Finite Group Databasebeta

← Group #72341548

Character table — Group #72341548

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122333344446666666666881212121212121212242424242424242424242424242424242424323232323232323232323232323232324848484848484848
order122244222244442222222244224444444422444444444444444436666666121212121212121244444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1
χ41111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-11111
χ51111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1111111-1-111-1-1
χ61111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111-1-111-1-111
χ71111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ81111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ911-1-1i−i1-11-1ii−i−i11-1-111-1-1i−i1-1ii−i−iii−i−i1-1i−i1-1i−ii−i1-11-11-1i−i11-111-1-1-1ii−i−iii−i−i1-1i−ii−i1-1
χ1011-1-1i−i1-11-1ii−i−i11-1-111-1-1i−i1-1ii−i−iii−i−i-11−ii-11−ii−ii-111-1-11−ii11-111-1-1-1ii−i−iii−i−i-11−ii−ii-11
χ1111-1-1i−i1-11-1−i−iii11-1-111-1-1i−i-11ii−i−i−i−iii1-1i−i-11−iii−i-11-111-1−ii11-1-1-111-1ii−i−i−i−iii1-1i−i−ii-11
χ1211-1-1i−i1-11-1−i−iii11-1-111-1-1i−i-11ii−i−i−i−iii-11−ii1-1i−i−ii1-1-11-11i−i11-1-1-111-1ii−i−i−i−iii-11−iii−i1-1
χ1311-1-1−ii1-11-1ii−i−i11-1-111-1-1−ii-11−i−iiiii−i−i1-1−ii-11i−i−ii-11-111-1i−i11-1-1-111-1−i−iiiii−i−i1-1−iii−i-11
χ1411-1-1−ii1-11-1ii−i−i11-1-111-1-1−ii-11−i−iiiii−i−i-11i−i1-1−iii−i1-1-11-11−ii11-1-1-111-1−i−iiiii−i−i-11i−i−ii1-1
χ1511-1-1−ii1-11-1−i−iii11-1-111-1-1−ii1-1−i−iii−i−iii1-1−ii1-1−ii−ii1-11-11-1−ii11-111-1-1-1−i−iii−i−iii1-1−ii−ii1-1
χ1611-1-1−ii1-11-1−i−iii11-1-111-1-1−ii1-1−i−iii−i−iii-11i−i-11i−ii−i-111-1-11i−i11-111-1-1-1−i−iii−i−iii-11i−ii−i-11
χ172222222222222222222222222222222222000000000000220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222222-2-2-2-22222222222-2-22222-2-2-2-2000000000000-2-20000-1-1-11111-1-1-1-1-1111100000000
χ192222-2-22222222222222222-2-2-2-2-2-2-2-22222000000000000-2-20000-1-1-11111-11111-1-1-1-100000000
χ202222-2-22222-2-2-2-222222222-2-222-2-2-2-2-2-2-2-2000000000000220000-1-1-1-1-1-1-1-11111111100000000
χ2122-2-22i−2i2-22-22i2i−2i−2i22-2-222-2-22i−2i2-22i2i−2i−2i2i2i−2i−2i0000000000002-20000-1-11-1-1111−i−iii−i−iii00000000
χ2222-2-22i−2i2-22-2−2i−2i2i2i22-2-222-2-22i−2i-222i2i−2i−2i−2i−2i2i2i000000000000-220000-1-1111-1-11−i−iiiii−i−i00000000
χ2322-2-2−2i2i2-22-22i2i−2i−2i22-2-222-2-2−2i2i-22−2i−2i2i2i2i2i−2i−2i000000000000-220000-1-1111-1-11ii−i−i−i−iii00000000
χ2422-2-2−2i2i2-22-2−2i−2i2i2i22-2-222-2-2−2i2i2-2−2i−2i2i2i−2i−2i2i2i0000000000002-20000-1-11-1-1111ii−i−iii−i−i00000000
χ252-22-200-222-22i−2i2i−2i2-22-22-22-2000000002i−2i2i−2i0000000000000000002-220000-200002i−2i2i−2i00000000
