Finite Group Databasebeta

← Group #72341518

Character table — Group #72341518

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122333344446666666666881212121212121212242424242424242424242424242424242424323232323232323232323232323232324848484848484848
order124424224422442222244444242244444422224444444444444436666666121212121212121244444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1
χ41111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111
χ51111-1-111111111-111111111-1-1-1-1-1-1-111111-11-11-11-1-1-111-1-111-1-11-1-111-1-1111-1-111-1-111-1-111-1-1
χ61111-1-111111111-111111111-1-1-1-1-1-1-11111-11-11-11-11-1-1-1-111-1-1111-1-111-1-1111-1-111-1-1-1-111-1-111
χ71111-1-11111-1-1-1-1-111111111-111-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-111
χ81111-1-11111-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-111-1-111-111-1-11111-1-11-1-1-1-111111-1-1-1-111-1-11111-1-1
χ911-1-11-111-1-111-1-111111-1-1-1-1-11-111-1-111-1-11-11-1-11-111-11-11-11-11-111111111-1-1-1-1-1-1-1-11-11-11-11-1
χ1011-1-11-111-1-111-1-111111-1-1-1-1-11-111-1-111-1-1-11-111-11-11-1-11-11-11-1111111111-1-1-1-1-1-1-1-1-11-11-11-11
χ1111-1-11-111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-1-11-111-1-111-11-1-11-11111-1-1-1-11-1-1-1-111111-11-1-11-11
χ1211-1-11-111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-111-111-11-1-11-11-11-111-11-1111-1-1-1-11-1-1-1-11111-11-111-11-1
χ1311-1-1-1111-1-111-1-1-11111-1-1-1-11-11-1-11111-1-11111-1-1-1-1-111-1-111-1-111-1-111-1-11-1-111-1-1111-1-111-1-11
χ1411-1-1-1111-1-111-1-1-11111-1-1-1-11-11-1-11111-1-1-1-1-1-11111-11-111-1-111-11-1-111-1-11-1-111-1-111-111-1-111-1
χ1511-1-1-1111-1-1-1-111-11111-1-1-1-111-1-1-111-1-11111-1-1-1-1111-11-1-11-111-11-1-1-1-1111-1-11111-1-11-1-11-111-1
χ1611-1-1-1111-1-1-1-111-11111-1-1-1-111-1-1-111-1-111-1-11111-1-11-1-111-11-1-111-1-1-1-1111-1-11111-1-1-111-11-1-11
χ172222222222222222222222222222222222000000002200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222222-2-2-2-22222222222-2-22222-2-2-2-200000000-2-200000000-1-1-11111-1-1-1-1-1111100000000
χ192222-2-222222222-222222222-2-2-2-2-2-2-2222200000000-2-200000000-111-1-111-1-1-111-1-11100000000
χ202222-2-22222-2-2-2-2-222222222-222-2-2-2-2-2-2-2-2000000002200000000-11111-1-1-1-1-11111-1-100000000
χ2122-2-22-222-2-222-2-222222-2-2-2-2-22-222-2-222-2-2000000002-200000000-1-1-1-1-1-1-1-11111111100000000
χ2222-2-22-222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-22200000000-2200000000-1-1-11111-11111-1-1-1-100000000
χ2322-2-2-2222-2-222-2-2-22222-2-2-2-22-22-2-22222-2-200000000-2200000000-111-1-111-111-1-111-1-100000000
χ2422-2-2-2222-2-2-2-222-22222-2-2-2-222-2-2-222-2-222000000002-200000000-11111-1-1-111-1-1-1-11100000000
