444-4-4444-1-4-44-44-4-4-4-44411-1001-1-1-1-1-1-111-111-1-1111111-1-111-1-11111-1-1-1-100000000000000000000000000000000000000000000000005−5−5500
χ6744-4-44-2-2-2-222-2-21422-221-1-1-1-111-4-4444-44-2-211-222-22211-1-1-1-122-2-222-2-2-1-1-1-11111-4-44-2-2-2-222-2-222-2211-1-1-1-11100000000000000000000000000000000
χ6844-4-44-2-2-2-222-2-21422-221-1-1-1-111-4-44-4-4-44-2-211-222-22211-1-1-1-122-2-222-2-2-1-1-1-1111144-42222-2-222-2-22-2-1-11111-1-100000000000000000000000000000000
χ694-400044-4-40000440000-400000000-44-4004444-400-400-4-4000000000000000000000004-44-4000000004-400000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.