χ262-22-200-222-22i−2i2i−2i2-22-22-22-2000000002i−2i2i−2i000000000000000000-11-1−i3i3−i3i313−33−3−ii−ii00000000
χ272-22-200-222-22i−2i2i−2i2-22-22-22-2000000002i−2i2i−2i000000000000000000-11-1i3−i3i3−i31−33−33−ii−ii00000000
χ282-22-200-222-2−2i2i−2i2i2-22-22-22-200000000−2i2i−2i2i0000000000000000002-220000-20000−2i2i−2i2i00000000
χ292-22-200-222-2−2i2i−2i2i2-22-22-22-200000000−2i2i−2i2i000000000000000000-11-1−i3i3−i3i31−33−33i−ii−i00000000
χ302-22-200-222-2−2i2i−2i2i2-22-22-22-200000000−2i2i−2i2i000000000000000000-11-1i3−i3i3−i313−33−3i−ii−i00000000
χ312-2-2200-2-2222-2-222-2-222-2-22000000002-2-220000000000000000002-2-20000200002-2-2200000000
χ322-2-2200-2-2222-2-222-2-222-2-22000000002-2-22000000000000000000-111−i3i3i3−i3-1−i3i3i3−i3-111-100000000
χ332-2-2200-2-2222-2-222-2-222-2-22000000002-2-22000000000000000000-111i3−i3−i3i3-1i3−i3−i3i3-111-100000000
χ342-2-2200-2-222-222-22-2-222-2-2200000000-222-20000000000000000002-2-2000020000-222-200000000
χ352-2-2200-2-222-222-22-2-222-2-2200000000-222-2000000000000000000-111−i3i3i3−i3-1i3−i3−i3i31-1-1100000000
χ362-2-2200-2-222-222-22-2-222-2-2200000000-222-2000000000000000000-111i3−i3−i3i3-1−i3i3i3−i31-1-1100000000
χ3733333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1111111111111-1-111110000000000000000-1-1-1-1-1-1-1-1
χ3833333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111
χ393333333333-3-3-3-3-1-1-1-1-1-1-1-133-3-3-1-1-1-111111111-1-1-1-111-1-11111-1-10000000000000000-1-1-1-11111
χ403333333333-3-3-3-3-1-1-1-1-1-1-1-133-3-3-1-1-1-11111-1-1-1-11111-1-11111-1-11100000000000000001111-1-1-1-1
χ413333-3-333333333-1-1-1-1-1-1-1-1-3-3-3-31111-1-1-1-111-1-1-1-111-1-1-1-11111110000000000000000-1-111-1-111
χ423333-3-333333333-1-1-1-1-1-1-1-1-3-3-3-31111-1-1-1-1-1-11111-1-1111111-1-1-1-1000000000000000011-1-111-1-1
χ433333-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-3-3331111111111-1-111-1-1-1-111-1-111-1-10000000000000000-1-11111-1-1
χ443333-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-3-33311111111-1-111-1-11111-1-1-1-1-1-111000000000000000011-1-1-1-111
χ4533-3-33i−3i3-33-33i3i−3i−3i-1-111-1-1113i−3i3-3−i−iii−i−iii1-1i−i1-1i−ii−i1-1-111-1i−i0000000000000000-11−ii−ii-11
χ4633-3-33i−3i3-33-33i3i−3i−3i-1-111-1-1113i−3i3-3−i−iii−i−iii-11−ii-11−ii−ii-11-11-11−ii00000000000000001-1i−ii−i1-1
χ4733-3-33i−3i3-33-3−3i−3i3i3i-1-111-1-1113i−3i-33−i−iiiii−i−i1-1i−i-11−iii−i-111-11-1−ii0000000000000000-11−iii−i1-1
χ4833-3-33i−3i3-33-3−3i−3i3i3i-1-111-1-1113i−3i-33−i−iiiii−i−i-11−ii1-1i−i−ii1-11-1-11i−i00000000000000001-1i−i−ii-11
χ4933-3-3−3i3i3-33-33i3i−3i−3i-1-111-1-111−3i3i-33ii−i−i−i−iii1-1−ii-11i−i−ii-111-11-1i−i0000000000000000-11i−i−ii1-1