χ252-22i−2i002-22i−2i2-22i−2i022-2-22i2i−2i−2i00000002-22i−2i0000000000000000002002-200-22i−2i002i−2i0000000000
χ262-22i−2i002-22i−2i2-22i−2i022-2-22i2i−2i−2i00000002-22i−2i000000000000000000-1−i3i3-11−i3i31−ii3−3−ii3−300000000
χ272-22i−2i002-22i−2i2-22i−2i022-2-22i2i−2i−2i00000002-22i−2i000000000000000000-1i3−i3-11i3−i31−ii−33−ii−3300000000
χ282-22i−2i002-22i−2i-22−2i2i022-2-22i2i−2i−2i0000000-22−2i2i000000000000000000200-2200-22i−2i00−2i2i0000000000
χ292-22i−2i002-22i−2i-22−2i2i022-2-22i2i−2i−2i0000000-22−2i2i000000000000000000-1−i3i31-1i3−i31−ii3−3i−i−3300000000
χ302-22i−2i002-22i−2i-22−2i2i022-2-22i2i−2i−2i0000000-22−2i2i000000000000000000-1i3−i31-1−i3i31−ii−33i−i3−300000000
χ312-2−2i2i002-2−2i2i2-2−2i2i022-2-2−2i−2i2i2i00000002-2−2i2i0000000000000000002002-200-2−2i2i00−2i2i0000000000
χ322-2−2i2i002-2−2i2i2-2−2i2i022-2-2−2i−2i2i2i00000002-2−2i2i000000000000000000-1−i3i3-11−i3i31i−i−33i−i−3300000000
χ332-2−2i2i002-2−2i2i2-2−2i2i022-2-2−2i−2i2i2i00000002-2−2i2i000000000000000000-1i3−i3-11i3−i31i−i3−3i−i3−300000000
χ342-2−2i2i002-2−2i2i-222i−2i022-2-2−2i−2i2i2i0000000-222i−2i000000000000000000200-2200-2−2i2i002i−2i0000000000
χ352-2−2i2i002-2−2i2i-222i−2i022-2-2−2i−2i2i2i0000000-222i−2i000000000000000000-1−i3i31-1i3−i31i−i−33−ii3−300000000
χ362-2−2i2i002-2−2i2i-222i−2i022-2-2−2i−2i2i2i0000000-222i−2i000000000000000000-1i3−i31-1−i3i31i−i3−3−ii−3300000000
χ37333333333333333-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-111111111-1-1111111110000000000000000-1-1-1-1-1-1-1-1
χ38333333333333333-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111
χ393333333333-3-3-3-33-1-1-1-1-1-1-1-13-3-3-1-1-1-1111111-1-111-1-1111111-1-1-1-10000000000000000-1-1-1-11111
χ403333333333-3-3-3-33-1-1-1-1-1-1-1-13-3-3-1-1-1-11111-1-111-1-11111-1-1-1-1111100000000000000001111-1-1-1-1
χ413333-3-333333333-3-1-1-1-1-1-1-1-1-3-3-31111-1-1-1-11-11-11-11-11111-1-111-1-10000000000000000-1-111-1-111
χ423333-3-333333333-3-1-1-1-1-1-1-1-1-3-3-31111-1-1-1-1-11-11-11-1111-1-111-1-111000000000000000011-1-111-1-1
χ433333-3-33333-3-3-3-3-3-1-1-1-1-1-1-1-1-333111111111-1-111-1-11-1-111-1-1-1-1110000000000000000-1-11111-1-1
χ443333-3-33333-3-3-3-3-3-1-1-1-1-1-1-1-1-33311111111-111-1-111-1-1-1-1-11111-1-1000000000000000011-1-1-1-111
χ4533-3-33-333-3-333-3-33-1-1-1-11111-33-3-1-111-1-1111-11-1-11-11-111-11-11-11-10000000000000000-11-11-11-11
χ4633-3-33-333-3-333-3-33-1-1-1-11111-33-3-1-111-1-111-11-111-11-1-11-11-11-11-1100000000000000001-11-11-11-1
χ4733-3-33-333-3-3-3-3333-1-1-1-11111-3-33-1-11111-1-11-1-11-111-11-11-11-1-11-110000000000000000-11-111-11-1
χ4833-3-33-333-3-3-3-3333-1-1-1-11111-3-33-1-11111-1-1-111-11-1-111-1-11-111-11-100000000000000001-11-1-11-11
χ4933-3-3-3333-3-333-3-3-3-1-1-1-111113-3311-1-1-1-1111111-1-1-1-11-11-1-111-1-110000000000000000-111-1-111-1