χ5033-3-3−3i3i3-33-33i3i−3i−3i-1-111-1-111−3i3i-33ii−i−i−i−iii-11i−i1-1−iii−i1-11-1-11−ii00000000000000001-1−iii−i-11
χ5133-3-3−3i3i3-33-3−3i−3i3i3i-1-111-1-111−3i3i3-3ii−i−iii−i−i1-1−ii1-1−ii−ii1-1-111-1−ii0000000000000000-11i−ii−i-11
χ5233-3-3−3i3i3-33-3−3i−3i3i3i-1-111-1-111−3i3i3-3ii−i−iii−i−i-11i−i-11i−ii−i-11-11-11i−i00000000000000001-1−ii−ii1-1
χ53666666-2-2-2-200002-22-2-22-22-2-2002-22-200000000222200-2-20000-2-2000000000000000000000000
χ54666666-2-2-2-200002-22-2-22-22-2-2002-22-200000000-2-2-2-20022000022000000000000000000000000
χ55666666-2-2-2-20000-22-222-22-2-2-200-22-22000022220000-2-20000-2-200000000000000000000000000
χ56666666-2-2-2-20000-22-222-22-2-2-200-22-220000-2-2-2-200002200002200000000000000000000000000
χ576666-6-6-2-2-2-200002-22-2-22-222200-22-220000000022-2-200-2-2000022000000000000000000000000
χ586666-6-6-2-2-2-200002-22-2-22-222200-22-2200000000-2-22200220000-2-2000000000000000000000000
χ596666-6-6-2-2-2-20000-22-222-22-222002-22-2000022-2-20000220000-2-200000000000000000000000000
χ606666-6-6-2-2-2-20000-22-222-22-222002-22-20000-2-2220000-2-200002200000000000000000000000000
χ6166-6-66i−6i-22-2200002-2-22-222-2−2i2i002i−2i−2i2i000000002-22i−2i00-220000−2i2i000000000000000000000000
χ6266-6-66i−6i-22-2200002-2-22-222-2−2i2i002i−2i−2i2i00000000-22−2i2i002-200002i−2i000000000000000000000000
χ6366-6-66i−6i-22-220000-222-22-2-22−2i2i00−2i2i2i−2i00002-22i−2i0000−2i2i0000-2200000000000000000000000000
χ6466-6-66i−6i-22-220000-222-22-2-22−2i2i00−2i2i2i−2i0000-22−2i2i00002i−2i00002-200000000000000000000000000
χ6566-6-6−6i6i-22-2200002-2-22-222-22i−2i00−2i2i2i−2i000000002-2−2i2i00-2200002i−2i000000000000000000000000
χ6666-6-6−6i6i-22-2200002-2-22-222-22i−2i00−2i2i2i−2i00000000-222i−2i002-20000−2i2i000000000000000000000000
χ6766-6-6−6i6i-22-220000-222-22-2-222i−2i002i−2i−2i2i00002-2−2i2i00002i−2i0000-2200000000000000000000000000
χ6866-6-6−6i6i-22-220000-222-22-2-222i−2i002i−2i−2i2i0000-222i−2i0000−2i2i00002-200000000000000000000000000
χ696-66-600-666-66i−6i6i−6i-22-22-22-2200000000−2i2i−2i2i000000000000000000000000000000000000000000
χ706-66-600-666-6−6i6i−6i6i-22-22-22-22000000002i−2i2i−2i000000000000000000000000000000000000000000
χ716-6-6600-6-6666-6-66-222-2-222-200000000-222-2000000000000000000000000000000000000000000
χ726-6-6600-6-666-666-6-222-2-222-2000000002-2-22000000000000000000000000000000000000000000
χ7312-1212-12004-4-4400004444-4-4-4-4000000000000000000000000000000000000000000000000000000
χ7412-1212-12004-4-440000-4-4-4-44444000000000000000000000000000000000000000000000000000000
χ7512-12-12120044-4-4000044-4-4-4-444000000000000000000000000000000000000000000000000000000
χ7612-12-12120044-4-40000-4-44444-4-4000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).