χ5033-3-3-3333-3-333-3-3-3-1-1-1-111113-3311-1-1-1-111-1-1-1-111111-1-111-1-111-100000000000000001-1-111-1-11
χ5133-3-3-3333-3-3-3-333-3-1-1-1-1111133-311-1-111-1-111-1-1-1-111-111-1-11-111-10000000000000000-111-11-1-11
χ5233-3-3-3333-3-3-3-333-3-1-1-1-1111133-311-1-111-1-1-1-11111-1-1-11-111-11-1-1100000000000000001-1-11-111-1
χ53666666-2-2-2-20000-22-22-22-22-2-2002-22-2000000220022000000-2-2-2-2000000000000000000000000
χ54666666-2-2-2-20000-22-22-22-22-2-2002-22-2000000-2-200-2-20000002222000000000000000000000000
χ55666666-2-2-2-20000-2-22-22-22-22-200-22-2200002200220000-2-2-2-20000000000000000000000000000
χ56666666-2-2-2-20000-2-22-22-22-22-200-22-220000-2-200-2-2000022220000000000000000000000000000
χ576666-6-6-2-2-2-2000022-22-22-22-2200-22-220000002-2002-2000000-2-222000000000000000000000000
χ586666-6-6-2-2-2-2000022-22-22-22-2200-22-22000000-2200-2200000022-2-2000000000000000000000000
χ596666-6-6-2-2-2-200002-22-22-22-222002-22-200002-2002-20000-2-2220000000000000000000000000000
χ606666-6-6-2-2-2-200002-22-22-22-222002-22-20000-2200-22000022-2-20000000000000000000000000000
χ6166-6-66-6-2-2220000-22-22-2-22-222002-2-220000002-200-22000000-22-22000000000000000000000000
χ6266-6-66-6-2-2220000-22-22-2-22-222002-2-22000000-22002-20000002-22-2000000000000000000000000
χ6366-6-66-6-2-2220000-2-22-222-22-2200-222-200002-200-220000-22-220000000000000000000000000000
χ6466-6-66-6-2-2220000-2-22-222-22-2200-222-20000-22002-200002-22-20000000000000000000000000000
χ6566-6-6-66-2-222000022-22-2-22-22-200-222-20000002200-2-2000000-222-2000000000000000000000000
χ6666-6-6-66-2-222000022-22-2-22-22-200-222-2000000-2-200220000002-2-22000000000000000000000000
χ6766-6-6-66-2-22200002-22-222-22-2-2002-2-2200002200-2-20000-222-20000000000000000000000000000
χ6866-6-6-66-2-22200002-22-222-22-2-2002-2-220000-2-2002200002-2-220000000000000000000000000000
χ696-66i−6i006-66i−6i6-66i−6i0-2-222−2i−2i2i2i0000000-22−2i2i000000000000000000000000000000000000000000
χ706-66i−6i006-66i−6i-66−6i6i0-2-222−2i−2i2i2i00000002-22i−2i000000000000000000000000000000000000000000
χ716-6−6i6i006-6−6i6i6-6−6i6i0-2-2222i2i−2i−2i0000000-222i−2i000000000000000000000000000000000000000000
χ726-6−6i6i006-6−6i6i-666i−6i0-2-2222i2i−2i−2i00000002-2−2i2i000000000000000000000000000000000000000000
χ7312-1212i−12i00-44−4i4i000004-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ7412-1212i−12i00-44−4i4i00000-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ7512-12−12i12i00-444i−4i000004-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ7612-12−12i12i00-444i−4i00000-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000

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